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Barely three months into the new year and we are happy to announce a monumental milestone reached - 150 million downloads.
\n\nThis achievement solidifies IntechOpen’s place as a pioneer in Open Access publishing and the home to some of the most relevant scientific research available through Open Access.
\n\nWe are so proud to have worked with so many bright minds throughout the years who have helped us spread knowledge through the power of Open Access and we look forward to continuing to support some of the greatest thinkers of our day.
\n\nThank you for making IntechOpen your place of learning, sharing, and discovery, and here’s to 150 million more!
\n\n\n\n\n'}],latestNews:[{slug:"intechopen-partners-with-ehs-for-digital-advertising-representation-20210416",title:"IntechOpen Partners with EHS for Digital Advertising Representation"},{slug:"intechopen-signs-new-contract-with-cepiec-china-for-distribution-of-open-access-books-20210319",title:"IntechOpen Signs New Contract with CEPIEC, China for Distribution of Open Access Books"},{slug:"150-million-downloads-and-counting-20210316",title:"150 Million Downloads and Counting"},{slug:"intechopen-secures-indefinite-content-preservation-with-clockss-20210309",title:"IntechOpen Secures Indefinite Content Preservation with CLOCKSS"},{slug:"intechopen-expands-to-all-global-amazon-channels-with-full-catalog-of-books-20210308",title:"IntechOpen Expands to All Global Amazon Channels with Full Catalog of Books"},{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"}]},book:{item:{type:"book",id:"6865",leadTitle:null,fullTitle:"Becoming Human with Humanoid - From Physical Interaction to Social Intelligence",title:"Becoming Human with Humanoid",subtitle:"From Physical Interaction to Social Intelligence",reviewType:"peer-reviewed",abstract:"Nowadays, our expectations of robots have been significantly increases. 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\r\n\tIn textbooks and manuals, diplomacy is often defined as "the science of foreign relations" and "the art of negotiation." This certainly makes a lot of sense. A balanced analysis of the global situation and the correct consideration of the balance of power in the international arena are essential for the development of truly scientific, deeply grounded recommendations in the field of foreign policy. It is necessary to carefully study historical trends, fully take into account the different directions and trends in international relations, to be able to seek and attract allies to desired side, to achieve the isolation of the most aggressive and hostile circles. One can really expect success only if diplomacy acts in principle and, at the same time, pragmatically and flexibly, avoids dogmatism and sectarianism, and is not afraid of compromises that ultimately benefit national interests. Hence, the importance of mastering a number of sciences: history of individual countries and international relations, international law, complex sciences related to the study of the world economy and the economies of individual countries, comparative political science and law, philosophy, psychology, and etc. In short, diplomacy should rely on the laws of social life and consider the findings of the relevant sciences.
\r\n\r\n\tThis book intends to provide the reader with a comprehensive understanding of the real essence of public diplomacy. Public diplomacy and related concepts such as ""strategic communication"" and ""national branding"" are a part of increasingly common public administration practices. It also represents an area of research with significant growth potential. The nation states have in various contexts recognized the need to communicate with foreign communities and to develop networks through various forms of interaction, including international communication, exchange programmes and cultural diplomacy. As a result, public diplomacy has become an effective tool of purposeful communication with the foreign public to promote short-term political goals, to develop long-term relations, and to address pressing issues of transnational politics. Nevertheless, there are big problems that lie behind the popularization of modern public diplomacy initiatives which will also be discussed in the book.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"ca82945156946b18f4e457ce91ac6643",bookSignature:"Dr. Galina V. Timofeeva and Ms. Alexandra Baranova",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8535.jpg",keywords:"Diplomatic Service, Cultural Diplomacy, Negotiation, Tools, Mechanisms, Actors, Official Diplomacy, Digital Diplomacy, Conflict Resolution, Intergovernmental Organizations, Cooperation",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 13th 2019",dateEndSecondStepPublish:"March 27th 2020",dateEndThirdStepPublish:"May 26th 2020",dateEndFourthStepPublish:"August 14th 2020",dateEndFifthStepPublish:"October 13th 2020",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"311522",title:"Dr.",name:"Galina",middleName:"V.",surname:"Timofeeva",slug:"galina-timofeeva",fullName:"Galina Timofeeva",profilePictureURL:"https://mts.intechopen.com/storage/users/311522/images/system/311522.jpg",biography:"Galina V. Timofeeva, PhD is a Professor at the Department of Economics and Public Diplomacy at the Institute of Public Service and Management of the Russian Presidential Academy of National Economy and Public Administration (RANEPA). Professor Timofeeva is an expert of the Higher Attestation Commission of the Ministry of Education and Science of the Russian Federation. She is also an expert and a scientific editor of the strategy of socio-economic development of the Republic of Abkhazia-2025, as well as the specialist at the Russian Foundation for Basic Research.",institutionString:"Russian Presidential Academy of National Economy and Public Administration",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Russian Presidential Academy of National Economy and Public Administration",institutionURL:null,country:{name:"Russia"}}}],coeditorOne:{id:"312195",title:"Ms.",name:"Alexandra",middleName:null,surname:"Baranova",slug:"alexandra-baranova",fullName:"Alexandra Baranova",profilePictureURL:"https://mts.intechopen.com/storage/users/no_image.jpg",biography:"Dr. Alexandra Baranova is a lecturer at the Russian Academy of National Economy and Public Administration. Her scientific interests include linguistic tools of public diplomacy, as well as the role of mass media in diplomatic processes.",institutionString:"Russian Presidential Academy of National Economy and Public Administration",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Russian Presidential Academy of National Economy and Public Administration",institutionURL:null,country:{name:"Russia"}}},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"23",title:"Social Sciences",slug:"social-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"247041",firstName:"Dolores",lastName:"Kuzelj",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/247041/images/7108_n.jpg",email:"dolores@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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The remaining 80–85% buried at higher depths can possibly be recovered with underground-type mining employing in situ techniques. The Great Canadian Oil Sands, now known as Suncor Energy Inc., developed an open-pit mine, a hot water extraction plant and an upgrading complex in 1967. Their operation was followed in 1979 by Syncrude Canada Ltd.’s open-pit mine at Mildred Lake. Currently, Suncor Energy Inc., Syncrude Canada Ltd., Albian Sands Energy Inc., and Canadian Natural Resources Ltd. employ surface mining [1, 2, 3].
\nA typical surface mining operation, as shown in Figure 1, includes the following steps [1, 2]:
Removal of overburden using shovels and trucks
Mining oil-sand with hydraulic or electric shovels
Transport of oil-sand ore from the mine face to the crushers with trucks
Crushing of large oil-sand lumps into smaller parts
Gravity separation of bitumen froth
Diluted froth treatment to separate water and solids
Supplemental solvent recovery from tailings
Dewatering and concentrating the tailings
Major steps for bitumen recovery in surface mining operation [
Among the above mentioned steps,
Oil-sand lump ablation or size reduction
Liberation of bitumen from sand grains
Aeration of bitumen droplets
Oil-sand ore carried from the mine with conveyors was originally conditioned with rotating drums or tumblers [1]. Investigations into the possibility of replacing conveyors and tumblers with pipelines began at the Syncrude Research Center in the early 1980s [3, 4]. The idea was based on the examination of the pipelines transporting tailings from the separation vessels to the tailing ponds. Subsequently, a large-scale prototype of an oil-sand hydrotransport system known as the extraction auxiliary production system was commissioned in 1993. It became a successful commercial unit that could digest up to 5000 ton of oil-sand per hour. Since then, hydrotransport pipelines are being used in other commercial extraction plants to simultaneously transport and condition oil-sand ore. Roughly 60, 000 ton of oil-sand flowing as slurry of about 60 wt% solids is digested per hour to produce ½ million barrels of bitumen per day at present [3, 5]. Commercial applications of hydrotransport pipelines enabled the conditioning process to be carried out at considerably lower temperatures [6]. Syncrude Aurora now operates their 5 km hydrotransport line at 35–40°C [7].
