\r\n\tskeletal, and smooth. The muscle cells are not only complex but also fascinating. In \r\n\trecent years, there has been a substantial amount of advancement in the area of muscle cell \r\n\tbiology, especially in the areas ranging from molecular anatomy, basic physiology, \r\n\tunderstanding disease mechanisms, and therapeutic targets. This book's main \r\n\tfocus will be not only on the biology of myocytes, but also on all-encompassing \r\n\tdisciplines pertaining to muscle tissue, such as fundamental physiology, molecular \r\n\tmechanism of diseases, tissue engineering and regeneration, for all three types \r\n\tof muscle (skeletal, cardiac, and smooth muscle). The goal of this book is to consolidate the recent advances in the area of muscle cell biology/diseases/regeneration/repair by covering a broad-range of inter-related topics \r\n\tin a timely fashion and to disseminate that knowledge in a lucid way to a greater \r\n\tscientific audience. The topics of interest will include but will not be limited to the following: \r\n\tMuscle stem cells \r\n\tMuscle cell differentiation \r\n\tMuscle cell niche \r\n\tMuscle cell biology \r\n\tMuscle disorders and therapy \r\n\tMuscle gene therapy \r\n\tMuscle cell functional genomics/transcriptomics/proteomics/metabolomics \r\n\tMuscle physiology and nanotechnology, and Muscle tissue engineering and regeneration.
",isbn:"978-1-78923-968-3",printIsbn:"978-1-78923-967-6",pdfIsbn:null,doi:null,price:0,priceEur:null,priceUsd:null,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"64634d90d737661d1e606cac28b79969",bookSignature:"Dr. Mani T. Valarmathi",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/7870.jpg",keywords:"Muscle Cytoskeleton, Muscle Cell Signaling, Muscle Stem Cells, Muscle Cell Niche, Muscle Tissue Engineering, Cardiac Tissue Engineeing, Musclar Dystrophies, Inflammatory Muscle Diseases, Muscle Genomes, Muscle Proteomes, Muscle Transcriptomes, Muscle Metabolome",numberOfDownloads:887,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 16th 2018",dateEndSecondStepPublish:"November 6th 2018",dateEndThirdStepPublish:"January 5th 2019",dateEndFourthStepPublish:"March 26th 2019",dateEndFifthStepPublish:"May 25th 2019",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,editors:[{id:"69697",title:"Dr.",name:"Mani T.",middleName:null,surname:"Valarmathi",slug:"mani-t.-valarmathi",fullName:"Mani T. Valarmathi",profilePictureURL:"https://mts.intechopen.com/storage/users/69697/images/system/69697.jpg",biography:"Dr. Mani T. Valarmathi received his B.Sc. in Chemistry, M.B.B.S. in Medicine & Surgery and M.D. in Pathology from the University of Madras, Madras, India; as well as Ph.D. in Medical Biotechnology from All-India Institute of Medical Sciences (AIIMS), New Delhi, India. He was appointed as an Assistant Professor in the Department of Pathology in SRMC & RI (Deemed University), affiliated with Harvard Medical International, Madras, India. He received a Visiting Scientist Fellowship from the National Institute of Health (NIH) and spent two years with Dr. Ira Pastan in the Laboratory of Molecular Biology (LMB). He joined the Department of Comparative Biosciences at the University of Illinois at Urbana-Champaign (UIUC) in 2013 after working as a Research Assistant Professor at the University of South Carolina (USC) in Columbia, South Carolina. In UIUC, he conducted his cardiovascular physiology teaching and cardiovascular research in College of Medicine, College of Veterinary Medicine and the Beckman Institute for Advanced Science and Technology. His past research experience includes human cancer genetics. He is serving as a member of various prestigious national and international scientific societies and organizations such as ISSCR, TERMIS, AACR, ASIP, ACS, ESC, ISHR, ASGCT and AHA. 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1. Introduction
Physical and chemical properties of natural fluids are used to understand geological processes in crustal and mantel rock. The fluid phase plays an important role in processes in diagenesis, metamorphism, deformation, magmatism, and ore formation. The environment of these processes reaches depths of maximally 5 km in oceanic crusts, and 65 km in continental crusts, e.g. [1, 2], which corresponds to pressures and temperatures up to 2 GPa and 1000 ˚C, respectively. Although in deep environments the low porosity in solid rock does not allow the presence of large amounts of fluid phases, fluids may be entrapped in crystals as fluid inclusions, i.e. nm to µm sized cavities, e.g. [3], and fluid components may be present within the crystal lattice, e.g. [4]. The properties of the fluid phase can be approximated with equations of state (Eq. 1), which are mathematical formula that describe the relation between intensive properties of the fluid phase, such as pressure (p), temperature (T), composition (x), and molar volume (Vm).
p(T,Vm,x)E1
\n\t\t\t
This pressure equation can be transformed according to thermodynamic principles [5], to calculate a variety of extensive properties, such as entropy, internal energy, enthalpy, Helmholtz energy, Gibbs energy, et al., as well as liquid-vapour equilibria and homogenization conditions of fluid inclusions, i.e. dew point curve, bubble point curve, and critical points, e.g. [6]. The partial derivative of Eq. 1 with respect to temperature is used to calculate total entropy change (dS in Eq. 2) and total internal energy change (dU in Eq. 3), according to the Maxwell\'s relations [5].
dS=(∂p∂T)V,nTdVE2
\n\t\t\t
dU=[T⋅(∂p∂T)V,nT−p]dVE3
\n\t\t\t
where nT is the total amount of substance in the system. The enthalpy (H) can be directly obtained from the internal energy and the product of pressure and volume according to Eq. 4.
H=U+p⋅VE4
\n\t\t\t
The Helmholtz energy (A) can be calculated by combining the internal energy and entropy (Eq. 5), or by a direct integration of pressure (Eq. 1) in terms of total volume (Eq. 6).
A=U−TSE5
\n\t\t\t
dA=−pdVE6
\n\t\t\t
The Gibbs energy (G) is calculated in a similar procedure according to its definition in Eq. 7.
G=U+p⋅V−T⋅SE7
\n\t\t\t
The chemical potential (µi) of a specific fluid component (i) in a gas mixture or pure gas (Eq. 8) is obtained from the partial derivative of the Helmholtz energy (Eq. 5) with respect to the amount of substance of this component (ni).
μi=(∂A∂ni)T,V,njE8
\n\t\t\t
The fugacity (f) can be directly obtained from chemical potentials (Eq. 9) and from the definition of the fugacity coefficient (φi) with independent variables V and T (Eq. 10).
RTln(fifi0)=μi−μi0E9
\n\t\t\t
where µi0 and fi0 are the chemical potential and fugacity, respectively, of component i at standard conditions (0.1 MPa).
RTlnφi=∫V∞[(∂p∂ni)T,V,nj−RTV]dV−RTlnzE10
.
where φi and z (compressibility factor) are defined according to Eq. 11 and 12, respectively.
φi=fixi⋅pE11
\n\t\t\t
z=pVnTRTE12
2. Two-constant cubic equation of state
The general formulation that summarizes two-constant cubic equations of state according to van der Waals [7], Redlich and Kwong [8], Soave [9], and Peng and Robinson [10] is illustrated in Eq. 13 and 14, see also [11]. In the following paragraphs, these equations are abbreviated with Weos, RKeos,\n\t\t\t\tSeos, and PReos.
p=RTVm−ζ1−ζ2Vm⋅(Vm+ζ3)+ζ4⋅(Vm−ζ4)E13
\n\t\t\t
p=nTRTV−nTζ1−nT2ζ2V2+nTζ3V+nTζ4V−nT2ζ42E14
\n\t\t\t
where p is pressure (in MPa), T is temperature (in Kelvin), R is the gas constant (8.3144621 J mol-1K-1), V is volume (in cm3), Vm is molar volume (in cm3 mol-1), nT is the total amount of substance (in mol). The parameters ζ1, ζ2, ζ3, and ζ4 are defined according to the specific equations of state (Table 1), and are assigned specific values of the two constants a and b, as originally designed by Waals [7]. The a parameter reflects attractive forces between molecules, whereas the b parameter reflects the volume of molecules.
W
RK
S
PR
ζ1
b
b
b
b
ζ2
a
a·T -0.5
a
a
ζ3
-
b
b
b
ζ4
-
-
-
b
Table 1.
Definitions of ζ1, ζ2, ζ3, and ζ4 according to van der Waals (W), Redlich and Kwong (RK), Soave (S) and Peng and Robinson (PR).
This type of equation of state can be transformed in the form of a cubic equation to define volume (Eq. 15) and compressibility factor (Eq. 16).
a0V3+a1V2+a2V+a3=0E15
\n\t\t\t
b0z3+b1z2+b2z+b3=0E16
\n\t\t\t
where a0, a1, a2, and a3 are defined in Eq. 17, 18, 19, and 20, respectively; b0, b1, b2, and b3 are defined in Eq. 21, 22, 23, and 24, respectively.
a0=pE17
\n\t\t\t
a1=nTp⋅(ζ3+ζ4−ζ1)−nTRTE18
\n\t\t\t
a2=−nT2p⋅(ζ42+ζ1ζ3+ζ1ζ4)−nT2RT⋅(ζ3+ζ4)+nT2ζ2E19
\n\t\t\t
a3=nT3p⋅ζ1ζ42+nT3RT⋅ζ42−nT3⋅ζ1ζ2E20
\n\t\t\t
b0=(RTp)3E21
\n\t\t\t
b1=(RTp)2⋅(ζ3+ζ4−ζ1−RTp)E22
\n\t\t\t
b2=(RTp)⋅(−ζ42−(ζ3+ζ4)⋅(ζ1+RTp)+ζ2p)E23
\n\t\t\t
b3=(ζ1+RTp)⋅ζ42−ζ1ζ2pE24
\n\t\t\t
The advantage of a cubic equation is the possibility to have multiple solutions (maximally three) for volume at specific temperature and pressure conditions, which may reflect coexisting liquid and vapour phases. Liquid-vapour equilibria can only be calculated from the same equation of state if multiple solution of volume can be calculated at the same temperature and pressure. The calculation of thermodynamic properties with this type of equation of state is based on splitting Eq. 14 in two parts (Eq. 25), i.e. an ideal pressure (from the ideal gas law) and a departure (or residual) pressure, see also [6].
p=pideal+presidualE25
\n\t\t\t
where
pideal=nTRTVE26
\n\t\t\t
The residual pressure (presidual) can be defined as the difference (Δp, Eq. 27) between ideal pressure and reel pressure as expressed in Eq. 14.
The partial derivative of pressure with respect to temperature (Eq. 28) is the main equation to estimate the thermodynamic properties of fluids (see Eqs. 2 and 3).
Eqs. 31 and 32 already include the assumption that the parameters ζ1, ζ2, ζ3, and ζ4 are independent of volume. Finally, the partial derivative of pressure in respect to the amount of substance of a specific component in the fluid mixture (ni) is also used to characterize thermodynamic properties of fluid mixtures (Eq. 33).
The entropy (S) is obtained from the integration defined in Eq. 2 at constant temperature (Eqs. 34 and 35).
∫S0S1dS=∫V0V1(∂p∂T)V,nTdVE34
\n\t\t\t
S1=S0+∫V0V1(∂pideal∂T+∂Δp∂T)dVE35
\n\t\t\t
The limits of integration are defined as a reference ideal gas at S0 and V0, and a real gas at S1 and V1. This integration can be split into two parts, according to the ideal pressure and residual pressure definition (Eqs. 25, 26, and 27). The integral has different solutions dependent on the values of ζ3 and ζ4: Eq. 36 for ζ3 = 0 and ζ4 = 0, and Eqs. 37 and 38 for ζ3 > 0.
The RKeos and Seos define q asnTb, whereas in the PReos\n\t\t\t\tq is equal tonTb8, according to the values for ζ3 and ζ4 listed in Table 1. Eqs. 36 and 37 can be simplified by assuming that the lower limit of the integration corresponds to a large number of V0. As a consequence, part of the natural logarithms in Eqs. 36 and 37 can be replaced by the unit value 1 or 0 (Eqs. 39, 40, and 41).
limV0→∞(V0V0−nTζ1)=1E39
\n\t\t\t
limV0→∞(1V0)=0E40
\n\t\t\t
limV0→∞(2V0+nT(ζ3+ζ4)−q2V0+nT(ζ3+ζ4)+q)=1E41
\n\t\t\t
The entropy change that is caused by a volume change of ideal gases corresponds to the second term on the right-hand side of Eqs. 36 and 37. This term can be used to express the behaviour of an ideal mixture of perfected gases. Each individual gas in a mixture expands from their partial volume (vi) to the total volume at a pressure of 0.1 MPa, which results in a new expression for this term (Eq. 42)
nTRln(V1V0)ideal.mix=∑i[niRln(V1vi)]E42
\n\t\t\t
where ni is the amount of substance of component i in the fluid mixture. In addition, the partial volume of an ideal gas is related to the standard pressure p0 (0.1 MPa) according to the ideal gas law (Eq. 43, compare with Eq. 26).
vi=niRTp0E43
\n\t\t\t
Finally, the entropy of fluid phases containing gas mixtures at any temperature and total volume according to the two-constant cubic equation of state is given by Eq. 44 for ζ3 = 0 and ζ4 = 0, and Eq. 45 for ζ3 > 0.
The subscripts "1" for the upper limit of integration is eliminated to present a pronounced equation. The standard state entropy (S0) of a mixture of ideal gases is defined according to the arithmetic average principle (Eq. 46).
S0=∑ini⋅si0E46
\n\t\t\t
where si0 is the molar entropy of a pure component i in an ideal gas mixture at temperature T.
The internal energy (U, see Eq. 3) is obtained from the pressure equation (Eq. 14) and its partial derivative with respect to temperature (Eqs. 28 and 30):
Similar to the integral in the entropy definition (see Eqs. 44 and 45), Eq. 48 has different solutions dependent on the values of ζ3 and ζ4: Eq. 49 for ζ3 = 0 and ζ4 = 0, and Eq. 50 for ζ3 > 0.
The definition of q is given in Eq. 38. The standard state internal energy (U0) of a mixture of ideal gases is defined according to the arithmetic average principle (Eq. 51).
U0=∑ini⋅ui0E51
where ui0 is the molar internal energy of a pure component i in an ideal gas mixture at temperature T.
Enthalpy (Eq. 52 for ζ3 = 0 and ζ4 = 0, and Eq. 53 for ζ3 > 0), Helmholtz energy (Eq. 55 for ζ3 = 0 and ζ4 = 0, and Eq. 56 for ζ3 > 0), and Gibbs energy (Eq. 58 for ζ3 = 0 and ζ4 = 0, and Eq. 59 for ζ3 > 0) can be obtained from the definitions of pressure, entropy and internal energy according to standard thermodynamic relations, as illustrated in Eq. 4, 5, and 7. Standard state enthalpy (H0), standard state Helmholtz energy (A0), and standard state Gibbs energy (G0) of an ideal gas mixture at 0.1 MPa and temperature T are defined in Eqs. 54, 57, and 60, respectively.