\nThe use of hydrotransport pipelines improved the oil-sand conditioning at lower temperatures [1]. As the efficiency of the conditioning process significantly influences the final recovery of the bitumen, achieving an efficient method for the conditioning has always been the target among oil-sand producers [1, 3]. In addition, reducing the production cost and greenhouse gas emissions has also been ongoing targets in the industry [1]. Continued process improvements have led to more economic bitumen production process and reduced environmental footprint [8]. Presently, oil-sand companies aim to eliminate the use of expensive trucks to transport the ore to the slurry plant by conditioning the oil-sand slurry at the mine face [2]. This kind of onsite conditioning would demand a consequent reduction of pipeline length, which would potentially cause incomplete conditioning and could especially affect lump ablation [2]. In order to resolve the problem, an accelerated conditioning process would be required. Before implementing any significant changes in the oil-sand conditioning, a better understanding on the fundamentals of OSLA must be developed.
\nAs the first step of conditioning, the crushed and screened oil-sand lumps (size range, 50–150 mm) are ablated or digested inside the hydrotransport pipeline [9]. The ablation occurs due to the dual effects of heat transfer and mechanical energy [6]. Generally, bitumen acts as a glue to hold the matrix of sand grains together. It should be mentioned that the viscosity of bitumen is a strong function of temperature. As a result, the viscosity of the bitumen on the surface layer of the lump reduces considerably as an oil-sand lump is exposed to the hot slurry medium. The softened surface layer is then sheared away due to the shearing inside the hydrotransport pipeline, and, thereby, a new lump surface is exposed to the hot medium. The new surface undergoes the same mechanism. This process repeats itself to the point that the entire lump is ablated. The heat transfer from the slurry and the contacts of a lump to neighboring lumps as well as the pipe wall control the rate of ablation [10]. The parameters that mostly affect OSLA can be identified as temperature and composition of the slurry, size and temperature of the initial lump, and mechanical shear imparted to the lump [1, 11].
\nThe current chapter aims to contribute to the better understanding of the lump ablation process. It would assist to identify the important parameters that affect the OSLA and to recognize the way in which each one of these parameters influences the ablation process. The oil-sand conditioning process can be improved by changing one or more of these factors to achieve accelerated ablation and conditioning as required. Previous studies of oil-sand lump ablation are also described, and important areas not covered by those investigations are identified. In addition, some background theory needed in the development of improved ablation models is introduced.
\nAs mentioned previously, the ablation of oil-sand lumps is the result of two important phenomena: heat transfer and shear forces [1]. Any factor that affects these phenomena would have an effect on the ablation process. The most important of this kind of parameters, viz., slurry temperature, initial lump size, pipeline diameter, and pipeline velocity or shear stress, are discussed here.
\nSince the commissioning of the first commercial oil-sand mining and bitumen extraction operation, attempts to reduce bitumen production costs and environmental impacts have driven process improvements and flowsheet changes [6]. One way to reduce both simultaneously is to operate the process at a lower slurry temperature. Slurry temperature is effectively the most important parameter in the extraction of bitumen from Athabasca oil-sand, as it affects all three steps of oil-sand conditioning, i.e., oil-sand lump ablation, bitumen liberation, and air attachment.
\nBitumen, because of its high viscosity, holds the mixture of sand grains and fine minerals together within an oil-sand lump [6]. The viscosity of bitumen decreases sharply with increasing temperature as shown in Figure 2. Since the viscosity is above 105 mPa.s at room temperature (T = 20°C), bitumen looks like a solid, and it is essentially impossible to separate bitumen from the sand grains at this temperature. When the temperature increases to 50°C, bitumen viscosity reduces by more than one order of magnitude, i.e., to the order of 103 mPa.s. The separation of bitumen from sand grains occurs relatively quickly at such temperature. Lower viscosity of bitumen must be attained in order to reduce the lump size and liberate bitumen from sand grains efficiently [6, 12]. It should be mentioned that froth quality and bitumen recovery are also dependent on slurry temperature as the temperature influences the air bubble-bitumen attachment. Although oil-sand producers ultimately wish to operate hydrotransport pipelines at low temperatures due to the reduced operating costs and environmental impacts, they are well aware that a balance between bitumen recovery and temperature reduction must be attained. At this point, operating temperatures between 40 and 55°C are common in the industry [6].
\nViscosity of Athabasca bitumen as a function of temperature [
The heat transfer to an oil-sand lump is an important factor in ablation process [13]. The thickness of the layer softened and ablated away is equal in essence for all lump sizes under comparable thermal conditions. Therefore, the fraction of lump mass that is removed decreases as the lump size increases. In other words, the time necessary for complete digestion of a lump increases with the initial lump size [1].
\nPipeline diameter is a key parameter in the ablation of an oil-sand lump. For a specific slurry flow rate, more energy is dissipated in a pipe having smaller diameter, and this leads to the higher interparticle shear stresses [1]. The relationship between energy dissipation and pipe diameter can be expressed as follows [14]:
\nwhere,
\n\n\n
According to Eq. (1), energy dissipated in a pipe inversely varies with the diameter of the pipe. Consequently, higher energy dissipation, i.e., higher ablation rate, is expected in smaller pipelines. On the other hand, the residence time of an oil-sand lump inside a smaller pipe will be shorter as the bulk velocity is higher in the pipe for a constant slurry flow rate. A shorter residence time is likely to result in a lower ablation rate [1]. A balance must be sought between the residence time and the energy dissipation in order to achieve an acceptable ablation rate. That is, the pipeline diameter should be optimized for a specific flow condition.
\nAn oil-sand lump moves at a different velocity than the surrounding slurry and contacts with the pipe wall as well as other lumps present in the slurry. The difference in the velocities results in a shear stress on the lump surface [1]. In a pipeline, the shear force acting on the lump surface is expected to increase with increasing mixture velocity and concentration. Higher slurry concentrations promote particle-particle interactions and particle-wall interactions [1, 3]. Thus, all steps of the oil-sand slurry conditioning process depend on the slurry velocity in a hydrotransport pipeline [5]. However, more research has been conducted to study the effect of shear exposure on bitumen liberation and bitumen aeration than lump ablation. Clearly, this area demands further investigations.
\nImportant examples of previous experimental and modeling studies on lump ablation are briefly discussed in this section. The parameters considered in each study are summarized, and the parameters that need further investigations are identified.
\nTraynis [15] studied the grinding or crushing of coal particles using a wheel test stand (WTS). It was experimentally demonstrated that the pressure losses for slurry in a WTS agree quite well with that in a horizontal pipeline. This agreement was a result of the similarities in energy dissipation mechanisms of moving solid particles in both systems. The mechanism of energy dissipation was found to determine the process of the particle crushing.
\nMost of the tests reported in [15] were completed using a WTS made of a 200-mm diameter pipe. Three runs were repeated with another WTS made of 300-mm diameter pipe to investigate the effect of pipe size on particle crushing or grinding. Pipes were polished using abrasive materials like quartz to ensure that the pipe wall was smooth when the experiments were started. The apparatus was filled up to 1/3 of the total volume with a mixture of water and coal. For each run using the smaller WTS, 10–40 kg of coal was loaded. Coal particles from two different hydraulic mines were used for the experiments. At certain time intervals, the degree of size reduction of the coal particles was determined by measuring the particle size distribution of the remainder of the particles. To reconfirm that the WTS system was representative of the horizontal pipeline, a number of experiments were replicated by circulating slurry in 4 and 1.3-km long pipelines. The effects of slurry velocity and concentration, pipe diameter, coal particle size, existence of abrasive rocks, pipe length, and mechanical properties (strength and hardness) of the coal particles on the size reduction of the coal particles were investigated. The outcomes of the experimental investigation can be summarized as follows:
The results obtained using short pipelines (∼10 km) agreed with those of the wheel test stand experiments. However, transporting the coal particles for a long distance (>20 km) resulted in faster crushing. This is probably because the mixture passed through the feed pump many times. It caused more rapid size reduction of the coal particles. The effect was more evident when the initial coal particle size was large.
The slurry velocity was changed from 1.8 to 6 m/s for experiments with different coal types. In all cases, velocity had an insignificant effect on the crushing of coal particles.
Slurry concentrations were varied from 1:16 to 1:2 (mass of solid, mass of liquid). These experimental runs showed that size reduction of the coal particles was independent of slurry concentration.
The pipe size of the wheel test stand did not affect the extent of size reduction of the coal particles.