The Helmholtz energy equation (Eqs. 55, 56, and 57) is used for the definition of chemical potential (μi) of a component in either vapour or liquid phase gas mixtures (compare with Eq. 8), Eq. 61 for ζ3 = 0 and ζ4 = 0, and Eq. 62 for ζ3 > 0, calculated with two-constant cubic equations of state.
The definitions of the partial derivative of q in respect to amount of substance (Eq. 63) according to ζ3 = b and ζ4 = 0 [8, 9] is illustrated in Eq. 64, and ζ3 = b and ζ4 = b [10] in Eq. 65.
∂q∂ni=∂(nTb)∂niE64
∂q∂ni=8⋅∂(nTb)∂niE65
The fugacity coefficient (φi) is defined according to Eqs. 9 and 10 from the difference between the chemical potential of a real gas mixture and an ideal gas mixture at standard conditions (0.1 MPa), see Eq. 66 for ζ3 = 0 and ζ4 = 0, and Eq. 67 for ζ3 > 0. Fugacity coefficient defined in Eq. 66 is applied to Weos and Eq. 67 is applied to RKeos, Seos, and PReos.
The stability limit of a fluid mixture can be calculated with two-constant cubic equations of state, e.g. see [6]. This limit is defined by the spinodal line, i.e. the locus of points on the surface of the Helmholtz energy or Gibbs energy functions that are inflection points, e.g. see [12] and references therein. The stability limit occurs at conditions where phase separation into a liquid and vapour phase should take place, which is defined by the binodal. Metastability is directly related to spinodal conditions, for example, nucleation of a vapour bubble in a cooling liquid phase within small constant volume cavities, such as fluid inclusions in minerals (< 100 µm diameter) occurs at conditions well below homogenization conditions of these phases in a heating experiment. The maximum temperature difference of nucleation and homogenization is defined by the spinodal. In multi-component fluid systems, the partial derivatives of the Helmholtz energy with respect to volume and amount of substance of each component can be arranged in a matrix that has a determinant (Dspin) equal to zero (Eq. 68) at spinodal conditions.
This matrix is square and contains a specific number of columns that is defined by the number of differentiation variables, i.e. volume and number of components in the fluid mixture minus 1. The individual components of this matrix are defined according to Eqs. 69, 70, 71, 72, 73, and 74. The exact definition of these components according to two-constant cubic equations of state can be obtained from the web site http://fluids.unileoben.ac.at (see also [6]).
AVV=(∂2A∂V2)n1,n2,⋯E69
\n\t\t\t
An1n1=(∂2A∂n12)n2,V,⋯E70
\n\t\t\t
An2n2=(∂2A∂n22)n1,V,⋯E71
\n\t\t\t
An1V=(∂2A∂n1∂V)n2,⋯=AVn1E72
\n\t\t\t
An2V=(∂2A∂n2∂V)n1,⋯=AVn2E73
\n\t\t\t
An1n2=(∂2A∂n1∂n2)V,⋯=An2n1E74
\n\t\t\t
The determinant in Eq. 68 is calculated with the Laplacian expansion that contains "minors" and "cofactors", e.g. see [13]. The mathematical computation time increases exponential with increasing number of components. Therefore, the LU decomposition [14] can be applied in computer programming to reduce this time.
The spinodal curve, binodal curve and critical point of a binary CO2-CH4 mixture with x(CO2) = 0.9 are illustrated in Figure 1, which are calculated with the PReos [10]. The spinodal has a small loop near the critical point, and may reach negative pressures at lower temperatures. The binodal remains within the positive pressure part at all temperatures. The binodal is obtained from equality of fugacity (Eq. 66 and 67) of each component in both liquid and vapour phase, and marks the boundary between a homogeneous fluid mixture and fluid immiscibility [6, 15].
Figure 1.
a) Temperature-pressure diagram of a binary CO2-CH4 fluid mixture, with x(CO2) = 0.9. The shaded area illustrates T-p condition of immiscibility of a CO2-rich liquid phase and a CH4-rich vapour phase (the binodal). The red dashed line is the spinodal. All lines are calculated with the equation of state according to PReos [10]. The calculated critical point is indicated with cPR. cDK is the interpolated critical point from experimental data [16]. (b) enlargement of (a) indicated with the square in thin lines.
5. Pseudo critical point
The pseudo critical point is defined according to the first and second partial derivatives of pressure with respect to volume (Eqs. 31 and 32). This point is defined in a p-V diagram where the inflection point and extremum coincide at a specific temperature, i.e. Eqs. 31 and 32 are equal to 0. The pseudo critical point is equal to the critical point for pure gas fluids, however, the critical point in mixtures cannot be obtained from Eqs. 31 and 32. The pseudo critical point estimation is used to define the two-constants (a and b) for pure gas fluids in cubic equations of state according to the following procedure. The molar volume of the pseudo critical point that is derived from Eqs 31 and 32 is presented in the form of a cubic equation (Eq. 75).
The solution of this cubic equation can be obtained from its reduced form, see page 9 in [15]:
x3+f⋅x+g=0E76
\n\t\t\t
where
f=3⋅[ζ42−ζ1⋅(ζ1+ζ3+ζ4)]E77
\n\t\t\t
g=−2ζ13+ζ1⋅[2ζ42−(ζ3+ζ4)2]+(ζ3+ζ4)⋅[ζ42−3ζ12]E78
\n\t\t\t
Vm=x+ζ1E79
\n\t\t\t
The values of f and g in terms of the b parameters for the individual two-constant cubic equations of state are given in Table 2. The molar volume at pseudo critical conditions is directly related to the b parameter in each equation of state: Weos\n\t\t\t\tEq. 80; RKeos\n\t\t\t\tEq. 81; Seos also Eq. 81; and PReos\n\t\t\t\tEq. 82.
Weos:Vmpc=3⋅bE80
\n\t\t\t
RKeos:Vmpc=b23−1≈3.847322⋅bE81
\n\t\t\t
PReos:Vmpc=[1+Q]⋅b≈3.951373⋅bE82
\n\t\t\t
where Q is defined according to Eq. 83, the superscript "pc" is the abbreviation for "pseudo critical".
Q=(4+8)13+(4−8)13E83
\n\t\t\t
Equation of state
f
g
b in Eqs. 80-82
b in Eqs. 94-96
difference
van der Waals [7]
-3b2
-2b3
31.3727
42.8453
37 %
Redlich and Kwong [8]
-6b2
-6b3
24.4633
29.6971
21 %
Soave [9]
-6b2
-6b3
24.4633
29.6971
21 %
Peng and Robinson [10]
-6b2
-8b3
23.8191
26.6656
12 %
Table 2.
Definitions of f and g according to Eq. 77 and 78, respectively. The values of b are calculated for the critical conditions of pure CO2: Vm,C = 94.118 cm3 mol-1, TC = 304.128 K and pC = 7.3773 MPa [18]. The last column gives the percentage of difference between the values of b (Eqs. 80-82 and 94-96).
The temperature at pseudo critical conditions is obtained from the combination of Eqs. 80-82 and the first partial derivative of pressure with respect to volume (Eq. 31).
where Q is defined according to Eq. 83. The order of equations (84, 85, 86) is according to the order of equations of state in Eq. 80, 81,and 82. The parameter ζ2 is used in Eqs. 84, 85 and, 86 instead of the constant a (see Table 1). Eq. 87 illustrates the transformation of Eq. 85 for the RKeos [8] by substitution of ζ2 according to its value given in Table 1.
Tpc=(23−1)43⋅(3abR)23E87
\n\t\t\t
Any temperature dependency of the a constant has an effect on the definition of the pseudo critical temperature. The pressure at pseudo critical condition (Eqs. 88-90) is obtained from a combination of the pressure equation (Eq.14), pseudo critical temperature (Eqs. 84-87) and pseudo critical molar volume (Eqs. 80-82).
Weos:ppc=127⋅ζ2b2≈0.03703704⋅ζ2b2E88
\n\t\t\t
RKeos:ppc=(23−1)3⋅ζ2b2≈0.01755999⋅ζ2b2E89
\n\t\t\t
PReos:ppc=Q2−2(Q2+4Q+2)2⋅ζ2b2≈0.01227198⋅ζ2b2E90
\n\t\t\t
where Q is defined according to Eq. 83. The order of equations (88, 89, and 90) is according to the order of equations of state in Eqs. 80, 81, and 82. These equations define the relation between the a and b constant in two-constant cubic equations of state and critical conditions, i.e. temperature, pressure, and molar volume of pure gas fluids. Therefore, knowledge of these conditions from experimental data can be used to determine the values of a (or ζ2) and b, which can be defined as a function of only temperature and pressure (Eqs. 91-93, and 94-96, respectively).
where TC and pC are the critical temperature and critical pressure, and Q is defined according to Eq. 83. The order of equations (91-93, and 94-96) is according to the order of equations of state in Eqs. 80-82. Comparison of the value of b calculated with experimental critical volume (Eqs. 80, 81 and 82) and critical temperature and pressure (Eqs. 94, 95, and 96) is illustrated in Table 2. The difference indicates the ability of a specific equation of state to reproduce fluid properties of pure gases. A large difference indicates that the geometry or morphology of the selected equation of state in the p-V-T-x parameter space is not exactly reproducing fluid properties of pure gases. The empirical modifications of the van-der-Waals equation of state according to Peng and Robinson [10] result in the most accurate equation in Table 2 (11% for pure CO2).
6. Critical point and curve
The critical point is the highest temperature and pressure in a pure gas system where boiling may occur, i.e. where a distinction can be made between a liquid and vapour phase at constant temperature and pressure. At temperatures and pressures higher than the critical point the pure fluid is in a homogeneous supercritical state. The critical point of pure gases and multi-component fluid mixtures can be calculated exactly with the Helmholtz energy equation (Eqs. 55-57) that is obtained from two-constant cubic equations of state, e.g. see [17, 18], and it marks that part of the surface described with a Helmholtz energy function where two inflection points of the spinodal coincide. Therefore, the conditions of the spinodal are also applied to the critical point. In addition, the critical curve is defined by the determinant (Dcrit) of the matrix illustrated in Eq. 97, see also [6].
The number of rows in Eq.97 is defined by the differentiation variables volume and number of components minus 2. The last row is reserved for the partial derivatives of the determinant Dspin from Eq. 68:
DV=∂Dspin∂VE98
\n\t\t\t
Dn1=∂Dspin∂n1E99
\n\t\t\t
Dn2=∂Dspin∂n2E100
\n\t\t\t
The derivatives of the spinodal determinant (Eqs. 98-100) are calculated from the sum of the element-by-element products of the matrix of "cofactors" (or adjoint matrix) of the spinodal (Eq. 101) and the matrix of the third derivatives of the Helmholtz energy function (Eq. 102).
Calculated critical points of binary CO2-CH4 fluid mixtures in terms of temperature (red line) and pressure (green line), obtained from the PReos [10]. Solid circles are experimental data [16, 19]. The open squares are the critical point of pure CO2 [20].
where Cxy are the individual elements in the matrix of "cofactors", as obtained from the Laplacian expansion. The subscript K refers to the variable that is used in the third differentiation (volume, amount of substance of the components 1 and 2. To reduce computation time in software that uses this calculation method, the LU decomposition has been used to calculate the determinant in Eq. 97. The determinants in Eqs. 68 and 97 are both used to calculate exactly the critical point of any fluid mixture and pure gases, based on two-constant cubic equations of state that define the Helmholtz energy function.
An example of a calculated critical curve, i.e. critical points for a variety of compositions in a binary fluid system, is illustrated in Figure 2. The prediction of critical temperatures of fluid mixtures corresponds to experimental data [16, 19], whereas calculated critical pressures are slightly overestimated at higher fraction of CH4. This example illustrates that the PReos [10] is a favourable modification that can be used to calculate sub-critical conditions of CO2-CH4 fluid mixtures.
7. Mixing rules and definitions of ζ1 and ζ2
All modifications of the van-der-Waals two-constant cubic equation of state [7] have an empirical character. The main modifications are defined by Redlich and Kwong, Soave and Peng and Robinson (see Table 1), and all modification can by summarized by specific adaptations of the values of ζ1, ζ2, ζ3, and ζ4 to fit experimental data. The original definition [7] of ζ1\n\t\t\t\t(b) and ζ2\n\t\t\t\t(a) for pure gases is obtained from the pseudo critical conditions (Eqs. 91-93, and 94-96). This principle is adapted in most modifications of the van-der-Waals equation of state, e.g. RKeos [8]. Soave [9] and Peng and Robinson [10] adjusted the definition of ζ2 with a temperature dependent correction parameter α (Eqs. 103-105).
ζ2=aC⋅αE103
\n\t\t\t
α=[1+m(1−TTC)]2E104
\n\t\t\t
m=∑i=0,1,2mi⋅ωiE105
\n\t\t\t
where ac is defined by the pseudo critical conditions (Eqs. 91-93), and ω is the acentric factor. The summation in Eq. 105 does not exceed i = 2 for Soave [9] and Peng and Robinson [10]. The definition of the acentric factor is arbitrary and chosen for convenience [5] and is a purely empirical modification. These two equations of state have different definitions of pseudo critical conditions (see Eqs. 91-93 and 94-96), therefore, the values of mi must be different for each equation (Table 3).
The two-constant cubic equation of state can be applied to determine the properties of fluid mixtures by using "mixing rules" for the parameters ζ1 and ζ2 which are defined for individual pure gases according to pseudo critical conditions. These mixing rules are based on simplified molecular behaviour of each component (i and j) in mixtures [21, 22] that describe the interaction between two molecules:
ζ1mix=∑i∑jxi⋅ζ1(i)E106
\n\t\t\t
ζ2mix=∑i∑jxixj⋅ζ2(i,j)E107
\n\t\t\t
where
ζ2(i,j)=ζ2(i)⋅ζ2(j)E108
\n\t\t\t
These mixing rules have been subject to a variety of modifications, in order to predict fluid properties of newly available experimental data of mixtures. Soave [9] and Peng and Robinson [10] modified Eq. 108 by adding an extra correction factor (Eq. 109).
ζ2(i,j)=(1−δij)⋅ζ2(i)⋅ζ2(j)E109
\n\t\t\t
where δij has a constant value dependent on the nature of component i and j.
8. Experimental data
As mentioned before, modifications of two-constant cubic equation of state was mainly performed to obtain a better fit with experimental data for a multitude of possible gas mixtures and pure gases. Two types of experimental data of fluid properties were used: 1. homogeneous fluid mixtures at supercritical conditions; and 2. immiscible two-fluid systems at subcritical conditions (mainly in petroleum fluid research). The experimental data consist mainly of pressure, temperature, density (or molar volume) and compositional data, but can also include less parameters. Figure 3 gives an example of the misfit between the first type of experimental data for binary CO2-CH4 mixtures [19] and calculated fluid properties with RKeos [8] at a constant temperature (15 ˚C). The RKeos uses the pseudo critical defined parameters ζ1 and ζ2 (Eqs. 92 and 95) and mixing rules according to Eqs. 106-108 and is only approximately reproducing the fluid properties of CO2-CH4 mixtures at subcritical conditions
Experimental data of homogeneous supercritical gas mixtures in the ternary CO2-CH4-N2 system [23] are compared with the two-constant cubic equations of state in Table 4. The Weos [7] clearly overestimates (up to 14.1 %) experimentally determined molar volumes at 100 MPa and 200 ˚C. The Seos [9] is the most accurate model in Table 4, but still reach deviations of up to 2.3 % for CO2-rich gas mixtures. The PReos [10] gives highly underestimated molar volumes at these conditions.
Figure 3.
Modelled immiscibility of binary CO2-CH4 gas mixtures (shaded areas) in a pressure - amount CH4 fraction diagram (a) and amount CH4 fraction - molar volume diagram (b) at 15 ˚C. The solid and open circles are experimental data [16]. The red squares are the properties of pure CO2 [20]. The yellow triangle (Cexp) is the interpolated critical point for experimental data, and the green triangle (CRK) is the calculated critical point [8]. tie1 and tie 2 in (b) are calculated tie-lines between two phases at constant pressures 6.891 and 6.036 MPa, respectively.
composition
Vm(exp) cm3·mol-1
W
RK
S
PR
CO2
CH4
N2
0.8
0.1
0.1
56.64
64.61 (14.1%)
54.90 (-3.1%)
57.94 (2.3%)
53.59 (-5.4%)
0.8
0.2
0.2
58.92
65.81 (11.7%)
56.61 (-3.9%)
59.61 (1.2%)
56.93 (-6.1%)
0.4
0.3
0.3
61.08
67.08 (9.6%)
58.27 (-4.6%)
61.12 (0.1%)
56.93 (-6.8%)
0.2
0.4
0.4
62.90
68.28 (8.6%)
59.83 (-4.9%)
62.42 (-0.8%)
58.28 (-7.3%)
Table 4.
Comparison of supercritical experimental molar volumes [23] at 100 MPa and 200 ˚C with two-constant cubic equations of state (abbreviations see Table 1). The percentage of deviation from experimentally obtained molar volumes is indicated in brackets.
Figure 3 and Table 4 illustrate that these modified two-constant cubic equations of state still need to be modified again to obtain a better model to reproduce fluid properties at sub- and supercritical conditions.
9. Modifications of modified equations of state
The number of publications that have modified the previously mentioned two-constant cubic equations of state are numerous, see also [11], and they developed highly complex, but purely empirical equations to define the parameters ζ1 and ζ2. A few examples are illustrated in the following paragraphs.
9.1. Chueh and Prausnitz [24]
The constant values in the definition of ζ1 and ζ2 (Eqs. 92 and 95) are modified for individual gases by Chueh and Prausnitz [24]. This equation is an arbitrary modification of the RKeos [8]. Consequently, the calculation of the value of ζ1 and ζ2 is not any more defined by pseudo critical conditions, which give exact mathematical definition of these constants. Although the prediction of fluid properties of a variety of gas mixtures was improved by these modifications, the morphology of the Helmholtz energy equation in the p-V-T-x parameter space is not any more related to observed fluid properties. The theory of pseudo critical conditions is violated according to these modifications.
The mixing rules in Eqs. 106-108 were further refined by arbitrary definitions of critical temperature, pressure, volume and compressibility for fluid mixtures.
ζ2(i,j)=Ωi+Ωj2⋅R2TCij2pCijE110
\n\t\t\t\t
aij=Ωi+Ωj2⋅R2TCij2.5pCijE111
\n\t\t\t\t
where Ωi and Ωj are the newly defined constant values of component i and j, and TCij and pCij are defined according to complex mixing rules [see 24]. The values of TCij and pCij are not related to true critical temperatures and pressures of specific binary gas mixtures.
The prediction of the properties of homogeneous fluids at supercritical conditions (Table 5) is only slightly improved compared to RKeos [10], but it is not exceeding the accuracy of the Seos [11]. At sub-critical condition (Figure 4), the Chueh-Prausnitz equation is less accurate than the Redlich-Kwong equation (compare Figure 3) in the binary CO2-CH4 fluid mixture at 15 ˚C.
composition
Vm(exp) cm3·mol-1
CP
H
B1
B2
CO2
CH4
N2
0.8
0.1
0.1
56.64
56.42 (-0.4%)
55.96 (-0.6%)
56.84 (0.4%)
56.53 (-0.2%)
0.8
0.2
0.2
58.92
57.85 (-1.8%)
57.68 (-2.1%)
59.43 (0.9%)
58.81 (-0.2%)
0.4
0.3
0.3
61.08
59.21 (-3.1%)
59.17 (-3.1%)
61.67 (1.0%)
60.79 (-0.5%)
0.2
0.4
0.4
62.90
60.44 (-3.9%)
60.38 (-4.0%)
63.45 (0.9%)
62.40 (-0.8%)
Table 5.
The same experimental molar volumes as in Table 4 compared with two-constant equations of state according to Chueh and Prausnitz [24] (CP), Holloway [25, 26] (H), Bakker [27] [B1], and Bakker [28] (B2). The percentage of deviation from experimentally obtained molar volumes is indicated in brackets.
The equation of Holloway [25, 26] is another modification of the RKeos [8]. The modification is mainly based on the improvement of predictions of homogenous fluid properties of H2O and CO2 mixtures, using calculated experimental data [29]. The value for ζ1 and ζ3 (both b) of H2O is arbitrarily selected at 14.6 cm3 mol-1, whereas other pure gases are defined according to pseudo critical conditions. The definition of ζ2 (i.e. a) for H2O as a function of temperature was subjected to a variety of best-fit procedures [25, 26]. The fitting was improved from four experimental data points [25] to six [26] (Figure 5), but was restricted to temperatures above 350 ˚C. Bakker [27] improved the best-fit equation by including the entire data set [29], down to 50 ˚C (Eq. 112).
Figure 4.
See Figure 3 for details. The RKeos is indicated by dashed lines in (a) and (b). The shaded areas are immiscibility conditions calculated with the Chueh-Prausnitz equation. tie1 and tie 2 in (b) are calculated tie-lines between two phases at constant pressures 6.944 and 5.984 MPa, respectively.
Figure 5.
Temperature dependence of the a constant for pure H2O in the modified cubic equation of state [25, 26]. The open circles are calculated experimental data [29]. fit [25] is the range of fitting in the definition of Holloway [25], and fit [26] of Holloway [26]. RK illustrates the constant value calculated from pseudo critical condition [8].
where T is temperature in Kelvin, and the dimension of a is cm6 MPa K0.5 mol-2. The properties of homogeneous pure CO2, CH4 and N2 fluids [27] were also used to obtain a temperature dependent a constant (Eqs. 113, 114, and 115, respectively).
The aij value of fluid mixtures with a H2O and CO2 component (as in Eqs. 106-108 and 110-111) is not defined by the value of pure H2O and CO2 (Eqs. 112 and 113), but from a temperature independent constant value (Eqs. 116 and 117, respectively). In addition, a correction factor is used only for binary H2O-CO2 mixtures, see [25, 29].
a0(H2O)=3.5464⋅106MPa⋅cm6⋅K0.5⋅mol2E116
\n\t\t\t\t
a0(CO2)=4.661⋅106MPa⋅cm6⋅K0.5⋅mol2E117
\n\t\t\t\t
Table 5 illustrates that the equation of Holloway [25] is not improving the accuracy of predicted properties of supercritical CO2-CH4-N2 fluids, compared to Chueh-Prausnitz [24] or Seos [9], and it is only a small improvement compared to the RKeos [8]. The accuracy of this equation is highly improved by using the definitions of a constants according to Bakker [27] (see Eqs. 112-115), and result in a maximum deviation of only 1% from experimental data in Table 5.
Experimental data, including molar volumes of binary H2O-CO2 fluid mixtures at supercritical conditions [30, 31, 32] are used to estimate fugacities of H2O and CO2 according to Eq. 118 (compare Eq. 10).
RTlnφi=∫0p[Vm,i−Vmideal]dpE118
\n\t\t\t\t
where Vm,i - Vmideal is the difference between the partial molar volume of component i and the molar volume of an ideal gas (see also Eq. 43). The difference between Eqs. 118 and 10 is the mathematical formulation and the use of different independent variables, which are temperature and pressure in Eq. 118. The integration to calculate the fugacity coefficient can be graphically obtained by measuring the surface of a diagram of the difference between the ideal molar volume and the partial molar volume (i.e. Vm,i - Vmideal) as a function of pressure (Figure 6). The surface obtained from experimental data can be directly compared to calculated curves from equations of state, according to Eq. 10 (Table 6).
The dashed line in Figure 6 is calculated with another type of equation of state: a modification of the Lee-Kesler equation of state [33] that is not treated in this manuscript because it is not a two-constant cubic equation of state. Fugacity estimations of H2O are similar according to both equations, and reveal only a minor improvement for the two-constant cubic equation of state [27]. The experimental data to determine fugacity of CO2 in this fluid mixture is inconsistent at relative low pressures (< 100 MPa). The calculated fugacity [27] is approximately compatible with the experimental data from [31, 32].
Figure 6.
Fugacity estimation in a pressure - dv diagram at 873 K and a composition of x(CO2) = 0.3 in the binary H2O-CO2 system, where dv is the molar volume difference of an ideal gas and the partial molar volume of either H2O or CO2 in binary mixtures. Experimental data are illustrated with circles, triangles and squares (solid for CO2 and open for H2O. The red lines are calculated with Bakker [27], and the shaded area is a measure for the fugacity coefficient of H2O (Eq. 118).
Pressure (MPa)
Exp. fugacity (MPa)
B1 fugacity (MPa)
10
6.692
6.659 (-0.5%)
50
27.962
27.3061 (-2.3%)
100
45.341
44.6971 (-1.4%)
200
77.278
75.0515 (-2.9%)
300
114.221
111.072 (-2.8%)
400
160.105
157.145 (-1.8%)
500
219.252
216.817 (-1.1%)
600
295.350
294.216 (-04%)
Table 6.
Fugacities of H2O in H2O-CO2 fluid mixtures, x(CO2) = 0.3, at 873.15 K and variable pressures. B1 fugacity is calculated with Bakker [27]. The deviation (in %) is illustrated in brackets.
9.3. Bowers and Helgeson [34] and Bakker [28]
Most natural occurring fluid phases in rock contain variable amounts of NaCl, which have an important influence on the fluid properties. Bowers and Helgeson [34] modified the RKeos [8] to be able to reproduce the properties of homogeneous supercritical fluids in the H2O-CO2-NaCl system, but only up to 35 mass% NaCl. The model is originally restricted between 350 and 600 ˚C and pressures above 50 MPa, according to the experimental data [35] that was used to design this equation. This model was modified by Bakker [28] including CH4, N2, and additionally any gas with a (ζ2) and b (ζ1) constants defined by the pseudo critical conditions (Eqs. 91-93 and 94-96). Experimental data in this multi-component fluid system with NaCl can be accurately reproduced up to 1000 MPa and 1300 K. Table 5 illustrates that this modification results in the best estimated molar volumes in the ternary CO2-CH4-N2 fluid system at 100 MPa and 673 K. Similar to all modifications of the RKeos [8], this model cannot be used in and near the immiscibility conditions and critical points (i.e. sub-critical conditions).
10. Application to fluid inclusion research
Knowledge of the properties of fluid phases is of major importance in geological sciences. The interaction between rock and a fluid phase plays a role in many geological processes, such as development of magma [36], metamorphic reactions [37] and ore formation processes [38]. The fluid that is involved in these processes can be entrapped within single crystal of many minerals (e.g. quartz), which may be preserved over millions of years. The information obtained from fluid inclusions includes 1. fluid composition; 2. fluid density; 3. temperature and pressure condition of entrapment; and 4. a temporal evolution of the rock can be reconstructed from presence of various generation of fluid inclusions. An equation of state of fluid phases is the major tool to obtain this information. Microthermometry [39] is an analytical technique that directly uses equations of state to obtain fluid composition and density of fluid inclusions. For example, cooling and heating experiment may reveal fluid phase changes at specific temperatures, such as dissolution and homogenization, which can be transformed in composition and density by using the proper equations of state.
The calculation method of fluid properties is extensive and is susceptible to errors, which is obvious from the mathematics presented in the previous paragraphs. The computer package FLUIDS [6, 40, 41] was developed to facilitate calculations of fluid properties in fluid inclusions, and fluids in general. This package includes the group "Loners" that handles a large variety of equations of state according to individual publications. This group allows researchers to perform mathematical experiments with equations of state and to test the accuracy by comparison with experimental data.
The equations of state handled in this study can be downloaded from the web site http://fluids.unileoben.ac.at and include 1. "LonerW" [7]; 2. "LonerRK" [8]; 3. "LonerS" [9]; 4. "LonerPR" [10]; 5. "LonerCP" [24]; 6. "LonerH" [25, 26, 27]; and 7. "LonerB" [28, 34]. Each program has to possibility to calculate a variety of fluid properties, including pressure, temperature, molar volume, fugacity, activity, liquid-vapour equilibria, homogenization conditions, spinodal, critical point, entropy, internal energy, enthalpy, Helmholtz energy, Gibbs energy, chemical potentials of pure gases and fluid mixtures. In addition, isochores can be calculated and exported in a text file. The diagrams and tables presented in this study are all calculated with these programs.