For coal particles having initial diameters in the ranges of 3–6 or 50–100 mm, the degree of size reduction was only affected by the initial particle size. For particles smaller than 3 mm, increasing the initial particle size resulted in more visible increase in the intensity of crushing.
The existence of abrasive rocks, which were 50–100 mm in diameter initially but were crushed to the 3–6 mm size range in the slurry, caused more rapid size reduction of particles. Considerable crushing was observed within the first 15 km.
The crushing rate was higher in the first few kilometers of the pipe, and it decreased as coal particles moved along the pipeline. This must be because of the fact that shear stress decreases as particle size decreases, which would be expected when the particle slip velocity decreases. Rounding of the edges of the particles within the first kilometers of the pipe might be another reason for reduction of the crushing rate with pipeline length.
Experiments using coal particles with initial size in the range of 6–13 mm showed that as the strength factor of the coal particles increased, the crushing rate decreased. Strength factor is an indicator of the grindability of the coal particles.
One of the strengths of this study is that it introduces a new experimental method for studying the mass loss of solid particles. In addition, this is the only study done on the effect of slurry velocity and concentration on the particle mass loss in slurry pipelines. However, one cannot directly apply the results of this research to oil-sand hydrotransport pipeline. This is because the nature of coal particles is very different from oil-sand lumps. Coal is a brittle organic sedimentary rock that contains varying amounts of carbon, hydrogen, nitrogen, oxygen, and sulfur [16]. On the other hand, oil-sand contains bitumen, sand grains, clays, and small amount of water, and the viscosity of bitumen highly varies with temperature [1]. As coal is brittle, coal particles tend to break down into smaller particles when they are exposed to the shear forces. However, mass loss from oil-sand lumps occurs by gradual mass removal from the surface of the lump. The amount of mass loss from an oil-sand lump depends on many parameters, although temperature seems to be the most important factor. Thus, one cannot study oil-sand lump ablation without considering the slurry temperature. Additionally, because the nature of the two materials is different, the effect of slurry concentration and velocity on their mass loss can be expected to be different.
\nLaw et al. [17] examined the ablation of frozen mixtures of water and paraffin wax (octadecane) with solid particles such as kaolinite clay, titanium oxide, aluminum powder, and sand. Because the ablation of oil-sand samples was complex, they chose to study the ablation of less complex materials. This investigation was conducted with the purpose of obtaining information from a well-controlled system and applying it for designing the rotating drums, which were used for oil-sand lump ablation at that time. A turbulent axisymmetric water jet, whose velocity varied between 1.7 and 2.8 m/s, was used. The temperature of the jet was changed from 32 to 60°C depending on the material being tested. The water temperature was chosen based on the sample’s melting point, which was 26–29°C for octadecane. Cylindrical samples (L = 150 mm, d = 11 mm) were manufactured and immediately frozen in liquid nitrogen. The samples were then placed in front of the jet using a sliding platform. The sliding platform was moved up and down by using a stepping motor. Before the start of the experimental run, the front of the sample was placed in-line with a certain point called the melt front pointer. During an experimental run, the sample was never moved from this point. Instead, the sliding platform was lowered at a speed equal to the ablation rate of the frozen sample. The downward movement of the sliding platform against time was recorded and plotted. The slope of this line, for each set of the experiments, was considered to be the ablation rate. It was observed that for each operating condition, the slope of the plotted line remained constant with time. The results of this study can be summarized as follows:
For all samples, an increase in the jet temperature increased the ablation rate. For instance, ablation rate of lumps made from octadecane and 60 (vol%) sand at V = 2.8 m/s and T = 60°C was equal to 4.4 × 10−3 m/s, whereas it was equal to 3 × 10−3 m/s at T = 50°C.
Increasing the jet velocity from 1.7 to 2.8 m/s increased the ablation rate equivalent to that of raising the jet temperature by approximately 10°C (from 50 to 60°C). This is because surface shear stress on the sample is proportional to V2.
Addition of solid particles to the samples affected the ablation rate in a complex way. The effect depended on the type of the solid particles and the lump material because thermal conductivity of the solid particles was different, so the heat transfer coefficient within the sample differed depending on the solid particles. In the case of octadecane-kaolinite samples, at a certain jet velocity and temperature (V = 2.06 m/s, T = 50 and 60°C), ablation rate gradually increased for solid content up to 17 vol%, and, for solids content beyond 17%, the ablation rate increased significantly. The reasons for this observation were mentioned to be the increase of the heat transfer area due to the roughening of the melting surface and the ablation of the sample as clusters instead of layers at high solid contents. That is, ablation can also depend on the type and components of the oil-sand ore.
Although this experimental study could provide a good indication of the way different parameters influence ablation, the study had some limitations such as:
Viscosities of the samples were significantly different from that of bitumen.
Sample was stationary and was exposed to water only from one face.
Ablation with only water was investigated.
The number of experimental runs using samples manufactured with sand particles was very limited.
More investigations need to be conducted on actual OSLA using a system that better represents the actual conditioning medium. These experiments are necessary to develop a predictive model applicable for all operating conditions.
\nIn 1996, an experimental study on the ablation of actual oil-sand lumps was conducted at the Saskatchewan Research Council (SRC) Pipe Flow Technology Centre™ [10]. Lump ablation at various operating conditions were investigated by loading a certain amount of lumps to a 264 mm pipe loop using a feeder close to the pump discharge. At certain time intervals, lumps were trapped with a basket before discharging into the storage tank. The trapped lumps were weighed and put back into the loop. The SRC experiments showed the following results:
For all types of the oil-sand lumps, the time or pipeline length required to reach a certain ablation rate was strongly dependent on the slurry temperature. As shown in Figure 3, the time required for the complete ablation at T = 50°C was one third of that at T = 30 and 18°C for soft lumps. It is worth noting that the effect of temperature on the ablation rate was found to be qualitatively similar for various oil-sand ores [1, 10].
The ablation rate was faster for lumps with lower initial temperature at higher slurry temperatures (T = 30 and 50°C)
SRC Experimental results showing the effect of slurry temperature on the ablation time of soft lumps [
This experimental study is very valuable, as it is the first available research on the ablation of actual oil-sand lumps. However, the research did not include the effects of important parameters such as slurry velocity and concentration on ablation.
\nMasliyah ablation model (model 1) was developed for the ablation of oil-sand lumps based on the fact that crushed oil-sand lumps and sand particles form a moving layer at the bottom of the pipe, while the fine solids—water blend known as the carrier fluid, exist within the whole pipe cross section [1, 6, 10]. The height of the bottom layer reduces with axial position along the pipeline when lump size reduces. It was assumed that the heated surface layer of the lump peeled off because of the shear stress inside the pipe. This process was presumed to repeat up to the point when 95% of the lump mass would be removed. The SRC two-layer model was used to estimate the velocities of top and bottom layers of the flow. An average value of the shear stress on the lumps was calculated using the slurry viscosity and the axial flow velocity [1, 6]. The model was validated with the data available in [10]. The predicted effects of mixture velocity, pipeline diameter, slurry temperature, initial lump size, slurry density, and pipeline length are discussed as follows [1]:
Raising the slurry velocity does not cause any significant enhancement in the oil-sand lump ablation rate. As shown in Figure 4, the beneficial effects of increasing velocity are offset by the reduced residence time of the lump.
The rate of lump digestion reduces with the increasing pipe diameter at T = 25°C (Figure 5A). As a result, longer pipelines are needed for complete ablation. At T = 50°C, however, the effect of pipe diameter is not very significant (Figure 5B). This is probably because heat transfer is the dominant factor in the ablation of an oil-sand lump. At a higher temperature, the viscosity of the bitumen and the surface shear stress required for consequent removal of the soft surface layer reduce significantly.
Increasing the slurry density increases the ablation rate at a fixed temperature (Figure 6). This is because an increment in slurry density is caused by a reduced water flow rate, i.e., an increased residence time. For the same reason, ablation rate reduces with decreasing slurry density.
Smaller oil-sand lumps ablate more rapidly (Figure 7). A given mass of oil-sand ore in the form of smaller lumps is digested much faster than the same mass of ore in the form of larger lumps due to the larger surface area of the former.