\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/39512.pdf",chapterXML:"https://mts.intechopen.com/source/xml/39512.xml",downloadPdfUrl:"/chapter/pdf-download/39512",previewPdfUrl:"/chapter/pdf-preview/39512",totalDownloads:3159,totalViews:792,totalCrossrefCites:0,totalDimensionsCites:4,hasAltmetrics:0,dateSubmitted:"November 14th 2011",dateReviewed:"May 30th 2012",datePrePublished:null,datePublished:"October 3rd 2012",readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/39512",risUrl:"/chapter/ris/39512",book:{slug:"thermodynamics-fundamentals-and-its-application-in-science"},signatures:"Ronald J. Bakker",authors:[{id:"140617",title:"Dr.",name:"Ronald",middleName:"J.",surname:"Bakker",fullName:"Ronald Bakker",slug:"ronald-bakker",email:"bakker@unileoben.ac.at",position:"Ao. Dr. Prof.",institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Two-constant cubic equation of state",level:"1"},{id:"sec_3",title:"3. Thermodynamic parameters",level:"1"},{id:"sec_4",title:"4. Spinodal",level:"1"},{id:"sec_5",title:"5. Pseudo critical point",level:"1"},{id:"sec_6",title:"6. Critical point and curve",level:"1"},{id:"sec_7",title:"7. Mixing rules and definitions of ζ1 and ζ2",level:"1"},{id:"sec_8",title:"8. Experimental data",level:"1"},{id:"sec_9",title:"9. Modifications of modified equations of state",level:"1"},{id:"sec_9_2",title:"9.1. Chueh and Prausnitz [24]",level:"2"},{id:"sec_10_2",title:"9.2. Holloway [25, 26] and Bakker [27]",level:"2"},{id:"sec_11_2",title:"9.3. Bowers and Helgeson [34] and Bakker [28]",level:"2"},{id:"sec_13",title:"10. Application to fluid inclusion research",level:"1"}],chapterReferences:[{id:"B1",body:'Dziewonski AM, Anderson DL1981Preliminary reference Earth modelPhys. Earth Planet. In. 25297356'},{id:"B2",body:'PressF.SieverR.1999Understanding EarthFreeman, New York, 679 p.'},{id:"B3",body:'RoedderE. (1984) Fluid inclusions, Reviews in Mineralogy 12, Mineralogical Association of America, 646 p.'},{id:"B4",body:'Bakker RJ2009Reequilibration of fluid inclusions: Bulk diffusionLithos112277288'},{id:"B5",body:'PrausnitzJ. M.RNLichtenthalerGomes.de AzevedoE.1986Molecular thermodynamics of fluid-phase equilibriaPrentice-Hall, Englewood Cliffs, NJ, 600 p.'},{id:"B6",body:'Bakker RJ2009Package FLUIDS. Part 3: correlations between equations of state, thermodynamics and fluid inclusions. Geofluids 96374'},{id:"B7",body:'Waals JD van der1873De continuiteit van den gas- en vloeistof-toestand. PhD Thesis, University Leiden, 134 p.'},{id:"B8",body:'Redlich OR, Kwong JNS1949On the thermodynamics of solutions, V: An equation of state, fugacities of gaseous solutions. Chem Rev. 44233244'},{id:"B9",body:'SoaveG.1972Equilibrium constants from a modified Redlich-Kwong equation of stateChem. Eng. Sci. 2711971203'},{id:"B10",body:'Peng DY, Robinson DB1976A new two constant equation of state. Ind. Eng. Chem. Fundam. 155964'},{id:"B11",body:'Reid RC, Prausnitz JM, Poling BE1989The properties of gases and liquidsMcGraw-Hill Book Company, NJ, 741 p.'},{id:"B12",body:'Levelt-SengersJ.2002How fluids unmix, discoveries by the school of van der Waals and Kamerlingh Onnes.Koninklijke Nederlandse Akademie van Wetenschappen, Amsterdam, 302 p.'},{id:"B13",body:'Beyer WH1991CRC Standard mathematical tables and formulaeCRC Press, Boca Raton, Fl, 609 p.'},{id:"B14",body:'Horn RA, Johnson CR1985Matrix analysisCambridge University Press, Cambridge, 561 p.'},{id:"B15",body:'PrausnitzJ. M.AndersonT. F.GrensE. A.CAEckertHsieh. R.O’ConnellJ. P.1980Computer calculations for the multicomponent vapor-liquid and liquid-liquid equilibria. Prentice-Hall, Englewood Cliffs, NJ, 353 p.'},{id:"B16",body:'Donnelly HG, Katz DL1954Phase equilibria in the carbon dioxide- methane system. Ind. Eng. Chem. 46511517'},{id:"B17",body:'Baker LE, Luks KD (1980) Critical point and saturation pressure calculations for multipoint systems. Soc. Petrol. Eng. J. 20\n\t\t\t\t154 .'},{id:"B18",body:'Konynenburg PH van, Scott RL1980Critical lines and phase equilibria in binary van der Waals mixtures. Philos. T. Roy. Soc. 298495540'},{id:"B19",body:'AraiY.KaminishiG. I.SaitoS.1971The experimental determination of the P-V-T-X relations for carbon dioxide-nitrogen and carbon dioxide-methane systems. J. Chem. Eng. Japan 4113122'},{id:"B20",body:'SpanR.WagnerW.1996A new equation of state for carbon dioxide covering the fluid region from the triple point temperature to 1100 K at pressures up to 800 MPaJ. Phys. Chem. Ref. Data 2515091596'},{id:"B21",body:'Lorentz HA1881Über die Anwendung des Satzes vom Virial in den kinetischen Theorie der Gase. Ann. Phys. 12127136'},{id:"B22",body:'Waals JD van der1890Molekulartheorie eines Körpers, der aus zwei verschiedenen Stoffen besteht. Z. Ph. Chem. 5133173\n\t\t\t'},{id:"B23",body:'Seitz JC, Blencoe JG, Joyce DB, Bodnar RJ1994Volumetric properties of CO2-CH4-N2 fluids at 200 ˚C and 1000 bars: a comparison of equations of state and experimental data. Geochim. Cosmochim. Acta 5810651071'},{id:"B24",body:'Chueh PL, Prausnitz JM1967Vapor-liquid equilibria at high pressures. Vapor-phase fugacity coefficients in non-polar and quantum-gas mixtures. Ind. Eng. Chem. Fundam. 6492498\n\t\t\t'},{id:"B25",body:'Holloway JR1977Fugacity and activity of molecular species in supercritical fluids. In: Fraser DG, editor. Thermodynamics in geology, 161182'},{id:"B26",body:'Holloway JR1981Composition and volumes of supercritical fluids in the earth’s crust. In Hollister LS, Crawford MI, editors. Short course in fluid inclusions: Applications to petrology, 1338'},{id:"B27",body:'Bakker RJ1999aOptimal interpretation of microthermometrical data from fluid inclusions: thermodynamic modelling and computer programming. Habilitation Thesis, University Heidelberg, 50 p.'},{id:"B28",body:'Bakker RJ1999bAdaptation of the Bowers and Helgeson (1983) equation of state to the H2O-CO2-CH4-N2-NaCl system. Chem. Geol. 154225236'},{id:"B29",body:'SantisR.de BreedveldG. J. F.PrausnitzJ. M.1974Thermodynamic properties of aqueous gas mixtures at advanced pressuresInd. Eng. Chem. Process, Dess, Develop. 13374377'},{id:"B30",body:'Greenwood HJ1969The compressibility of gaseous mixtures of carbon dioxide and water between 0 and 500 bars pressure and 450 and 800 ˚Centigrade. Am. J.Sci. 267A: 191208'},{id:"B31",body:'FranckE. U.TödheideK.1959Thermische Eigenschaften überkritischer Mischungen von Kohlendioxyd und Wasser bis zu 750 ˚C und 2000 Atm. Z. Phys. Chem. Neue Fol. 22232245'},{id:"B32",body:'Sterner SM, Bodnar RJ1991Synthetic fluid inclusions X. Experimental determinations of the P-V-T-X properties in the CO2-H2O system to 6 kb and 700 ˚C. Am. J. Sci. 291154'},{id:"B33",body:'DuanZ.MøllerN.WeareJ. H.1996A general equation of state for supercritical fluid mixtures and molecular simulation of mixtures PVTX properties. Geochim. Cosmochim. Acta 6012091216'},{id:"B34",body:'Bowers TS, Helgeson HC1983Calculation of the thermodynamic and geochemical consequences of non-ideal mixing in the system H2O-CO2-NaCl on phase relations in geological systems: equation of state for H2O-CO2-NaCl fluids at high pressures and temperatures. Geochim. Cosmochim. Acta 4712471275'},{id:"B35",body:'GehrigM.1980Phasengleichgewichte und pVT-daten ternärer Mischungen aus Wasser, Kohlendioxide und Natriumchlorid bis 3 kbar und 550 ˚C. University Karlsruhe, PhD-thesis, Hochschul Verlag, Freiburg, 109 p.'},{id:"B36",body:'Thompson JFH1995Magmas, fluids, and ore depositsShort course 23, Mineralogical Association of Canada.'},{id:"B37",body:'Spear FS1995Metamorphic phase equilibria and pressure-temperature-time pathsMineralogical Society of America, Monograph, 799 p.'},{id:"B38",body:'Wilkinson JJ2001Fluid inclusions in hydrothermal ore deposits. Lithos 55229272'},{id:"B39",body:'Shepherd TJ, Rankin AH, Alderton DHM1985A practical guide to fluid inclusion studiesBlackie, Glasgow, 239 p.'},{id:"B40",body:'Bakker RJ2003Package FLUIDS 1. Computer programs for analysis of fluid inclusion data and for modelling bulk fluid propertiesChem. Geol. 194323'},{id:"B41",body:'Bakker RJ, Brown PE2003Computer modelling in fluid inclusion research. In: Samson I, Anderson A, Marshall D, editors. Short course 32, Mineralogical Association of Canada, 175212'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Ronald J. 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Fu",slug:"w.-n.-fu"},{id:"23951",title:"Dr.",name:"Lingling",middleName:null,surname:"Pang",fullName:"Lingling Pang",slug:"lingling-pang"}]},{id:"13445",title:"Induction Heating of Thin Strips in Transverse Flux Magnetic Field",slug:"induction-heating-of-thin-strips-in-transverse-flux-magnetic-field",signatures:"Jerzy Barglik",authors:[{id:"14398",title:"Prof.",name:"Jerzy",middleName:null,surname:"Barglik",fullName:"Jerzy Barglik",slug:"jerzy-barglik"}]},{id:"13446",title:"Microwave Processing of Metallic Glass/Polymer Composite in a Separated H-Field",slug:"microwave-processing-of-metallic-glass-polymer-composite-in-a-separated-h-field",signatures:"Song Li, Dmitri V Louzguine-Lugzin, Guoqiang Xie, Motoyasu Sato and Akihisa Inoue",authors:[{id:"14827",title:"Dr.",name:"Song",middleName:null,surname:"Li",fullName:"Song Li",slug:"song-li"},{id:"16585",title:"Prof",name:"Guoqiang",middleName:null,surname:"Xie",fullName:"Guoqiang Xie",slug:"guoqiang-xie"},{id:"16586",title:"Prof.",name:"Dmitri V.",middleName:null,surname:"Louzguine-Lugzin",fullName:"Dmitri V. Louzguine-Lugzin",slug:"dmitri-v.-louzguine-lugzin"},{id:"16587",title:"Prof.",name:"Motoyasu",middleName:null,surname:"Sato",fullName:"Motoyasu Sato",slug:"motoyasu-sato"},{id:"16588",title:"Dr.",name:"Akihisa",middleName:null,surname:"Inoue",fullName:"Akihisa Inoue",slug:"akihisa-inoue"}]},{id:"13447",title:"Thermal Microwave Processing of Materials",slug:"thermal-microwave-processing-of-materials",signatures:"Juan A. Aguilar-Garib",authors:[{id:"15364",title:"Dr.",name:"Juan",middleName:null,surname:"Aguilar-Garib",fullName:"Juan Aguilar-Garib",slug:"juan-aguilar-garib"}]},{id:"13448",title:"Evaporators with Induction Heating and Their Applications",slug:"evaporators-with-induction-heating-and-their-applications",signatures:"Anatoly Kuzmichev and Leonid Tsybulsky",authors:[{id:"16332",title:"Dr.",name:"Leonid",middleName:null,surname:"Tsybulski",fullName:"Leonid Tsybulski",slug:"leonid-tsybulski"},{id:"16571",title:"Prof.",name:"Anatoly",middleName:null,surname:"Kuzmichev",fullName:"Anatoly Kuzmichev",slug:"anatoly-kuzmichev"}]},{id:"13449",title:"Application of Microwave Heating to Recover Metallic Elements from Industrial Waste",slug:"application-of-microwave-heating-to-recover-metallic-elements-from-industrial-waste",signatures:"Joonho Lee and Taeyoung Kim",authors:[{id:"17547",title:"Dr.",name:"Joonho",middleName:null,surname:"Lee",fullName:"Joonho Lee",slug:"joonho-lee"},{id:"17549",title:"Prof.",name:"Taeyoung",middleName:null,surname:"Kim",fullName:"Taeyoung Kim",slug:"taeyoung-kim"}]},{id:"13450",title:"Microwave Heating for Emolliating and Fracture of Rocks",slug:"microwave-heating-for-emolliating-and-fracture-of-rocks",signatures:"Aleksandr Prokopenko",authors:[{id:"16694",title:"Dr.",name:"Aleksandr",middleName:null,surname:"Prokopenko",fullName:"Aleksandr Prokopenko",slug:"aleksandr-prokopenko"}]},{id:"13451",title:"Use of Induction Heating in Plastic Injection Molding",slug:"use-of-induction-heating-in-plastic-injection-molding",signatures:"Udo Hinzpeter and Elmar Wrona",authors:[{id:"16064",title:"Prof.",name:"Elmar",middleName:null,surname:"Wrona",fullName:"Elmar Wrona",slug:"elmar-wrona"},{id:"34726",title:"Dr.",name:"Udo",middleName:null,surname:"Hinzpeter",fullName:"Udo Hinzpeter",slug:"udo-hinzpeter"}]},{id:"13452",title:"Microwave-Assisted Synthesis of Coordination and Organometallic Compounds",slug:"microwave-assisted-synthesis-of-coordination-and-organometallic-compounds",signatures:"Oxana V. Kharissova, Boris I. Kharisov and Ubaldo Ortiz Méndez",authors:[{id:"13939",title:"Dr.",name:"Boris",middleName:null,surname:"Kharisov",fullName:"Boris Kharisov",slug:"boris-kharisov"},{id:"13941",title:"Dr.",name:"Oxana V.",middleName:null,surname:"Kharissova",fullName:"Oxana V. Kharissova",slug:"oxana-v.-kharissova"},{id:"13942",title:"Dr.",name:"Ubaldo",middleName:null,surname:"Ortiz Mendez",fullName:"Ubaldo Ortiz Mendez",slug:"ubaldo-ortiz-mendez"}]},{id:"13453",title:"The Effects of Microwave Heating on the Isothermal Kinetics of Chemicals Reactions and Physicochemical Processes",slug:"the-effects-of-microwave-heating-on-the-isothermal-kinetics-of-chemicals-reactions-and-physicochemic",signatures:"Borivoj Adnadjevic and Jelena Jovanovic",authors:[{id:"16551",title:"Dr.",name:"Jelena",middleName:null,surname:"Jovanovic",fullName:"Jelena Jovanovic",slug:"jelena-jovanovic"},{id:"16623",title:"Dr.",name:"Borivoj",middleName:null,surname:"Adnadjevic",fullName:"Borivoj Adnadjevic",slug:"borivoj-adnadjevic"}]},{id:"13454",title:"The Use of Microwave Energy in Dental Prosthesis",slug:"the-use-of-microwave-energy-in-dental-prosthesis",signatures:"Célia M. Rizzatti-Barbosa, Altair A. Del Bel Cury and Renata C. M. Rodrigues Garcia",authors:[{id:"14720",title:"Prof.",name:"Celia Marisa",middleName:null,surname:"Rizzatti-Barbosa",fullName:"Celia Marisa Rizzatti-Barbosa",slug:"celia-marisa-rizzatti-barbosa"},{id:"16737",title:"Dr.",name:"Altair Antoninha",middleName:null,surname:"Del Bel Cury",fullName:"Altair Antoninha Del Bel Cury",slug:"altair-antoninha-del-bel-cury"},{id:"16738",title:"Dr.",name:"Renata",middleName:"Cunha Matheus",surname:"Rodrigues Garcia",fullName:"Renata Rodrigues Garcia",slug:"renata-rodrigues-garcia"}]},{id:"13455",title:"Ultra-Fast Microwave Heating for Large Bandgap Semiconductor Processing",slug:"ultra-fast-microwave-heating-for-large-bandgap-semiconductor-processing",signatures:"Mulpuri V. Rao",authors:[{id:"22899",title:"Prof.",name:"Mulpuri",middleName:null,surname:"Venkata Rao",fullName:"Mulpuri Venkata Rao",slug:"mulpuri-venkata-rao"}]},{id:"13456",title:"Magnetic Induction Heating of Nano-Sized Ferrite Particle",slug:"magnetic-induction-heating-of-nano-sized-ferrite-particle",signatures:"Yi Zhang and Ya Zhai",authors:[{id:"14300",title:"Prof.",name:"Ya",middleName:null,surname:"Zhai",fullName:"Ya Zhai",slug:"ya-zhai"},{id:"20620",title:"Dr.",name:"Yi",middleName:null,surname:"Zhang",fullName:"Yi Zhang",slug:"yi-zhang"}]},{id:"13457",title:"Changes in Microwave-Treated Wheat Grain Properties",slug:"changes-in-microwave-treated-wheat-grain-properties",signatures:"Jerzy R. Warchalewski, Justyna Gralik, Stanisław Grundas, Anna Pruska-Kędzior and Zenon Kędzior",authors:[{id:"14397",title:"Prof.",name:"Stanisław",middleName:"Teodor",surname:"Grundas",fullName:"Stanisław Grundas",slug:"stanislaw-grundas"},{id:"17935",title:"Dr.",name:"Justyna",middleName:null,surname:"Gralik",fullName:"Justyna Gralik",slug:"justyna-gralik"},{id:"23863",title:"Dr.",name:"Jerzy R.",middleName:null,surname:"Warchalewski",fullName:"Jerzy R. Warchalewski",slug:"jerzy-r.