Effect of mixture bulk velocity on the oil-sand lump ablation (T = 50°C; T0L = 5°C; d = 20 mm) [
Effect of pipe diameter on the ablation of oil sand lumps (T0L = 5°C; V = 3.8 m/s; ρm = 1550 kg/m3; d = 20 mm): (A) T = 25°C; (B) T = 50°C [
Effect of slurry density on the ablation of oil sand lumps (T0L = 0°C; D = 710 mm; d = 100 mm and T = 40°C) [
Effect of initial lump size on the ablation of oil-sand lumps (T0L = 0°C; D = 710 mm; ρm = 1548 kg/m3 and T = 40°C) [
Although model 1 is one of the pioneer models that can be used for industrial-scale ablation of oil-sand lumps, it has a number of limitations. Some of the limitations are identified as follows:
Only one set of experimental data was available for validating this model. The data was also limited to a certain pipeline size and a set of velocities.
A part of the model, namely, the method of estimating surface shear force on the lumps is yet to be verified.
The version of the SRC two-layer model used for the modeling is out-of-date. The SRC model has been improved lately. However, the improvements were never integrated into model 1.
According to model 1, the bulk velocity was used to calculate the shear stress acting on the oil-sand lumps. However, the velocity of the lumps in slurry is about 90% of the bulk velocity. This means, the relative velocity causing the shear stress on the lump is likely to be only 10% of the velocity. Therefore, the shear stress used in Model 1 might be overestimated.
Eskin et al. model (Model 2) was developed for the ablation of a spherical oil-sand lump using a hypothesis similar to that of Masliyah model [13]. The following assumptions were used for the purpose:
The effects of shear stresses and heating were integrated with respect to a surface critical temperature. The critical temperature remained constant during the ablation and was related to the minimum adhesive strength of the bitumen. This model-specific temperature was determined using the experimental results available in [17].
The lump was considered to retain its spherical shape during ablation.
Based on the assumptions, the complex phenomena were simplified as a one-dimensional heat conduction problem for a shrinking sphere. The critical temperature was used as an input to the applied convection boundary condition. A correlation between the reduction of sphere size and the critical temperature was found by simplifying the boundary condition-based equations. The heat conduction equations were also included in the model. The model was applied to study the effect of lump size and initial temperature on OSLA.
\nAlthough the fundamental concepts used for model 2 agree with general hypothesis of how individual oil-sand lumps ablate, the way of integrating shear stress to a critical temperature is debatable. Moreover, the effects of slurry velocity and slurry concentration on ablation cannot be investigated with the model. Most importantly, the model was never validated against any experimental data.
\nPazouki [18] applied an innovative method by using strain gauge technology for online tracking of the mass loss of the anchored oil-sand lumps. Four small strain gauges looped in a full-bridge circuit were used for the measurements. The new method also allowed measuring the drag force on ablating and non-ablating objects. The accuracy of the drag force measuring technique was evaluated by comparing the measured drag force with the calculated drag force on the number of smooth spheres in water.
\nAs part of the experiment, an idealized oil-sand lump was anchored in a basket at the height of 40DL, where DL is the diameter of the cylindrical lump. Artificially manufactured oil-sand lumps were used for the experiments. Slurries (C = 0.15 and 0.30) were prepared by mixing pre-weighed industrial quartz (d50 = 0.190 mm) with water. The flow temperature was adjusted using a double-pipe heat exchanger located in the vertical section of the pipeline loop. DASYlab 10.0 software was used to the readings of strain gauges, temperature, and flow meter.
\nIn addition to experimentation, Pazouki [18] also developed a new modeling approach. The overall outcomes of this study can be summarized as follows:
The online measurement method and the experimental apparatus built at SRC provide the opportunity to test OSLA at many different operating conditions. The strain gauge measurement method also enables measuring the drag force on the ablating oil-sand lump.
The data obtained using the artificially produced oil-sand lumps were repeatable.
The OSLA was enhanced significantly with the increasing flow temperature. Heat transfer played a more important role for ablation in the slurry where surface shear stresses can be expected to be lower.
The slurry velocity was found to affect OSLA appreciably. The ablation rate increased with Vn, where n = 2–4.7. The value of n was a function of temperature.
Ablation in water occurred at a slower rate than that in the slurry. However, an increase of slurry concentration from 15 to 30% at T = 30°C reduced the ablation rate. This reduction was most likely related to the turbulence modulation in slurries that could affect both shear force and heat transfer.
For the range of concentrations used for the study, the slurry concentration did not have a significant influence on the ablation of oil-sand lumps.
The drag force acting on a lump depended on the slurry concentration.
The equivalent fluid model was found to be most appropriate for simulating the drag force. In this model, the slurry is treated like a single-phase fluid with density and viscosity related to the solid concentration.
The proposed model demonstrated the ablation rate to be a primary function of surface shear force and temperature. In the model, the effect of temperature was implemented as the change in the bitumen viscosity.
The model was validated with respect to the experimental measurements. An example of the validation results is presented in Figure 8. In course of the validation, it was found to better predict the ablation rate than other existing models.
Comparison of measured and predicted ablation rate for slurry (C = 0.30) at T = 45°C [
Even though the study advanced both experimentation and modeling of OSLA, it suffers from the similar limitations of previous studies. It neither clarifies the procedure to apply the experimental findings to the actual hydrotransport pipelines nor verifies the model with industrial-scale data.
\nIn order to estimate the ablation rate of the oil-sand lumps inside the hydrotransport pipeline, the shear stress acting on the lumps and the temperature profile of the lump at different times must be determined. The most relevant models for the estimation are follows:
SRC two-layer model
Shear stress decay law
The benefits and drawbacks of each model are discussed in the subsequent sections.
\nRecall that an early version of SRC model was used to estimate the shear stress acting on the oil-sand lump(s) in model 1. If one intends to use a similar approach, it would be advisable to use a more recent version of the model. The theory behind the development of the SRC two-layer model is explained in this section. Also, the validity of this approach for calculating the shear stress acting on a lump is discussed.
\nIn a slurry pipeline similar to the hydrotransport pipeline, fine particles (particles <0.074 mm) are considered to augment the viscosity and density of the suspending liquid, i.e., the carrier fluid. The coarse particles that are suspended by fluid turbulence are assumed to be at a constant volume fraction throughout the flow domain. The other part of the coarse particles, that is, the fraction not effectively suspended by fluid turbulence, is supposed to transmit the immersed weight to the pipe wall. These particles are found in the lower layer and contribute Coulombic or sliding bed friction [11]. The continuous concentration profile of the coarse particles was simplified to a step-change, i.e. two layers for the purpose of writing force balance equations. The velocity within each layer was assumed to be constant. Figure 9 shows the idealized concentration and velocity distributions.
\nIdealized concentration and velocity distributions used in the SRC two-layer model [
The SRC two-layer model was developed using mass and force balances for the two layers of the slurry. The force balance produces an equation for the axial pressure gradient in horizontal slurry as a function of friction losses in top layer, bottom layer, and the interface between the layers [19].
\nTo estimate the ablation rate of an oil-sand lump, the actual shear stress on the lump needs to be estimated. If one assumes an oil-sand lump is located at the interface between the two layers, the surface shear stress acting on this lump can be assumed to be equal to the shear stress at the interface. The shear stress at the interface is calculated using the following correlation [11]:
\nwhere ρ1 denotes the slurry density in the upper layer and f12 is the interfacial friction factor that can be estimated from a modified Colebrook friction factor equation:
\nwhere Y is the 0 for d/D < 0.0015 and Y is calculated using the following equation when 0.0015 < d/D < 0.15:
\nEquation (4) has been formulated based on the data taken at Archimedes number, Ar < 3 × 105.
\nIt is inferred from Eq. (2) that the shear stress acting on a lump is proportional to (V1 − V2)2. Calculating the velocity of the layers using the SRC two-layer model shows that V2 is substantially small compared to V1 and (V1 − V2) is approximately equal to the slurry bulk velocity (V). On the other hand, other research conducted at the Saskatchewan Research Council showed that the velocity of a large particle in horizontal slurry flow was about 0.9 V. That is, the shear stress on the oil-sand lump would be proportional to (0.1 V)2, which is considerably smaller than (V1 − V2)2. In other words, the shear stress calculated using Eq. (2) might overestimate the shear stress acting on an individual lump.