-warchalewski"},{id:"23864",title:"Dr.",name:"Zenon",middleName:null,surname:"Kedzior",fullName:"Zenon Kedzior",slug:"zenon-kedzior"},{id:"23905",title:"Dr.",name:"Anna",middleName:null,surname:"Pruska-Kedzior",fullName:"Anna Pruska-Kedzior",slug:"anna-pruska-kedzior"}]},{id:"13458",title:"The Use of Microwave Radiation Energy to Process Cereal, Root and Tuber-based Products",slug:"the-use-of-microwave-radiation-energy-to-process-cereal-root-and-tuber-based-products",signatures:"Yoon Kil Chang, Caroline Joy Steel and Maria Teresa Pedrosa Silva Clerici",authors:[{id:"15049",title:"Prof.",name:"Yoon Kil",middleName:null,surname:"Chang",fullName:"Yoon Kil Chang",slug:"yoon-kil-chang"},{id:"17184",title:"Prof.",name:"Caroline",middleName:null,surname:"Steel",fullName:"Caroline Steel",slug:"caroline-steel"},{id:"17186",title:"Dr",name:"Maria Teresa",middleName:"Pedrosa Silva",surname:"Clerici",fullName:"Maria Teresa Clerici",slug:"maria-teresa-clerici"}]},{id:"13459",title:"Microwave Heating in Moist Materials",slug:"microwave-heating-in-moist-materials",signatures:"Graham Brodie",authors:[{id:"14683",title:"Dr.",name:"Graham",middleName:null,surname:"Brodie",fullName:"Graham Brodie",slug:"graham-brodie"}]},{id:"13460",title:"Assessment of Microwave versus Conventional Heating Induced Degradation of Olive Oil by VIS Raman Spectroscopy and Classical Methods",slug:"assessment-of-microwave-versus-conventional-heating-induced-degradation-of-olive-oil-by-vis-raman-sp",signatures:"Rasha M. El-Abassy, Patrice Donfack and Arnulf Materny",authors:[{id:"14406",title:"Dr.",name:"Arnulf",middleName:null,surname:"Materny",fullName:"Arnulf Materny",slug:"arnulf-materny"},{id:"16733",title:"Prof.",name:"Rasha M.",middleName:null,surname:"El-Abassy",fullName:"Rasha M. El-Abassy",slug:"rasha-m.-el-abassy"},{id:"16734",title:"Prof.",name:"Patrice",middleName:null,surname:"Donfack",fullName:"Patrice Donfack",slug:"patrice-donfack"}]},{id:"13461",title:"Microwave Heating: A Time Saving Technology or a Way to Induce Vegetable Oils Oxidation?",slug:"microwave-heating-a-time-saving-technology-or-a-way-to-induce-vegetable-oils-oxidation-",signatures:"Ricardo Malheiro, Susana Casal, Elsa Ramalhosa and José Alberto Pereira",authors:[{id:"16928",title:"Dr.",name:"José Alberto",middleName:null,surname:"Pereira",fullName:"José Alberto Pereira",slug:"jose-alberto-pereira"},{id:"23911",title:"Prof.",name:"Susana",middleName:null,surname:"Casal",fullName:"Susana Casal",slug:"susana-casal"},{id:"23912",title:"Prof.",name:"Elsa",middleName:null,surname:"Ramalhosa",fullName:"Elsa Ramalhosa",slug:"elsa-ramalhosa"},{id:"23913",title:"PhD.",name:"Ricardo",middleName:null,surname:"Malheiro",fullName:"Ricardo Malheiro",slug:"ricardo-malheiro"}]},{id:"13462",title:"Experimental and Simulation Studies of the Primary and Secondary Vacuum Freeze Drying at Microwave Heating",slug:"experimental-and-simulation-studies-of-the-primary-and-secondary-vacuum-freeze-drying-at-microwave-h",signatures:"Józef Nastaj and Konrad Witkiewicz",authors:[{id:"15124",title:"Dr.",name:"Józef",middleName:null,surname:"Nastaj",fullName:"Józef Nastaj",slug:"jozef-nastaj"},{id:"15908",title:"Dr.",name:"Konrad",middleName:null,surname:"Witkiewicz",fullName:"Konrad Witkiewicz",slug:"konrad-witkiewicz"}]},{id:"13463",title:"Application of Microwave Heating on the Facile Synthesis of Porous Molecular Sieve Membranes",slug:"application-of-microwave-heating-on-the-facile-synthesis-of-porous-molecular-sieve-membranes",signatures:"Aisheng Huang and Jürgen Caro",authors:[{id:"15461",title:"Dr.",name:"Aisheng",middleName:null,surname:"Huang",fullName:"Aisheng Huang",slug:"aisheng-huang"},{id:"23709",title:"Dr.",name:"Jürgen",middleName:null,surname:"Caro",fullName:"Jürgen Caro",slug:"jurgen-caro"}]},{id:"13464",title:"Microwave-Assisted Domino Reaction in Organic Synthesis",slug:"microwave-assisted-domino-reaction-in-organic-synthesis",signatures:"Shu-Jiang Tu and Bo Jiang",authors:[{id:"16059",title:"Dr.",name:"Shu-Jiang",middleName:null,surname:"Tu",fullName:"Shu-Jiang Tu",slug:"shu-jiang-tu"},{id:"16487",title:"Dr.",name:"Bo",middleName:null,surname:"Jiang",fullName:"Bo Jiang",slug:"bo-jiang"}]},{id:"13465",title:"Application of Microwave Technology for Utilization of Recalcitrant Biomass",slug:"application-of-microwave-technology-for-utilization-of-recalcitrant-biomass",signatures:"Shuntaro Tsubaki and Jun-Ichi Azuma",authors:[{id:"16619",title:"Dr.",name:"Shuntaro",middleName:null,surname:"Tsubaki",fullName:"Shuntaro Tsubaki",slug:"shuntaro-tsubaki"},{id:"16775",title:"Prof.",name:"Jun-Ichi",middleName:null,surname:"Azuma",fullName:"Jun-Ichi Azuma",slug:"jun-ichi-azuma"}]},{id:"13466",title:"Microwave Heating Applied to Pyrolysis",slug:"microwave-heating-applied-to-pyrolysis",signatures:"Yolanda Fernandez, Ana Arenillas and J. Angel Menendez",authors:[{id:"14045",title:"Dr.",name:"J. Angel",middleName:null,surname:"Menéndez Díaz",fullName:"J. Angel Menéndez Díaz",slug:"j.-angel-menendez-diaz"},{id:"15134",title:"Dr.",name:"Ana",middleName:null,surname:"Arenillas",fullName:"Ana Arenillas",slug:"ana-arenillas"},{id:"15135",title:"Dr.",name:"Yolanda",middleName:null,surname:"Fernandez",fullName:"Yolanda Fernandez",slug:"yolanda-fernandez"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"68659",title:"Operative Machinery Costs Analysis within Forest Management Implementation Frame",doi:"10.5772/intechopen.87572",slug:"operative-machinery-costs-analysis-within-forest-management-implementation-frame",body:'\n
\n
1. Introduction
\n
Forests cover about 4.0 billion hectares in the world. All decisions and/or actions adopted in order to preserve, to conserve, and to harvest forests and trees within them Bettinger et al. [1] Grebner et al. [2] are expression of the forest management. It is also defined as a tool that forest-owners use to achieve social, economic, and environmental targets or also to implement sustainable forest management. Two of the following approaches characterize forest management:
Monitoring approach, through observation, monitoring, elaboration data, and e-reporting of forest ecosystem state
Technologic approach, through machines, tools, materials, and forest workers
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The first approach concerns primary forest area, while the second is adopted in modified forests, planted forests, and other areas with trees that consist of 2.7 billion hectares (Figure 1) of the global forest area. For the modified forests, one of the most relevant actions is stand management. This management is
necessary, given the alteration (structural and compositional) these ecosystems have recorded over the centuries due to human activities;
functional, to ensure the ecosystem perpetuity and guarantee overtime forest ecosystem services that influence the well-being of the humankind; and
appropriate, in order to increase the resilient capacity of ecosystems currently under strong pressure due to socio-economic activities, climate change, and other global and local disturbance processes.
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Figure 1.
The 4.0 billion hectares of forest area in the world articulated for anthropization categories (data × 1000 hectares). Source: FAO (2015).
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This action satisfies the aims of both forest landowners (FLOs) and logging companies (LCs). Using silvicultural criteria and proper manners, FLOs quantify the intervention in order to ensure the perpetuity of ecosystem (long-term vision) given by the forest’s natural renovation capacity. LCs’ point of view concerns the wood fraction exploitable (stand removal), which is the main output in timber transformation chains (short-term view). In the sustainable economic development policy, forests assume relevant roles [3]. That can be shortly explained as follows:
Wood is a renewable natural resource.
Timber is the main tangible output compared to other nontimber products.
Timber in itself is an ecosystem service provider that provides bio-based resources and also biomass for clean energy production.
Forest ecosystems guarantee regulative ecosystem services related to climate change contrast strategies and other global degradation processes.
Forest ecosystems are areas where individuals or groups can live important social and sensorial experiences and increase their knowledge on natural life processes.
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Using the Italian forest system as background, this topic has been developed in order to provide an international dimension.
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A complementary relation exists between FLOs and LCs (Figure 2). FLOs are responsible overtime for the stand management. Silvicultural managements implemented during forest lifetime have influence on timber and nontimber products. However, FLOs normally do not have resources and knowledge to implement silvicultural management by themselves and sell timber products. The high investments needed for achieving an efficient and technological mechanization level, from an economic and financial point of view, would not be justified if the FLOs manage periodically small forest area, as the majority of FLOs in Europe. According to these evidences, FLOs entrust this job to specialized units, such as LCs, which have machines, technologies, materials, and workers with the knowledge of timber transformation process. Finally, LCs have proper knowledge to achieve the highest market price, given the market situation and the current economic trends.
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Figure 2.
Relationship between forest land owners and logging companies. Source: Our elaboration.
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Regardless of how stand management is entrusted to LCs, one of the mandatory steps is to determine the related costs. In dedicated literature [4, 5, 6], this topic is solved considering the operative cost only. However, differences exist between the type of costs and the calculation method, while transaction and overhead costs and revenues are not considered at all.
\n
In the 1990s, the reducing impact logging (RIL) technique [7, 8] was introduced in the tropical region. It was defined as an “Intensively planned and carefully controlled implementation of harvesting operations to minimise the impact on forest stands and soils, usually in individual tree selection cutting” [9, 10]. The main idea was to adopt a more rational and structured method for forest exploitation. So far, new transaction and overhead cost were introduced in the forest management. More recently, according to the social and environmental relevance of forests, in many countries, forest management is strongly influenced by decisions of forest institution. The main institutions concern the: (a) introduction of forestry and environmental laws and rules; (b) introduction of administrative procedures for safeguarding forest public interest; (c) definition of roles and responsibilities for the economic subjects involved in the transformation process; and (d) redaction of the accidental risks and promotion of high health standards to forest workers.
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The main assumptions adopted in the contribution concern economic subjects, operators, and capitals (workers, machines, material, etc.) involved in the transformation processes. Each of them must be paid for the performances provided. Technical and legal aspects are presented as background, while the core is based on the introduction of transformation steps, from being trees of the forest ecosystem to becoming market products. Timber production is one of the ecosystem services of forest ecosystems. Using the analytical approach, costs and revenue have been identified for each technical centrum of expenditure. Dedicated presentation and information have been provided on calculation method and data sources; however, in Table 1, a glossary of the main controversial terms has been developed.
\n\n\n
\n
\n
\n\n
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Wood
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It is the hard, fibrous, and structural tissues, composed of chains of cellulose, which forms the main substance of the trunk, branches, and roots of trees or shrubs.
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\n
\n
Timber
\n
It is the term to identify products obtained from the trunk, branches, and roofs of trees, at any stage after the tree has been felled. It includes the raw material, also known as rough timber or the processed material, used for construction, as firewood, and as other bio-based products.
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\n
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Price
\n
It is the amount of money that a buyer and a seller agree at the end of a negotiation to exchange between goods for money. In particular, there are a buyer willingness to pay and a seller willingness to accept in order to exchange the property right of goods and services. That information is collected specifically from the market.
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\n
\n
Value
\n
It is an amount (or datum) expressed in monetary metric, produced by experts or single individuals, using simple or complex elaborations, with the support of higher or lower technologies. Given a market price if it was subjected to any elaboration, example timber market price (€) multiply by quality (ton), the result is a value [€ × ton].
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\n
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Forest management
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It is all decisions and/or actions adopted in order to preserve, conserve, and use forests and trees within them.
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\n
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Stand management
\n
It is all decisions and/or actions related to the stand.
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\n
\n
Silviculture management
\n
It is the mode by which forest management is implemented.
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\n
\n
Forest utilization
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It is the action usually developed from the LC. Selected trees are felled and processed to obtain marketable timber.
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\n\n
Table 1.
Glossary of the terms used in the chapter.
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2. Legal and technical aspects
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\n
2.1 Legal aspects
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2.1.1 Public interest on forest ecosystems
\n
Forests provide a large spectrum of ecosystem services that produce well-being to the humanity. Consequently, many institutions currently put silvicultural management under laws and regulations discipline. The target of institutions and administrative proceedings is to safeguard the public interest on forest ecosystems [11].
\n
The following are the two main consequences:
Introduction of administrative procedures, at the end of which the FLOs obtain the right to perform the silvicultural intervention
Introduction of transaction costs to prepare the technical documentation necessary to satisfy the administrative process
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\n
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2.1.2 Entrustment of the silvicultural intervention
\n
Utilization intervention can take place under the regime of the following:
Sale: with which the property transfers to the LCs the property rights of the forest stand destined to be felled
Contract: with which the FLOs entrust through the acquisition of LC services, the forest harvesting operations, while they maintain the timber ownership
Economy: where the FLOs, in particular the public ones, decide to carry out the work in-house, using the own property, in particular machinery, other tools, and forest workers enrolled
\n
Regardless of the regime, the entrustment can be done in terms of the following:
Purchase all timber at fixed price: LC undertakes to carry out the intervention at the agreed and invariable price respecting the identified unit and following technical indications from the project and the subsequent notes of the competent institutions.
Based on a fixed price for unit: regime that requires the commitment by the property to pay the intervention at the fixed price per unit (usually volume or area), as well as the commitment by the company to quantify ex-post the volume or the area.
Mixed, partly defined at fixed price, and partly on the fixed price for unit.
These aspects are usually clearly stated in the contract. Further mutual fundamental obligations are:
for the FLOs: to certify that they have fulfilled all procedures necessary to obtain the authorization to carry out the silvicultural intervention and all provisions have been transposed in area (boundaries of the forest area under management have been marked, trees that shall be fell are also marked, etc.). Documents produced and received must be available to the LCs, which will be used at the end for monitoring the correctness of developed activity; and
for the LCs: to be aware of the territorial unit where they must operate, the characteristics of the stand and the area, as well as the nature of the silvicultural intervention to be implemented. The LCs certify to be fully aware of the technical and technological complexity level of the silvicultural intervention, to be aware of the appropriate methods to carry it out, as well as to have availability of equipment, workers, and materials necessary for its execution in due time.
\n
\n
\n
\n
2.2 Technical aspects
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Evaluation processes require relevant technical information such as: (a) the forest areas in which the stand involved in the management activity is located; (b) the timber volume that should be felled; and (c) the type of marketable products that could be obtained.
\n
\n
2.2.1 Entity of the volume removal
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If the stand of volume, silvicultural intervention, and felled timber are expressed in cubic meter, among them, the following relation subsists:
\n
\n\nSoV\n=\nSI\n+\nTH\n\n
\n
And solved for SI, it becomes
\n
\n\nSI\n=\nSoV\n−\nTH\n\n
\n
where [SoV] is the volume of stand invested in the ground until cutting intervention starts; [SI] is the volume of trees left in the ground at the end of the harvesting process; and [TH] is the volume of the trees felled and transformed in market goods from the LCs. Silvicultural intervention is indirectly obtained by felling wood volume in excess, given the adopted forest management system. In other words, it is the result of the forest left in the ground after the trees cut by LCs are already in the market. The function is always verified at the time that felling activity starts.
\n
Silviculture proposes different management methods, in relation to the auto-ecology of the species and forest community, as well as the land characteristics, forest state and type of the previous management, objectives pursued, and infrastructures. The characteristics of each intervention are defined in terms of the following:
Volume of the stems that must be released
Characteristics of the trees to be released with respect to the horizontal (territorial distribution) and vertical (stand stratigraphy) plane
Characteristics of the trees to be released for environmental needs, biodiversity, and other nonproductive functions
\n
Given the total volume that insists in the area just before felling activity starts, the magnitude of the intervention can be quantified in terms of volume to be withdrawn \n\nπ\n=\n\n\nTH\nSTM\n\n\n\nor to be released \n\nρ\n=\n\n\nSI\nSTM\n\n\n\n.
\n
Basing on the size of the withdrawal, it is possible to have a qualitative indication of the intervention and consequently an estimation of expected revenue (Table 2). Minor interventions, refereed to particularly small volume withdrawals, don’t need a high mechanization level, which determines the growing employment of workers and a modest productivity. The unit costs of the intervention are high, if compared to constant revenues, with a negative balance. Interventions with higher withdrawals allow the use of higher levels of mechanization, lower use of labor, and consequently greater productivity. These conditions lead to a growing budget balance.
\n
\n
\n
\n
\n
\n
\n
\n
\n\n
\n
Magnitude of treatment
\n
Mechanization level
\n
Workers’ qualification
\n
Productiveness
\n
Monetary results
\n
\n
\n
Costs
\n
Revenue
\n
Budget performance
\n
\n\n\n
\n
Slight
\n
Low
\n
Low skill
\n
Low
\n
High
\n
Low
\n
Negative
\n
\n
\n
Intermediate
\n
Medium skill
\n
Moderate
\n
Moderate—high
\n
Low
\n
Negative—variable
\n
\n
\n
Moderate
\n
Intermediate
\n
Medium skill
\n
Moderate—high
\n
Moderate
\n
Medium—good
\n
Positive
\n
\n
\n
Advanced
\n
Skill
\n
High
\n
Moderate—high
\n
Variable results
\n
Variable
\n
\n
\n
Effective
\n
Advanced
\n
Skill
\n
Very high
\n
Moderate—low
\n
Substantial
\n
Positive
\n
\n
\n
Intense
\n
High skill
\n
High
\n
Moderate
\n
Medium—good
\n
Variable
\n
\n
\n
Intensive
\n
Intense
\n
High skill
\n
Very high
\n
Low
\n
Substantial
\n
Positive
\n
\n\n
Table 2.
Orienting economic results for treatment magnitude types.
There are different types of forestry yard. The first classification is based on 4 mechanization levels (Tables 3,4,5, and 6). The former is characterized by high investments and high productivity, with decreasing average costs by increasing processed volumes (intense – Table 3); the lower mechanization level is characterized by increasing operating costs by decreasing productivity of processes and work (low or based on animal power—Table 6). Other mechanization levels are advanced (Table 4) and intense (Table 5).
\n
Table 3.
Level of mechanization applied in the forest yard: intense. Chainsaw is the machine common in all the levels, but reported only in this table, in order to limit the repetition.
\n
Table 4.
Level of mechanization applied in the forest yard: advanced.
\n
Table 5.
Level of mechanization applied in the forest yard: intermediate.
\n
Table 6.
Level of mechanization applied in the forest yard: low.
\n
The second classification can be based on the type of productions in the forest (or productions at the felling site). There are four logging system classes (Tables 7,8,9, and 10), such as the following:
Full tree logging system (Whole tree harvesting system) (Table 7)
Logging systems: Extraction of full trees (TLS) (branch and top).
\n
Table 8.
Logging system: Tree length (TLS). Extraction of full stem.
\n
Table 9.
Logging system: Intermediate system: Tree length/short wood (cut to length CTL). Extraction full stand cross cutting to multiple market assortments.
\n\n\n
Table 10.
Short wood system (SWS): Wood processed in final assortment in forest.
\n\n\n
Each type of forestry yard is characterized by different cost dynamics:
Cost for activity in forest: decreasing costs by reducing the work for each tree
Cost for bunching-extraction: increasing costs by increasing number of logs to be bunched to achieve that volume to make extraction efficient and economically convenient
\n
\n
\n
\n
\n
3. Costs and revenue in the transformation process
\n
\n
3.1 Transformation process
\n
The term “transformation process” refers to the whole process to get stand transformed in row timber material and allocated in the landing, in order to be sold. This process includes all actions that should be done by
the forest owner, directly by it or indirectly through performance of forest consultant, as in majority of cases and
the logging company, who develops the technological cycle.
\n
The starting point is the decision assumed by the forest owner to perform silvicultural intervention, while the end is when final monitoring of LCs’ activity is done and certification of the results is presented. This process is articulated in four steps, which are as follows:
Preliminary: aimed to acquire the permit for the silvicultural intervention to be executed.
Preparatory: which includes (a) the operations to transpose in the forest, the planning, and the administrative provisions; (b) the assignment of the work to an LC; and (c) the signing of the contract between FLO and LC.
Executive: in which LC performs silvicultural intervention. It includes selected trees felling, extraction, transportation, and stacking of the timber in the landing.
Conclusive: in which the goodness of the silvicultural intervention is verified.
\n
\n
\n
3.2 Costs
\n
In order to implement the four steps of the transformation process, many services and inputs must be purchased on the market. Total costs are the sum of three cost types (Table 10):
Transaction costs
Operative costs
Overhead costs
\n\n\n\n
\n
3.2.1 Transaction costs
\n
This type of cost includes all expenditures that have to be incurred in the process to fulfill the administrative procedures defined by rules, regulations, and laws, in order to manage the forest. Those expenditures are mainly necessary to acquire the permission to perform the silvicultural intervention, but they include the costs to prepare the forest area, to entrust LCs with the work, to ensure effectively results, and to monitor the results. The whole transaction costs are defined formally frame in which FCs and LCs must work in order to safeguard public interest as well as the forest and other social aspects (work safety aspect). Both FLOs and LCs sustain transaction costs.
\n
FLOs’ transaction costs include the following:
Forest consultancy
Technical documents and drafts
Administrative fees
Selecting and entrusting an LC with implementation of forest utilization
Technical responsibility to safeguard the FLO’s interest during the activity
Verification of the forest utilization conformity to the standard defined by the permission and the forest rules, regulations, and laws
\n
These costs per unit area usually decrease, but total cost increases according to the area interested in the process (proportional principle) (Figure 3). Expenditures for those performances are defined as bunched cost by
dedicated market survey;
negotiation between the LC and forest consultant;
tables issued by competent institutions. The amounts are changed proportionally with the volume of timber felled or with the forest area under management;
mixed approach, combining the two systems mentioned earlier; and
surveys on the dedicated market.
\n
Figure 3.
Transaction costs. Source: Our elaboration.
\n
The LCs’ transaction costs are related to the obligations concerning the following:
Healthy costs, capital investment to ensure high safety standard in the forestry yards and to the forest workers
Cost of refund deposit, caution money that forest owners can operate when LCs don’t pay the stumpage price and for penalty that LCs incurred during the activities
\n
The LC costs are defined by market survey.
\n
\n
\n
3.2.2 Operative costs
\n
All expenditures to implement technological cycle are defined as operative cost (Table 11). These costs are sustained to transform trees into marketable timber products, mainly by the LC and only a few for FL. They include expenditure to buy primary and secondary productive factors.
\n\n
\n
\n
\n
\n
\n
\n
\n
\n\n
\n
Type of costs
\n
Description
\n
\n
Calculation
\n
Details
\n
\n\n\n
\n
Land
\n
Structure
\n
Fixed costs
\n
Fee for recovery and storage of machines
\n
QRR
\n
\n\n\n=\n\n\nCC\n∗\n\ncc\n%\n\n∗\nA\n\n\n\n\n
\n
CC = building costs; cc% = recovery and storage coefficient; A = area
\n
\n
\n
Working capital
\n
Machines
\n
Amortization rate
\n
AR
\n
\n\n\n=\n\n\n\n\nMP\n−\nRV\n\n\nn\n\n\n\n\n
\n
MP = market price; RV = residual value; n = life time in years
\n
\n
\n
Interest
\n
Int
\n
\n\n\n=\n\n\nQA\n∗\nr\n\n\n\n\n
\n
QA = amortization rate
\n
\n
\n
Maintenance fee
\n
MF
\n
\n\n\n=\n\n\nQA\n∗\n\nmc\n%\n\n\n\n\n\n
\n
QA = amortization rate; mc% = maintenance cost in percent
Transformation cost types and calculation procedures.
The footnote symbol “*” means multiplication.
\n\n\n\n\n\n
Main primary factors are as follows:
Land: capital permanently invested in the ground. While it is very relevant for FLOs, for LCs, it is limited to the structures for recovery and storage of working capital, as machineries, machines, and other tools.
Capitals that include the following:
Working capital such as machines (forwarder, harvester, chainsaw, etc.) and other tools (winch, etc.). Those have a multiple-year employment, so the use cost must be distributed through the years they will contribute to the activity (amortization costs and annual interest). These costs are added to the maintenance costs, insurance and other contribution, cost of rapid consumption parts, etc. in order to define the cost machine.
Financial capital necessary for the possession and use of working capital above descripted, to remunerate workers as well as to cover the interest of financial advances for the activity development.
Labor, concerning employers involved in the transformation process, such as forest workers and other units that have administrative functions. In both cases, the remuneration changes according to the skill and qualifications. The fundamental information is not the payment for hour or day, but the costs sustained by the entrepreneur that include tax, insurance, and other costs paid as benefits or facilities for the future of workers.
Entrepreneur organization, done by the person who assumes the forest activity risk. Currently, the payment is split between equity profit and extra profit. The first covers the responsibility assumed by the forest entrepreneur to manage the activity and it is estimated as about 10% of the total cost and named as equity net profit, while extra profit is obtained as differential between total costs (include equity profit) and total revenues. This amount covers the risk management activity.
\n
\n
\n
3.2.3 Overhead costs
\n
Also named as indirect costs, these do not contribute directly to obtain the product but exist to ensure LC functioning. They are related to the LC unit as a whole, and they cannot be applied or traced to any specific unit of output. Overhead costs include the following:
Costs for managing goods and material purchases involved in the forest utilization process; costs due to the activity of timber trade in the market
Costs for managing of insurances, taxes, and other contributions due to the LC
Costs for managing markets and operator networks
Costs for the LC accounts
\n
\n
\n
\n
3.3 Revenues
\n
The output of the silvicultural activity can be expressed in terms of volume or value. The first results by measurement operations of the standing, with special emphasis to the volume of row timber material removal from the ground [V] differentiated for market destination [i] and expected to be sold in the polder (first competitive timber market). The latter is the result of the volume of row timber material for the relative market price [MP]. Data can be collected by market survey, or dedicated statistical publication.
Literature offers three approaches to answer the questions above, which are as follows:
Market price approach
Cost approach
Combination of the above-mentioned approaches
\n
In all these approaches, results are based on common comparative method. This method ensures a strictly direct or indirect connection between market and the good under evaluation.
\n
\n
4.1 Appraisal theory
\n
Theoretical background on evaluation method has been defined from International Valuation Standard Council [21]. In this contest, two main approaches are suitable: market comparison approach and cost approach. The first obtains the timber value by comparing the timber under evaluation with other similar timbers sold in the market; for which, price and at least one technical parameter are well known. The latter defines the value considering all expenditures that the enterprise have to sustain in order to obtain the product under evaluation.
\n
Timber evaluation can have different assessments depending on whether one of the following two objectives is pursued:
Timber optimization uses: FLOs’ target is to ensure the most appreciated market product.
Optimization of market functioning: FLOs target to create the most favorable conditions for large market participation by the LCs.
\n
The first target tends to favor the major LCs, even if the LCs who would take part in the market are very few in number, at least only one. Those LCs are technologically advanced, have greater financial availability, and have wider timber markets, as they can be international timber markets. The hypothesis is that this setting should ensure an effective use of timber and that it can achieve the highest addend value. On the other hand, the second target tends to align itself with the most frequent conditions compared to the local area framework, so as to allow the greatest participation of the local LCs at the market. The hypothesis is that if a large number of LCs take part in the market, that should ensure highest LC competition and the highest stumpage price.