\nIn order to estimate the effects of slurry velocity and concentration on OSLA, a simplified approach can be taken instead of using complex two-layer model. The following assumptions are necessary to apply the method:
The oil-sand lump is stationary compared to the slurry flow in the hydrotransport pipe.
Slurry flow has reached steady state.
Slurry density is constant throughout the pipe.
Based on the assumptions, the local shear stress where the solid particle is located in the hydrotransport pipeline can be estimated using the shear stress decay law [11]:
\nwhere s is the distance from pipe axis (m), τrz is the shear stress at y (Pa), τw is the pipe wall shear stress (Pa), and D is the pipe diameter (m).
\nFor a known value of the wall shear stress, the shear stress at any radial position of the pipe can be calculated using Eq. (5). However, calculating the wall shear stress for a hydrotransport pipeline is complex as wall shear stress and flow density are not constant around the pipe.
\nFlow is not uniform throughout the cross section in a hydrotransport pipeline at all. Significant concentration and velocity gradients can exist, particularly, if operating velocity is just higher than the deposition velocity (Vc) [10]. However, the concentration profile was found to be nearly uniform for highly concentrated settling slurries at velocities significantly higher than Vc, and, for these slurries, Coulombic friction was also found to be negligible relative to kinematic friction [19]. Moreover, Coulombic friction is typically negligible as long as the particle diameter is not too large (d50 ≤ 0.3 mm), and the mixture velocity is high (say, V > 2Vc) [11]. It is therefore worthwhile to consider the so-called kinematic friction loss component of the SRC pipe flow model [Eqs. (6) and (7)] to calculate the wall shear stress for such systems [10, 11]. Using this model, the kinematic friction loss component is determined so that it accounts for the friction associated with the flow of the carrier fluid, the friction related to particle collisions and the tempering effect of near-wall lift. If the Coulombic friction can be assumed to be negligible, then only the kinematic friction is important, and the τw can be calculated using the following equations [10, 11, 20]:
\nfor d + ≤ 21: \n
for d + ≥ 21:\n
The estimation of kinematic friction provides a tool for realistic assessment of the effects of slurry velocity and concentration on the local shear stress. To demonstrate the application, a model system is considered here. The system properties are chosen on an arbitrary basis and outlined in Table 1.
\nTerm | \nValue | \n
---|---|
D (mm) | \n103 | \n
s (mm) | \n20 | \n
ρf (kg/m3) | \n1000 | \n
μf (Pa.s) | \n0.001 | \n
d50 (mm) | \n0.120 | \n
ρs (kg/m3) | \n2650 | \n
Input parameters for estimating shear stress inside a pipe.
The local shear stress is shown in Figure 10 as a function of mixture velocity for two different solid concentrations. The graph indicates that, for a solid particle placed 20 mm from the center of a 103 mm pipe, the surface shear stress on the particle increases substantially at higher mixture velocities. It should be noted that the graph indicates the effect of velocity and concentration on shear stress qualitatively. The results do not represent the actual shear stress on the oil-sand lumps. This example shows the application of shear stress decay law for a simplified case, where the solid particle is stationary. However, in the actual hydrotransport pipelines, oil-sand lumps move along the pipe axis. In order to estimate the shear stress acting on the lump, the slip velocity of the lump must be considered.
\nPipeline local shear stress at different slurry velocities and concentrations.
A limited number of studies on the ablation of large particles exist in open literature. Among these studies, only a few looked at the effect of velocity and concentration on the ablation. Slurry concentration and velocity were experimentally demonstrated to have minimum effect on the grinding or crushing of the coal particles [15]. The effect of slurry velocity on OSLA was also shown to be insignificant with the application of model 1 [1]. Interestingly, increasing velocity was found to cause a considerable increase in the ablation rate for stationary samples [17, 18]. An estimate of pipe local shear stress based on a simplified application of shear stress decay law likewise shows that increasing slurry velocity enhances the shear stress inside the pipeline. That is, the velocity is likely to have a positive impact on OSLA. However, an increase in slurry concentration appears to have a more substantial effect on the increase of local shear stress at low slurry velocities. Rigorous investigations are required to clarify the impacts of slurry velocity and concentration on OSLA. To the best of authors’ knowledge, no significant research has been done until now to study the effect of slurry velocity and concentration on the ablation of actual oil-sand lumps. Also, a publicly available model that can estimate the ablation rate of the oil-sand lump as a function of shear stress forces is not available to date, although such a model is highly required for engineering usage in the industry.
\nA part of the manuscript was the outcome of a research project that was funded by the NSERC Industrial Research Chair in Pipeline Transport Processes (RSS). We are grateful to Canada’s Natural Sciences and Engineering Research Council (NSERC) and the Industrial Sponsors: Canadian Natural Resources Limited, CNOOC-Nexen Inc., Saskatchewan Research Council Pipe Flow Technology Centre™, Shell Canada Energy, Suncor Energy, Syncrude Canada Ltd., Total, Teck Resources Ltd., and Paterson & Cooke Consulting Engineers Ltd. We are especially thankful to Dr. Sanders (Professor, Department of Chemical and Materials Engineering, University of Alberta) for his advisory role in the research project.
\nA part of the manuscript is adapted from the first author’s PhD dissertation. area (m2) Archimedes number (−) solid volume concentration (−) pipe diameter (m) lump diameter (m) particle diameter (m) mean particle diameter (m) dimensionless particle diameter (−) Fanning friction factor (−) solid friction factor (−) length (m) radius (m) distance from pipe center (m) dimensionless distance from pipe center (−) temperature (°C) lump initial temperature °C time (s) bulk velocity (ms−1) solid object velocity (ms−1) deposition velocity (ms−1) local velocity (ms−1) viscosity (Pa.s) density (kgm−3) shear stress (Pa) wall shear stress (Pa) wall shear stress on solid object (Pa)Nomenclature
\n
In statistical physics only a few problems can be solved exactly. For complex problems, numerical methods can give exact results for problems that could only be solved in an approximate way. Numerical simulation can be a way to test the theory. The numerical results can be compared to the experimental results. The numerical simulation is placed between the fundamental and the experimental treatment; it has a quasi-experimental character (numerical experience). For problems of statistical physics, the most widely used simulation methods are the Monte Carlo method and the molecular dynamics method.
The first Monte Carlo simulation (MCS) was proposed by Metropolis et al. in 1953 [1]. The second Monte Carlo simulation was proposed by Wood and Parker in 1957 [2]. The obtained results were in good agreement with the experimental results of Bridgman [3] and those of Michels et al. [4]. In this method we attribute a series of initial positions chosen randomly to a system of N particles interacting through a defined potential. A sequence of particle configurations is generated by giving successive displacements to particles; we only retain configurations to ensure that the probability density is that of the chosen.
Molecular dynamics simulation (MDS) has been first introduced to simulate the behavior of fluids and solids at the molecular or atomic level. MDS was used for the first time by Alder and Wainwright in the late 1950s [5, 6] to study the interactions of hard spheres. The principle is the resolution of equations of motion for a hard sphere system in a simulation cell. The basic algorithm is Verlet’s algorithm [7].
In this chapter, we will present techniques of numerical simulations using the Monte Carlo method. We will present an application on the gas phase during plasma-enhanced chemical vapor deposition (PECVD) of thin films. The application concerns collisions between particles. Particles are in Brownian motion. Collisions, elastic or inelastic, are considered to be binary. Non-elastic collisions result in effective chemical reactions.
In Section 2, we cite some MCS and MDS works on PECVD processes. Section 3 presents general rules on numerical simulation methods. Section 4 presents how to simulate a physical problem using MCS? We present the Metropolis algorithm as a scheme to trait random configurations and different modules related to elaborate an MCS code. In Section 5, we apply the MCS on SiH4/H2 gas mixture during a PECVD process. Finally the conclusion summarizes the contents of the chapter.
The PECVD is the most widely used technique to produce hydrogenated amorphous silicon thin films (a-Si:H) for solar cells and for film transistors and electronic devices [8, 9]. Reactions during plasma deposition are complex and are not understood completely.
Gorbachev et al. [10, 11, 12] have developed a model that is based on chemical reactions and different processes in a PECVD reactor. The model takes into account the formation of SinHm oligomers (n ≤ 5). It presents a simulation of the growth of the films. Gorbachev et al. found that Si2H5 and Si3H7 strongly influence the growth of the film [11].
Valipa et al. [13] calculated the β reactivity of the SiH3 radical on a surface of a silicon lattice plane during the growth of a-Si:H using MDS. The mechanisms of physical and chemical interactions of low temperature plasmas with surfaces can be explored using MDS [14].
For a CH4/H2 mixture, Farouk et al. used the Monte Carlo method (PIC/MC); they calculated the ionization rate of the plasma and the deposition rate of the thin layer [15]. Rodgers et al. [16] have developed three-dimensional Monte Carlo simulations of diamond (100) surface CVD. Other works on MCS are in [17, 18, 19].
In our previous works [20, 21, 22, 23, 24], we were interested in the study of the gas phase and the interaction of plasmas with the surface, for SiH4/H2 and CH4/H2 gas mixtures during PECVD processes. The used numerical simulation techniques were MCS and MDS. To complete the studies, we used the fluid model [25].
The starting point of numerical simulation is a physical phenomenon; its purpose is to obtain useful physical results. Between these two points, several steps can be identified. These steps are general and they are applicable for MCS. The steps can be summarized as follows:
The physical phenomenon must be defined by the description of the dominant domain of physics. The main assumptions and simplifying approximations are necessary to understand the physical phenomenon and the design of the first model.
Mathematical model requires a mathematical formulation of the problem. It may be a problem of elements or discrete object or a problem of a continuous medium; it may be a spatiotemporal problem or frequency problem and may be a deterministic or probabilistic problem.
It would be interesting to know the mathematical equations that govern the phenomenon:
The forces between particles and elements
The potential interaction
The determination of a time scale
The determination of a length scale
Definition of constant magnitudes of motion and equilibrium magnitudes
Continuity equations, balance equations, transfer equations, etc.
The MCS technique has been chosen for this work; knowing its basic algorithm is necessary for elaborating the simulation. This step requires some actions:
Validation of the model on simple cases
Simulation calculation on complex phenomena
The MCS is based on a probabilistic process with a random choice of configurations and samples of the situation of the physical system. The two pedagogical examples most cited in the literature are the integration of a single variable function and Ising’s model of spin. In the following subsection, we define the integration of a single variable function. We introduce the Ising model at the end of Section 4.2.2.
Calculation of the definite integral for a function f(x) of a single variable x on domain {a, b} has been proposed (Figure 1):
The integral of a function f(x).
Let:
Let xi and yi be real random numbers (i = 1, 2,…, N), and let H be a real number greater than the f(x) for x belonging to the domain {a, b} (or x ∈ {a, b}).
Let r1 and r2 be two random numbers belonging to the domain {0, 1} according to a uniform distribution law. Generators (e.g., Ran, RANDOM, RANDUM, or other IMSL mathematical libraries) of random numbers can be used:
where xi and yi are random numbers (xi ∈ {a, b} and yi ∈ {0, H}).
The Monte Carlo (MC) method is based on a probabilistic process. Let N be the total number of cases chosen (possible cases). It is necessary to count the number of favorable cases (or the number of points below the curve y = f(x)); let yi ≤ f(xi)). The number of favorable cases is Nfav. When N➔∞, the value
An example [26] is the calculation of the value π by calculating the integral
We take a = 0.0, b = 1.0, and H = 1.0.
For different values of N, we show that the numerical solution tends to π = 4
Although this integral is simple, it shows the strength and simplicity of the method. The technique can be generalized for the integration of multivariate functions.
We note that integration by the MC method is based on:
The choice of
Each configuration chosen is either
For statistical physics problems, the probabilistic choice of configurations is not always deterministic; the favorable and unfavorable cases are not exclusive. According to the Metropolis algorithm [26, 27], the steps of the simulation are:
Choice of a simulation cell of adequate shape to the studied phenomena. The size of the simulation cell is related to a scale of length characteristic of the forces and interaction potential of the studied phenomenon. This cell may contain Npc particles (and/or elements).
Choice of an initial configuration that responds to some physical and thermodynamic properties. The total or internal energy of the system is Ei.
Infinitesimal random displacement of a particle (or element of the system) and calculation of the new internal energy of the system Ef. This displacement is related to the physical magnitudes: time scale and length scale.
If
If
If
Figure 2 shows how to choose between the selected configurations. Let
Configuration choice according to Metropolis scheme.
Numerical simulation using the MC method is a very important tool for the study of static properties. The basic algorithm is based on probability notions. Understanding of the distribution function and/or interaction potentials is the heart of the calculation.
In equilibrium statistical physics, the system has a certain probability that can be in any states. The probability of being in a state
where T is the absolute temperature and kB is called Boltzmann’s constant. It is conventional to denote the quantity (kBT)−1 by the symbol β. The normalizing factor Z, or partition function, is given by:
The average of a quantity Q fora system in equilibrium is:
The internal energy U, is given by:
which can be written in terms of a derivative of the partition function:
From thermodynamics we have expressions for the specific heat C, the entropy S, and the Helmholtz free energy F:
or
and
and
We can calculate other parameters affecting the system.
The Monte Carlo method is an excellent technique for estimating probabilities, and we can take advantage of this property in evaluating the results. The simplest and most popular model of a system of interacting variables in statistical physics is the Ising model. It consists of spins
The Ising model has been studied in one and two dimensions to obtain results of thermal properties, phase transition, and magnetic properties [26, 27, 28]. For chosen values of J and/or B, different steps may be taken for the calculations (simulation cell, initialization, configurations, boundary conditions, calculation algorithms). For any configuration, each spin takes the two possible directions. The detail of the calculation procedure is not the purpose of this chapter.
We give a system of N particles (atoms, molecules, ions or particles) placed in a cell of fixed volume, generally of cubic form. The initial positions may, depending on the case, be distributed randomly according to a certain law (uniform or otherwise) or have a given symmetry. In a fluid, a gas, or a plasma, the particles may have random positions in general; in a solid or surface, with a crystal structure, the particles take ordered positions. The choice of random initial positions allows great freedom on the choice of the number of particles in the cell.
At the first step, the particles are given velocities that are generally selected to have a zero total momentum. If the system is in thermodynamic equilibrium, the initial velocities will be randomly chosen according to a Maxwell-Boltzmann law. In the general case, the velocity distribution is according to the problem dealt with. All other phase properties can be initialized to the particles; the main thing is the conservation of the total quantities of the system.
The particles interact with each other according to chosen interaction potentials. Since the interaction potentials are specific for each “numerical experiment,” the main part of the work consists in calculating the interaction energies for each proposed configuration.
The choice of interaction potentials is directly related to the mathematical formulation of the problem according to the state of the medium: fluid, gas, plasma, or solid. It can be Lennard-Jones potential, Coulomb potential, Debye potential, Morse potential, Stillinger-Weber potential, Born-Mayer potential, Moliere potential, or others.
In general, two main boundary conditions are used: periodic boundary conditions (PBC) and minimum image convention (MIC) [29].
To minimize the surface effect, periodic boundary conditions (PBC) [30] are invariably imposed. The simulation cell is reproduced throughout the space to form an infinite mesh. We can simulate the properties of an infinite system. The particles that we follow are in the central cell; if a particle crosses a wall with a certain velocity, its image returns with the same velocity by the opposite wall. Under these conditions, the number of particles in the central cell, and consequently the density, is constant. These conditions also allow the conservation of the energy and the momentum of the system and do not introduce periodic effects (because of the interaction between particles).
According to the hypotheses and according to the geometry of the problem, other boundary conditions are proposed [26]. For example, in order to model thin films, the simulation cells are longitudinal and parallel to the film; one uses PBC in the directions parallel to the film. In the direction normal to the film, free edge boundary conditions can be used. In such cases, it may be appropriate to also include surface fields and surface interactions. In this way, one can study phenomena such as wetting, interface localization-delocalization transitions, surface-induced ordering and disordering, etc.
The core of the program includes calculating the potential energies of particle configuration and particle collisions. The interactions and collisions between particles can be elastic or inelastic; they can be binary or collective. For computation, the interaction energy of a particle with its neighbors is carried out by refocusing a base cell on the particle. This particle only interacts with particles in this region. This is called the “minimal image convention” (MIC) [1].
Generally, a RANDOM generator of real random numbers ri belonging to the domain {0, 1} (or ri ∈ {0, 1} is available. This distribution law is uniform.