\n
\n
4.1.1 Market value
\n
\n
4.1.1.1 The stumpage value
\n
The first step is to acquire an adequate observation numbers, at least not less than 4 for each variable used in model, of
market price (dependent variable);
technical variables (independent variables),
the value of the stand can be determined through two procedures:\n
a) By direct comparison, using the fundamental proportion to evaluate a market good. Having market prices and at least one technical parameter value, the proportion adapted to evaluate forest stand marketable is
where [SV] is the stumpage price, [Vol] is the volume felled, [i] is the number of market observations collected by a survey, and [x] are the data related to the stand under evaluation. Developing the proportion above in favor of SV, it becomes
where [Y] is the dependent variable vector of the stumpage price, [x] are the generic technical variables, and [i] is the type of variables such as forest area (hectares), timber volume (cubic meter), infrastructure index (qualitative data), and other parameters.
\n
The strong limits of both procedures are (a) the lower number of LCs that take the risk that low number of LCs have an informal agreement about the stumpage value, and the LC that acquire the stem it was decided before the timber market start officially; and (c) there isn’t a well structured culture on how and what forest data, technical and market, should be collected. Each forest owner has its collection, and each forest owner itself selects the variables that should be registered.
\n
\n
\n
4.1.1.2 Timber raw material market
\n
It is the market in which the trees, transformed in marketable products, are sold as timber raw material. That market has two relevant advantages for the evaluation proceeding: (a) even if the number of FLOs or LCs that support the supply is very low, the sawmills are much more so the market should have less distortion; and (b) it is the first market later to the stand felling.
\n
The market price of timber raw material is obtained by market survey. Database is built using the price registered in the market.
\n
\n
\n
\n
4.1.2 Forest management evaluation costs
\n
The production cost approach concerns the technological cycle step and it includes only the expenses necessary to carry it out. This circumstance mainly happens when forest management has social objectives or the timber raw material has high market value and the FLOs prefer it to be sold directly in the timber raw material market because they expect strong completion among sawmills. The FLOs operate on service markets. They purchase the LC services for felling, processing and transportation of plant to an area which is easy to access (landing). Timber raw material can be
evaluated to reduce forest management costs;
made available to the local community to pursue their objectives;
sold in the timber raw material, directly or through dedicated agencies.
\n
FLOs have to pay the LCs in any case. Activity is developed within the regulation code of “tender” to fell stand. The characteristic of this entrust is that FLOs have to pay LCs for their performance. The main national law states that an enterprise, as LCs, “assumes, (…), the fulfilment of a work or a service towards a consideration in money”1.
where [K] is the total costs, [k] is the elementary costs, [i] is the types of costs, [r] is the discount rate, and [t] time and [j, s] are, respectively, the day when the work finished and the day when the expenditure has been done.
\n
\n
\n
4.1.3 The transformation value
\n
The last procedure provides the evaluation of the stand as a comparison between the value of the timber raw material market and all costs necessary to transform the stand into marketable products. The transformation process increases timber value step by step until it becomes timber raw material. The evaluation process, on the other hand, moves in the opposite direction: starting from the market products to achieve the stumpage value (Figure 4).
\n
Figure 4.
Pathway of timber productions and value formation.
\n
The fundamental relationship at the base of the procedure is that timber raw material market price is equal to the sum of stumpage price with the costs of carrying out transforming process:
\n
\n\n\nMP\nTRM\n\n=\nSV\n+\n\nK\nTot\n\n\n
\n
where [MPRTM] is timber raw material market price in the first market after the stand is felled; [i] is the types of timber product obtained (timber construction, fuel wood, etc.); [SV] is the stumpage price; [KTot] is the total costs of transformation processes from stand to timber raw materials; and [j] is the types of costs. Resolving for the stumpage value, it becomes
The ex ante budget is the tool that foresters usually adopt, where in one site is reported the revenue and in the other site the expenditures. The balance between revenues and expenditures is the stumpage value that LCs take from the commitment to pay at the FLOs when agreement was signed.
\n
\n
\n
\n
4.2 Appraisal approach for entrusting types
\n
\n
4.2.1 Forest management in house
\n
The common model of this forest management is based on the ability of forest property (public or private) to carry out the forestry intervention. The owner directly or through an agency of the same subsidiary carries out forest utilization using personnel, machines, and tools in its possession. The economic and financial questions that accompany this approach are as follows:
What is the total cost of carrying out the intervention (Ktot)?
What is its operating cost (KOp)?
What is the market value of the timber raw material (MVTRM)?
\n
The total cost expresses the total amount of costs regardless of the evidence that the resources used are internal. The operating cost focuses only on the variable (additional) costs that are incurred only if the intervention is carried out, ignoring the costs related to the internal resources involved in the works and the costs that the property still support. The last question relates to the value of timber raw material, which is quantified through market surveys.
\n
\n
\n
4.2.2 Forest management by tender
\n
In this case, the silvicultural intervention is entrusted to an LC, which provides a service to the FLOs in exchange for payment of the service. The company that carries out the intervention is the one that, all other parameters being equal, ensures the service at the lowest price (Figure 5).
\n
Figure 5.
Services market: forest land owner purchase logging company service for felling, extraction, and processing timber production at lowest price. Source: Our elaboration.
\n
Different approaches to calculate operating costs are reported in the cost machine literature. The main frames are elaborated and reported in Tables 12 and 13, respectively, for FAO and USDA. The following are the common comments:
Transaction and overhead costs are not included.
Labor costs are not included.
The frame proposed is developed for machine that works in huge areas or regions.
Total costs have to be used as an approximation of the cost machines.
Some algorithms and parameters used for evaluating cost are not easy to understanding the economic ratio.
In the forest appraisals, the approach is to elaborate an ex ante budget of the silvicultural intervention including the expected costs to transform trees in marketable products and the expected revenue that should be obtained from the products sold.
\n
The differences between expected revenue and costs are the expected stumpage value of the trees that LCs should pay to the FLO to bay the stand, while only the amount of the expected costs is the price that FLO has to pay to the LC for the service of felling the stand. Stumpage price became the minimum price that FLO accepts to sell its stand. LCs that want to purchase it have to submit a proposal with a price higher than the minimum (Figure 6).
\n
Figure 6.
Commodities market: forest land owner sells its stand to the logging company that makes the highest price.
\n
\n
\n
\n
\n
5. Conclusions
\n
Growing awareness of the usefulness of forest ecosystems makes the operational cost significant as a component of the wider transformation cost. The latter includes both transaction costs in order to satisfy the provisions dictated by the legislative and regulatory forest and related forest disciplines, as well as the overhead costs that allow the correct functioning of the LCs.
\n
Approaches introduced by international institutions lend themselves to an assessment, very approximate of the costs of managing uniform forests that cover large and flat areas. Their limits are given by concentrating on the component of operating costs, excluding overhead and transaction costs, as well as the introduction of simplifications in order to increase the territorial scale of application. They determine an underestimation of forest management costs [22].
\n
A drawback instead overcomes the analytical approach, whose strong point is its adaptation to the context of intervention and to the specificities of the transformation cycle. This makes it possible to overcome the deformities that characterize forests, especially in the mountain areas, where it is possible to register a different stumpage value for two similar forests, close to each other and having the same productions. This approach also ensures transparency and traceability of the assessment process, as well as flexibility being able to be adapted to the different process for entrusting the management of the stand.
\n
\n
Acknowledgments
\n
This research was in part supported by the “Departments of Excellence—2018” Program of the Italian Ministry of Education, University and Research (Law 232/2016), financed. Department for Innovation in Biological, Agro-Food and Forest Systems (DIBAF)-University of Tuscia, Project “Landscape 4.0—Food, Well-being and Environment” and Department of Agriculture and Forest Science (DAFNE), University of Tuscia, Project (WP3).
\n
\n',keywords:"legal aspects, transformation process steps, types of costs, stumpage value, entrusting approach",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/68659.pdf",chapterXML:"https://mts.intechopen.com/source/xml/68659.xml",downloadPdfUrl:"/chapter/pdf-download/68659",previewPdfUrl:"/chapter/pdf-preview/68659",totalDownloads:92,totalViews:0,totalCrossrefCites:0,dateSubmitted:"December 13th 2018",dateReviewed:"June 6th 2019",datePrePublished:"August 20th 2019",datePublished:"December 4th 2019",readingETA:"0",abstract:"Forest management affecting most of the world’s forests is based on the implementation of forestry interventions. Their execution requires preliminary preparation based on technical documents, submission of the administrative procedures, and the execution of the forest harvesting. Market value of wood is achieved by determining the most probable transformation value. It is obtained as the difference of the revenues derived from the sale of marketable timber net of all the costs involved in transforming the tree into salable products. The chapter provides a theoretical framework of the evaluation approaches and the calculation methods of the timber value, considering the different forms of assignment of the forestry intervention to the logging company, as well as the types of ground and the types of product achievable based on the level of mechanization.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/68659",risUrl:"/chapter/ris/68659",signatures:"Francesco Carbone and Rodolfo Picchio",book:{id:"8299",title:"Timber Buildings and Sustainability",subtitle:null,fullTitle:"Timber Buildings and Sustainability",slug:"timber-buildings-and-sustainability",publishedDate:"December 4th 2019",bookSignature:"Giovanna Concu",coverURL:"https://cdn.intechopen.com/books/images_new/8299.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"108709",title:"Dr.",name:"Giovanna",middleName:null,surname:"Concu",slug:"giovanna-concu",fullName:"Giovanna Concu"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"289371",title:"Prof.",name:"Francesco",middleName:null,surname:"Carbone",fullName:"Francesco Carbone",slug:"francesco-carbone",email:"fcarbone@unitus.it",position:null,institution:null},{id:"301510",title:"Prof.",name:"Rodolfo",middleName:null,surname:"Picchio",fullName:"Rodolfo Picchio",slug:"rodolfo-picchio",email:"r.picchio@unitus.it",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Legal and technical aspects",level:"1"},{id:"sec_2_2",title:"2.1 Legal aspects",level:"2"},{id:"sec_2_3",title:"2.1.1 Public interest on forest ecosystems",level:"3"},{id:"sec_3_3",title:"2.1.2 Entrustment of the silvicultural intervention",level:"3"},{id:"sec_5_2",title:"2.2 Technical aspects",level:"2"},{id:"sec_5_3",title:"Table 2.",level:"3"},{id:"sec_6_3",title:"Table 3.",level:"3"},{id:"sec_9",title:"3. Costs and revenue in the transformation process",level:"1"},{id:"sec_9_2",title:"3.1 Transformation process",level:"2"},{id:"sec_10_2",title:"3.2 Costs",level:"2"},{id:"sec_10_3",title:"3.2.1 Transaction costs",level:"3"},{id:"sec_11_3",title:"Table 11.",level:"3"},{id:"sec_12_3",title:"3.2.3 Overhead costs",level:"3"},{id:"sec_14_2",title:"3.3 Revenues",level:"2"},{id:"sec_16",title:"4. Monetary evaluation of forest management",level:"1"},{id:"sec_16_2",title:"4.1 Appraisal theory",level:"2"},{id:"sec_16_3",title:"4.1.1 Market value",level:"3"},{id:"sec_16_4",title:"4.1.1.1 The stumpage value",level:"4"},{id:"sec_17_4",title:"4.1.1.2 Timber raw material market",level:"4"},{id:"sec_19_3",title:"4.1.2 Forest management evaluation costs",level:"3"},{id:"sec_20_3",title:"4.1.3 The transformation value",level:"3"},{id:"sec_22_2",title:"4.2 Appraisal approach for entrusting types",level:"2"},{id:"sec_22_3",title:"4.2.1 Forest management in house",level:"3"},{id:"sec_23_3",title:"Table 12.",level:"3"},{id:"sec_24_3",title:"4.2.3 Forest management by sale of stand",level:"3"},{id:"sec_27",title:"5. Conclusions",level:"1"},{id:"sec_28",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Bettinger P, Siry JP, Boston K, Grebner DL. Forest Management and Planning. Academic Press: Elsevier; 2017'},{id:"B2",body:'Grebner DL, Bettinger P, Siry JP. Introduction to Forestry and Natural Resources. Academic Press: Elsevier; 2012'},{id:"B3",body:'UN. 2015'},{id:"B4",body:'FAO. Cost Control in Forest Harvesting and Road Constraction. Roma: FAO; 1992'},{id:"B5",body:'FAO. Cost Control in Forest Harvesting and Road Construction. Food and Agriculture Organization of the United Nations; 1992, Forestry paper, n. 99'},{id:"B6",body:'Miyata ES. Determining fixed and operating costs of logging equipment. General Technical Report NC-55. North Central Forest Experiment Station, USDA Forest Service; 1980'},{id:"B7",body:'Marsh CW, Tay J, Pinard MA, Putz FE, Sullivan TE. Reduced impact logging: A pilot project in Sabah, Malaysia. In: Schulte A, Schöne D, editors. Dipterocarp Forest Ecosystems: Towards Sustainable Management. Singapore: World Scientific Publishing Co. Pte. Ltd; 1996. pp. 293-307'},{id:"B8",body:'Putz FE. Approaches to sustainable forest management. In: Working Paper No. 4. Bogor: CIFOR; 1994. pp. 7'},{id:"B9",body:'Putz FE, Sist P, Fredericksen T, Dykstra D. Reduced-impact logging: Challenges and opportunities. Forest Ecology and Management. 2008;256:1427-1433'},{id:"B10",body:'Sist P. Reduced impact logging in the tropics: Objectives, principles and impacts. International Forestry Review. 2000;2(1):3-10'},{id:"B11",body:'Carbone F. Institution, forest enterprises and transaction costs on the domestic market. Journal of Agricultural Economics. 