To have a real random number xi belonging to the domain {a, b} (or
To have a real random number xi belonging to the domain {a, b} (or xi ∈ {a,b}) according to a formula (or law) of nonuniform distribution f(x), a histogram technique is used. Let Nm be the number of intervals. If the mesh is regular (Figure 3):
Random number selection according to f (x) distribution.
We define:
We define the sequence:
and the sequence:
Hence each real random number ri belongs to the domain {0, 1} (where ri ∈ {0, 1}) (according to the uniform law); this number belongs to the domain {rxj-1, rxj}. It corresponds to a random value xran of the domain {xj-1, xj}; this number satisfies the formula (or the law) of nonuniform distribution f(x).
This technique can be generalized for a nonuniform distribution law f(x) with an irregular mesh Δxi, or with tabular data f(xi) with
The technique can be generalized, too, for a discrete distribution law f(i) with
In the literature, the reader can find simple algorithms for the choice of random numbers of some simple functions (Gaussian, etc.).
It is necessary to find some parameters allowing the control of the smooth course of the evolution of the system. We must look for the constants of movement. For example for an isolated system, we have the conservation of the total energy and the quantity of matter.
By using the numerical simulation, it is possible to calculate many spatiotemporal quantities F(r,t). These quantities can be positions, speeds, kinetic moments, particle energies, concentrations, transport coefficients, etc. It would then be possible to calculate all other quantities related to F(r,t).
For the calculation of the averages, one can note the quantities on the space, on the time or on both. The histogram methods can be used. Static or dynamic distribution functions and spatial or temporal correlation functions can be calculated. It should be noted that the SMC is much more adequate for static properties because of the probabilistic choice of configurations.
Any calculated function or parameter F(r,t) can be used for another application in another calculation program.
In the MCS model discussed extensively in this chapter, it’s more about collisions between particles. It’s
Other MCS models, named
For statistical physics problem solving (such as thin film deposition problems), MCS models use experimental, numerical, or theoretical data from other methods and models. Models can be improved to
Schematic of a hybrid model of three modules used to study gas mixtures in the PECVD [
To solve statistical physics problems with evolutions as a function of time,
Other CVD and PECVD works on MCS are presented in Ref.s [15, 34, 35, 36, 37, 38]. They show how MCS methods can study properties of gas mixtures and properties of the growth of thin films.
In this section, we present an example of PP-MCS of collisions and reactions in gas phase of SiH4/H2 mixture used in PECVD process. Some paragraphs have been treated in previous works [21, 24].
We use a MCS to study collisions and chemical reactions in gas phase of SiH4/H2 mixture used in the PECVD process. In this phase, important reactions have been identified that contribute to the production and the consumption of hydrogen (H), silylene (SiH2), and silyl (SiH3). The hydrogen consumption reactions SiH4 + H → SiH3 + H2 and SiH3 + H → SiH2 + H2 are found to play a central role in deciding the distribution of hydrogen [39].The plasma chemistry indicates that H atoms and SiH3 radicals play an important role in the a-Si:H deposition process [40]. Experimentally, it is generally accepted that SiH3 radicals dominate a-Si:H and μc-Si film growth from SiH4 plasmas in the PECVD; it is the key precursor of a-Si:H deposition [41]. The proposed MCS allowed to get the ratio SiH2/SiH3 and mean value of densities of species. It provides information on SiH4 dissociation and on the production of SiH3, H, SiH2, and Si2H6 and other important parameters.
The plasma in the PECVD reactor is weakly ionized. For our study, the mixture gas contains 22% of SiH4 and 78% of H2; the pressure is 100 mtorr, the temperature of the gas ranges from 373 to 723 K, the electron temperature is about 2.5 eV, and the electron density is 3. 108 cm−3. The process is considered to be stationary. We take into account electrons and eight neutral species (SiH4, SiH3, SiH2, H, H2, Si2H6, Si2H5, SiH).
Symbol | Reactions | Kreac (cm3/s) |
---|---|---|
R1 | SiH4 + e→SiH3 + H+e | k1 = 3 × 10−11 [42] |
R2 | SiH4 + e→SiH2 + 2H + e | K2 = 1.5 × 10−10 [42] |
R3 | SiH4 + e→SiH + H + H2 + e | K3 = 9.34 × 10−12 [42] |
R4 | SiH4 + e→SiH2 + H2 + e | K4 = 7.19 × 10−12 [42] |
R5 | H2 + e→2H + e | K5 = 4.49 × 10−12 [42] |
R6 | Si2H6 + e→SiH3 + SiH2 + H + e | K6 = 3.72 × 10−10 [42] |
R7 | Si2H6 + e→SiH4 + SiH2 +e | K7 = 1.1 × 1010× (1.(1./(1. + (0.63 × P)))) [43] |
R8 | SiH4 + H→SiH3 + H2 | K8 = 2.8 × 10−11 × exp.(−1250/T) [44] |
R9 | SiH4 + SiH2→Si2H6 | K9 = 1.1 × 1010 × (1.−(1./(1. + (0.63 × P)))) [43] |
R10 | SiH3 + SiH3→SiH4 + SiH2 | K10 = 0.45 × 1.5 × 10−10 [44] |
R11 | SiH4 + Si2H5→SiH3 + Si2H6 | K11 = 5 × 10−13 [42] |
R12 | SiH3 + H→SiH2 + H2 | K12 = 2 × 10−11 [44] |
R13 | SiH3 + Si2H6→SiH4 + Si2H5 | K13 = 4 × 10−10 × exp. (−2500/T) [44] |
R14 | SiH2 + H→SiH + H2 | k14 = 2 × 10−11 [44] |
R15 | Si2H6 + H→Si2H5 + H2 | K15 = 0.66 × 2.4 × 10−10 × exp. (−1250/T) [43] |
R16 | Si2H6 + H→SiH4 + SiH3 | K16 = 0.34 × 2.4 × 10−10 × exp. (−1250/T) [44] |
R17 | SiH + H2→SiH3 | K17 = 2 × 10−12 [43] |
R18 | SiH2 + SiH3→Si2H5 | K18 = 3.77 × 10−13 [43] |
R19 | SiH2 + H2→SiH4 | K19 = 3 × 10−12 × (1. + (1./1. + (0.03 × P))) [43] |
R20 | 2SiH3→Si2H6 | K20 = 0.1 × 1.5 × 10−10 [43] |
R21 | SiH4 + SiH→Si2H5 | K21 = (1.−(1./(1. + (0.33 × P)))) × (6.9 × 10−10) [43] |
List of gas phase reactions and corresponding rate constants [24].
Let
And chemical reaction for the production of A is as:
Rate production and consumption for any species A are taken as:
The MCS is based on binary collisions at the microscopic level. Elastic collisions are between all particles, and inelastic collisions (or effective collisions) are those that result in a chemical reaction. A chemical reaction needs a collision involving at least two particles (atoms, ions, electrons, or molecules). According to kinetic theory, gases consist of particles in random motion. These particles are
Form of the simulation cell.
Let ni be the density of neutral spice
The chosen particle takes randomly three components of space in cell
Let ni and nj be the densities of species
According to the kinetic theory of gases, we have for an incident particle
where <sij> is the cross section of the particle
The mean free path
The time between two collisions τij is then:
For chemical effective reactions (inelastic collisions) between two reactive species
General rules of collision theory are applied:
The new velocities of the colliding particles are calculated using conservation of energy and momentum for elastic collisions.
Conservation of total energy as isolated system.
Movement of the center of mass and relative motion around the center of mass.
The reader can refer to some fundamental physics books that deal with general notions of collisions and corresponding parameters [45, 46, 47, 48].
The plasma in the PECVD reactor is weakly ionized. At low temperature, particles interact occasionally with each other and move under the effect of thermal agitation. In reality, only a small fraction of collisions are effective (result in a chemical reaction) [21].
In our MCS, after traveling a random walk given by a Gaussian distribution, the first chosen particle collides with a second particle (molecule, atom, radical, or electron). The last particle
where
The activation energy is given by:
where the pre-exponential factor is assumed to be the collision frequency factor and Kreac is the rate constant of the gas phase reaction.