2012;1:89-121'},{id:"B12",body:'Hippoliti G. Appunti di Meccanizzazione Forestale. Società Editrice Fiorentina: Firenze, Italy; 1997'},{id:"B13",body:'Verani S, Sperandio G, Picchio R. First thinning in a coniferous plantation for biomass production: productivity and costs. In: Proceeding FORMEC 2010 Forest Engineering: Meeting the Needs of the Society and the Environment; 11-14 July 2010; Padova, Italy. 2010. ISBN 978 88 6129 569 8. Available from: http://www.tesaf.unipd.it/formec2010/Proceedings/Ab/ab100.pdf-'},{id:"B14",body:'Verani S, Sperandio G, Picchio R, Savelli S. La raccolta della biomassa forestale. Tecniche, economia e sicurezza sul lavoro. Vol. 1. Monterotondo (Roma): Grafica Salaria; 2009. p. 50'},{id:"B15",body:'Verani S, Sperandio G, Picchio R, Spinelli R, Picchi G. Field Handbook—Poplar Harvesting; Poplar Harvesting. International Poplar Commission Working Paper IPC/8. Forest Management Division. Rome: FAO; 2008. pp. 54'},{id:"B16",body:'Marchi E, Neri F, Fabiano F, Cambi M, Picchio R. Pianificazione, organizzazione e gestione delle utilizzazioni forestali per la prevenzione selvicolturale. In: Bovio G, Corona P, Leone V, editors. Gestione selvicolturale dei combustibili forestali per la prevenzione degli incendi boschivi. Arezzo: Compagnia delle Foreste; 2014'},{id:"B17",body:'Picchio R, Sirna A, Sperandio G, Spina R, Verani S. Mechanized harvesting of eucalypt coppice for biomass production using high mechanization level. Rivista Croatian Journal of Forest Engineering. 2012;33(1):15-24'},{id:"B18",body:'Picchio R, Spina R, Maesano M, Carbone F, Lo Monaco A, Marchi E. Stumpage value in the short wood system for the conversion into high forest of a oak coppice. Rivista Forestry Studies in China. 2011;13(4):252-262. DOI: 10.1007/s11632-013-0411-7'},{id:"B19",body:'Civitarese V, Sperandio G, Picchio R. Aspetti economici della produzione di cippato; capitolo di manuale tecnico: Processi di valorizzazione del cippato agroforestale PRO.VA.CI. AGR. Viterbo; 2015. p. 108, ISBN: 979-12-200-0444-2-'},{id:"B20",body:'Picchio R, Antogiovanni A, Calienno L, Caputo F, Marziali L, Venanzi R, Lo Monaco A. Utilizzazioni e meccanizzazione forestale; capitolo di libro: Progetto MORINABIO, L’Aquila, 2015. 134 p. ISBN: 978–88-95453-26-2'},{id:"B21",body:'International Valuation Standard Council. International valuation standard 2013. Framework and requirements. London; 2013'},{id:"B22",body:'Piegai F, Fratini R, Pettenella D. Costi macchina, confronto fra diversi metodi di calcolo, 2008. Sherwood—Foreste ed Alberi Oggi. Aulla Magna; no. 8. 2008. p. 27'}],footnotes:[{id:"fn1",explanation:"Civil Code, article 1655."}],contributors:[{corresp:"yes",contributorFullName:"Francesco Carbone",address:"fcarbone@unitus.it",affiliation:'
Department for Innovation in Biological, Agro-Food and Forest systems (DIBAF), University of Tuscia, Italy
Department of Agricultural and Forestry Science (DAFNE), University of Tuscia, Italy
'}],corrections:null},book:{id:"8299",title:"Timber Buildings and Sustainability",subtitle:null,fullTitle:"Timber Buildings and Sustainability",slug:"timber-buildings-and-sustainability",publishedDate:"December 4th 2019",bookSignature:"Giovanna Concu",coverURL:"https://cdn.intechopen.com/books/images_new/8299.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"108709",title:"Dr.",name:"Giovanna",middleName:null,surname:"Concu",slug:"giovanna-concu",fullName:"Giovanna Concu"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}}},profile:{item:{id:"72554",title:"Dr.",name:"Tetsuo",middleName:null,surname:"Fujita",email:"tfujita@cd5.so-net.ne.jp",fullName:"Tetsuo Fujita",slug:"tetsuo-fujita",position:null,biography:null,institutionString:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",totalCites:0,totalChapterViews:"0",outsideEditionCount:0,totalAuthoredChapters:"3",totalEditedBooks:"0",personalWebsiteURL:null,twitterURL:null,linkedinURL:null,institution:{name:"Kitasato University",institutionURL:null,country:{name:"Japan"}}},booksEdited:[],chaptersAuthored:[{title:"Prognostic Impact of Perirenal Fat or Adrenal Gland Involvement in Renal Cell Carcinoma Exhibiting Venous Vascular Extension",slug:"prognostic-impact-of-perirenal-fat-or-adrenal-gland-involvement-in-renal-cell-carcinoma-exhibiting-v",abstract:null,signatures:"Tetsuo Fujita, Masatsugu Iwamura, Shinji Kurosaka, Ken-ichi Tabata, Kazumasa Matsumoto, Kazunari Yoshida and Shiro Baba",authors:[{id:"72554",title:"Dr.",name:"Tetsuo",surname:"Fujita",fullName:"Tetsuo Fujita",slug:"tetsuo-fujita",email:"tfujita@cd5.so-net.ne.jp"},{id:"77105",title:"Dr.",name:"Masatsugu",surname:"Iwamura",fullName:"Masatsugu Iwamura",slug:"masatsugu-iwamura",email:"miwamura@med.kitasato-u.ac.jp"},{id:"77106",title:"Dr.",name:"Shinji",surname:"Kurosaka",fullName:"Shinji Kurosaka",slug:"shinji-kurosaka",email:"kurosaka969696@yahoo.co.jp"},{id:"77108",title:"Dr.",name:"Ken-Ichi",surname:"Tabata",fullName:"Ken-Ichi Tabata",slug:"ken-ichi-tabata",email:"ktabata@med.kitasato-u.ac.jp"},{id:"77109",title:"Dr.",name:"Kazumasa",surname:"Matsumoto",fullName:"Kazumasa Matsumoto",slug:"kazumasa-matsumoto",email:"kazumasa@cd5.so-net.ne.jp"},{id:"77110",title:"Dr.",name:"Kazunari",surname:"Yoshida",fullName:"Kazunari Yoshida",slug:"kazunari-yoshida",email:"kyoshida@med.kitasato-u.ac.jp"},{id:"77111",title:"Prof.",name:"Shiro",surname:"Baba",fullName:"Shiro Baba",slug:"shiro-baba",email:"sbaba@med.kitasato-u.ac.jp"}],book:{title:"Emerging Research and Treatments in Renal Cell Carcinoma",slug:"emerging-research-and-treatments-in-renal-cell-carcinoma",productType:{id:"1",title:"Edited Volume"}}},{title:"Signaling Pathways and Biomarkers in Renal Tumors",slug:"signaling-pathways-and-biomarkers-in-renal-tumors",abstract:null,signatures:"Tetsuo Fujita, Masatsugu Iwamura, Kazumasa Matsumoto and Kazunari Yoshida",authors:[{id:"72554",title:"Dr.",name:"Tetsuo",surname:"Fujita",fullName:"Tetsuo Fujita",slug:"tetsuo-fujita",email:"tfujita@cd5.so-net.ne.jp"},{id:"77105",title:"Dr.",name:"Masatsugu",surname:"Iwamura",fullName:"Masatsugu Iwamura",slug:"masatsugu-iwamura",email:"miwamura@med.kitasato-u.ac.jp"},{id:"77109",title:"Dr.",name:"Kazumasa",surname:"Matsumoto",fullName:"Kazumasa Matsumoto",slug:"kazumasa-matsumoto",email:"kazumasa@cd5.so-net.ne.jp"},{id:"77110",title:"Dr.",name:"Kazunari",surname:"Yoshida",fullName:"Kazunari Yoshida",slug:"kazunari-yoshida",email:"kyoshida@med.kitasato-u.ac.jp"}],book:{title:"Renal Tumor",slug:"renal-tumor",productType:{id:"1",title:"Edited Volume"}}},{title:"Dynamics of Cancer-Related Proteins in Patients with Bladder Cancer",slug:"dynamics-of-cancer-related-proteins-in-patients-with-bladder-cancer",abstract:"Bladder cancer (BC) is the second most common malignancy in the urologic field. Preoperative predictive biomarkers of cancer progression and prognosis are imperative for optimizing appropriate treatment for patients with BC. The prediction of patient outcomes before initial treatment would enable physicians to choose better modalities and avoid unnecessary aggressive treatments. In addition, preoperative molecular markers are expected to be a minimally invasive tool for predicting precise prognosis and progression in patients with BC. The proteins secreted from the tumor cells reflect various states of tumors in real time and at given conditions, and those expression patterns are different from normal cell components. Approximately 20–25% of cellular proteins are in extracellular spaces, and these proteins have important roles in invasion, angiogenesis, regulation of cell-to-cell interactions, and metastasis. It has been suggested that tumor-secreting proteins are a promising source for tumor diagnostic biomarkers. Proteomic analysis was utilized to identify the secreted proteins in sera from patients with BC. Several biomarkers associated with BC are reviewed here.",signatures:"Kazumasa Matsumoto, Morihiro Nishi, Hideyasu Tsumura, Ken-ichi Tabata, Tetsuo Fujita and Masatsugu Iwamura",authors:[{id:"72554",title:"Dr.",name:"Tetsuo",surname:"Fujita",fullName:"Tetsuo Fujita",slug:"tetsuo-fujita",email:"tfujita@cd5.so-net.ne.jp"},{id:"77105",title:"Dr.",name:"Masatsugu",surname:"Iwamura",fullName:"Masatsugu Iwamura",slug:"masatsugu-iwamura",email:"miwamura@med.kitasato-u.ac.jp"},{id:"77108",title:"Dr.",name:"Ken-Ichi",surname:"Tabata",fullName:"Ken-Ichi Tabata",slug:"ken-ichi-tabata",email:"ktabata@med.kitasato-u.ac.jp"},{id:"77109",title:"Dr.",name:"Kazumasa",surname:"Matsumoto",fullName:"Kazumasa Matsumoto",slug:"kazumasa-matsumoto",email:"kazumasa@cd5.so-net.ne.jp"},{id:"179613",title:"Dr.",name:"Morihiro",surname:"Nishi",fullName:"Morihiro Nishi",slug:"morihiro-nishi",email:"uromori2000@yahoo.co.jp"},{id:"179614",title:"Dr.",name:"Hideyasu",surname:"Tsumura",fullName:"Hideyasu Tsumura",slug:"hideyasu-tsumura",email:"tsumura@med.kitasato-u.ac.jp"}],book:{title:"Role of Biomarkers in Medicine",slug:"role-of-biomarkers-in-medicine",productType:{id:"1",title:"Edited Volume"}}}],collaborators:[{id:"71071",title:"BSc.",name:"Cristina",surname:"Battaglia",slug:"cristina-battaglia",fullName:"Cristina Battaglia",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Milan",institutionURL:null,country:{name:"Italy"}}},{id:"72170",title:"Prof.",name:"Wilson",surname:"Silva Jr.",slug:"wilson-silva-jr.",fullName:"Wilson Silva Jr.",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Sao Paulo",institutionURL:null,country:{name:"Brazil"}}},{id:"77169",title:"Dr.",name:"Eleonora",surname:"Mangano",slug:"eleonora-mangano",fullName:"Eleonora Mangano",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"National Research Council",institutionURL:null,country:{name:"Romania"}}},{id:"77171",title:"Dr.",name:"Ingrid",surname:"Cifola",slug:"ingrid-cifola",fullName:"Ingrid Cifola",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"77172",title:"BSc.",name:"Valentina",surname:"Tinaglia",slug:"valentina-tinaglia",fullName:"Valentina Tinaglia",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Milan",institutionURL:null,country:{name:"Italy"}}},{id:"77174",title:"Dr.",name:"Fabio",surname:"Frascati",slug:"fabio-frascati",fullName:"Fabio Frascati",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Institute of Biomedical Technologies",institutionURL:null,country:{name:"Italy"}}},{id:"77176",title:"Prof.",name:"Silvio",surname:"Bicciato",slug:"silvio-bicciato",fullName:"Silvio Bicciato",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Modena and Reggio Emilia",institutionURL:null,country:{name:"Italy"}}},{id:"77177",title:"Dr.",name:"Cristina",surname:"Bianchi",slug:"cristina-bianchi",fullName:"Cristina Bianchi",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Milan",institutionURL:null,country:{name:"Italy"}}},{id:"77178",title:"Prof.",name:"Roberto",surname:"Perego",slug:"roberto-perego",fullName:"Roberto Perego",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Milan",institutionURL:null,country:{name:"Italy"}}},{id:"126844",title:"Dr.",name:"Israel",surname:"Gomy",slug:"israel-gomy",fullName:"Israel Gomy",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/126844/images/9892_n.jpg",biography:"Dr. Israel Gomy graduated in Medicine at Pontificia Universidade Católica do Paraná, Curitiba, Brazil. He received his Master´s degree in Biomedical Research at Universidade de São Paulo, Ribeirão Preto, Brazil and his PhD in Oncology at Fundação Antônio Prudente, São Paulo, Brazil. Dr. Gomy is Assistant professor at Faculdades Pequeno Príncipe, Curitiba, Brazil and Assistant physician at Hospital de Clínicas da Universidade Federal do Paraná, Curitiba, Brazil.",institutionString:"Federal University Of Parana",institution:null}]},generic:{page:{slug:"WIS-cost",title:"What Does It Cost?",intro:"
Open Access publishing helps remove barriers and allows everyone to access valuable information, but article and book processing charges also exclude talented authors and editors who can’t afford to pay. The goal of our Women in Science program is to charge zero APCs, so none of our authors or editors have to pay for publication.
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I am also a member of the team in charge for the supervision of Ph.D. students in the fields of development of silicon based planar waveguide sensor devices, study of inelastic electron tunnelling in planar tunnelling nanostructures for sensing applications and development of organotellurium(IV) compounds for semiconductor applications. I am a specialist in data analysis techniques and nanosurface structure. 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After obtaining a Master's degree in Mechanical Engineering, he continued his PhD studies in Robotics at the Vienna University of Technology. Here he worked as a robotic researcher with the university's Intelligent Manufacturing Systems Group as well as a guest researcher at various European universities, including the Swiss Federal Institute of Technology Lausanne (EPFL). During this time he published more than 20 scientific papers, gave presentations, served as a reviewer for major robotic journals and conferences and most importantly he co-founded and built the International Journal of Advanced Robotic Systems- world's first Open Access journal in the field of robotics. Starting this journal was a pivotal point in his career, since it was a pathway to founding IntechOpen - Open Access publisher focused on addressing academic researchers needs. Alex is a personification of IntechOpen key values being trusted, open and entrepreneurial. 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He is the member of many Pharmaceutical Associations and acts as a reviewer of scientific journals and European projects under different research areas such as: drug delivery systems, nanotechnology and pharmaceutical biotechnology. Dr. Sezer is the author of many scientific publications in peer-reviewed journals and poster communications. Focus of his research activity is drug delivery, physico-chemical characterization and biological evaluation of biopolymers micro and nanoparticles as modified drug delivery system, and colloidal drug carriers (liposomes, nanoparticles etc.).",institutionString:null,institution:{name:"Marmara University",country:{name:"Turkey"}}},{id:"61051",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"100762",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"St David's Medical Center",country:{name:"United States of America"}}},{id:"107416",title:"Dr.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Texas Cardiac Arrhythmia",country:{name:"United States of America"}}},{id:"64434",title:"Dr.",name:"Angkoon",middleName:null,surname:"Phinyomark",slug:"angkoon-phinyomark",fullName:"Angkoon Phinyomark",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/64434/images/2619_n.jpg",biography:"My name is Angkoon Phinyomark. I received a B.Eng. degree in Computer Engineering with First Class Honors in 2008 from Prince of Songkla University, Songkhla, Thailand, where I received a Ph.D. degree in Electrical Engineering. My research interests are primarily in the area of biomedical signal processing and classification notably EMG (electromyography signal), EOG (electrooculography signal), and EEG (electroencephalography signal), image analysis notably breast cancer analysis and optical coherence tomography, and rehabilitation engineering. I became a student member of IEEE in 2008. During October 2011-March 2012, I had worked at School of Computer Science and Electronic Engineering, University of Essex, Colchester, Essex, United Kingdom. In addition, during a B.Eng. 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