The two colliding particles (e.g., the electron and SiH4 molecule) can interact by several reactions (R1, R2, R3, and R4 in Table 1); we choose randomly one of gas phase reactions occurring according to a,
where
All chemical systems go naturally toward states of minimum Gibbs free energy [21, 24]. A chemical reaction tends to occur in the direction of lower Gibbs free energy. To determine the direction of the reaction that is taking place, we use the old and new values of Kreac and the equilibrium constant with reactants and product concentrations. Each set of binary collisions can be related or converted into time. As cited in section (a), Table 1 gives gas phase reactions and corresponding rate constants used in this MCS.
To continue the simulation, after the elastic collision, particle
From Metropolis algorithm, the scheme of this MCS is as follows:
Choices of particle of spice
Choices of random collision with a spice j.
Study of collision type (elastic, inelastic). If the collision is elastic the particle i move with a new velocity and mean free path, and we return to step (b). If the collision is inelastic particles i and j give new particles i’ and j’, according to Metropolis scheme, and we return to step (a) or (b). Periodic boundary conditions are used to keep particles in the elementary cell.
At each step, we can note the different statistics.
Once the species are selected for the simulation model, an estimate of species densities should be made. Following the model of interaction and collisions between particles (binary, collective, etc.), a first choice of the minimum number Ni of particles of each species is made. A first estimate of the sizes (Lx, Ly, Lz) of the elementary cell is made.
The study of the types of interaction potentials and the calculation of the approximate values of the force ranges, the kinetic energies, the internal energies, and the energies of activation make it possible to correct the minimal numbers Ni of particles and the sizes (Lx, Ly, Lz) of the elementary cell.
Let kp be the number of a species, kp = 1,…, 9. The minimal numbers Qnp(kp) and the sizes (Lx, Ly, Lz) have to be discussed for statistical calculations.
For numerical programming, according to the programming language used and according to the size (or the computational capacity) of the computer, it is necessary to find a judicious choice of the tables of integer or real values and which values would be useful to save all during simulation. Let Ncol,m be the maximum number of elastic collisions per particle, and let Ncycle be the number of cycles to average the simulation calculations.
For this MCS, the numerical chosen values are in Table 2.
Cell dimensions and steps for collisions | Number of species Kp | Initial number of particles in cell | ||
---|---|---|---|---|
Lx (m) | 4.68 10−6 | 1 | Qnp(SiH4) | Qnp1 |
Ly (m) | 4.68 10−6 | 2 | Qnp(SiH3) | 10 |
Lz (m) | 20.0 10−3 | 3 | Qnp(SiH2) | 10 |
4 | Qnp(H) | 10 | ||
Ncol,m | 500 | 5 | Qnp(H2) | Qnp5 |
Ncycle internal cycle | 2000 | 6 | Qnp(Si2H6) | 10 |
Ncycle external cycle | 200,000 | 7 | Qnp(SiH) | 10 |
8 | Qnp(Si2H5) | 10 | ||
9 | Qnp(e) | Qnp9 |
Used quantities and parameters in calculations for the gas temperature Tg = 520 K.
For radicals (e.g., SiH3), particle numbers Qnp(k) are very small; we take Qnp(k) = 10. These numbers cannot take value 1 or 0, even if a species k is in trace form in the gas. The value 0 for a species k means that any other species k’ does not make a collision with the species k; and the value 1 means that we have no collisions between particles of the same species in the cell.
Qnp1, Qnp5, and Qnp9 are calculated from the volume of cell, the pressure, the temperature, and the total number of particles in the cell (Qnp1 = 0.81187824 * 109; Qnp5 = 0.20296956 * 109; Qnp9 = 131).
As we have chosen a stationary regime, we must reach the values and properties at equilibrium. The results of the simulation show this trend. In MCS, averaged values, distribution functions, autocorrelation functions, and correlation functions can be calculated. To ensure rapid convergence of calculations, it would be useful to look for statistically symmetric (or stationary or unsteady) parameters [26, 50].
As an example for our MCS calculation, we have:
The number of Si2H6, SiH, and Si2H5 particles reaching the surface is negligible.
Let Ns,i and Ns, H2 be the densities of a species
Let Ns,i be the density of a species
The reactions begin with the dissociation (consumption) of H2 and SiH4 by R5, R1, and R2 reactions.
The production of SiH3 is done by R8, and then there is production of SiH2 by R12.
The reaction R2: SiH4 + e → SiH2 + 2H + e plays the central role in SiH4 dissociation by electron impact [24]. This result is compatible with [39].
The second important chemical reaction in the SiH4 dissociation is R1: SiH4 + e → SiH3 + H + e [24]. This result is compatible with that of Perkins et al. [51] and that of Doyle et al. [52].
Type | H2 | SiH4 | H | SiH3 | SiH2 |
---|---|---|---|---|---|
Ns,i/Ns, H2 | 1 | 0.23 | 1.67 10−4 | 8.60 10−5 | 9.86 10−6 |
Ratios Ns,i/Ns, H2 of particles reaching the surface compared to H2.
Type | SiH4 | SiH3 | SiH2 |
---|---|---|---|
6.695 10−6 | 7.965 10−6 | 775 10−6 |
Ratios Ns,i/Nv,i of particles reaching the surface compared to volume.
MCS is a widely used method in statistical physics to study thermodynamic, structural, or phase properties. It is based on random and probabilistic processes. The purpose of this chapter is to present the technique for general use in physics for the study of thin film deposition problems. The technique can be generalized to other fields of science: biology, economics, transportation, and social sciences.
We started by presenting general rules for numerical simulation methods. Metropolis algorithm has been considered as the basic algorithm. After, we presented the different steps for the realization of a MCS code. We chose the particle-particle model MCS (PP-MCS) to explain the different steps and procedures to be applied in the deposition of thin layers by PECVD processes. We have shown that this technique can be generalized to the particle-in-cell MCS (PIC-MCS) case or kinetic MCS (kMCS), as it can be joined with other modules to give hybrid models. It is important to know how to choose random configurations from the laws or probability distributions in the system.
A numerical application is presented for collisions in a SiH4/H2 gas mixture in the PECVD process. A preliminary work of determination of the chemical reactions between molecules and radicals is made. A choice of the simulation cell is made, and the definition of the probabilities of the collisions between peers is made. The Metropolis algorithm makes it possible to follow the various elastic and inelastic collisions; it also makes it possible to make the statistics of the interactions with the surface. The results are compatible with [39, 51, 52].
Other questions may be asked to account for molecular ions, surface and volume kinetics, or thin film formation. The techniques and different models of the MCS (PP-MCS, MCS-PIC, kMCS) allow taking care of these questions.
The interconnection of the MCS with other models (MDS, hybrid model, fluid model, electromagnetic model, etc.) would allow answering more questions. The methods can be applied to other specialties than the physical sciences.
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\n'}]},successStories:{items:[]},authorsAndEditors:{filterParams:{sort:"featured,name"},profiles:[{id:"6700",title:"Dr.",name:"Abbass A.",middleName:null,surname:"Hashim",slug:"abbass-a.-hashim",fullName:"Abbass A. Hashim",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/6700/images/1864_n.jpg",biography:"Currently I am carrying out research in several areas of interest, mainly covering work on chemical and bio-sensors, semiconductor thin film device fabrication and characterisation.\nAt the moment I have very strong interest in radiation environmental pollution and bacteriology treatment. The teams of researchers are working very hard to bring novel results in this field. 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. I have served as the editor for many books, been a member of the editorial board in science journals, have published many papers and hold many patents.",institutionString:null,institution:{name:"Sheffield Hallam University",country:{name:"United Kingdom"}}},{id:"54525",title:"Prof.",name:"Abdul Latif",middleName:null,surname:"Ahmad",slug:"abdul-latif-ahmad",fullName:"Abdul Latif Ahmad",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"20567",title:"Prof.",name:"Ado",middleName:null,surname:"Jorio",slug:"ado-jorio",fullName:"Ado Jorio",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Universidade Federal de Minas Gerais",country:{name:"Brazil"}}},{id:"47940",title:"Dr.",name:"Alberto",middleName:null,surname:"Mantovani",slug:"alberto-mantovani",fullName:"Alberto Mantovani",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"12392",title:"Mr.",name:"Alex",middleName:null,surname:"Lazinica",slug:"alex-lazinica",fullName:"Alex Lazinica",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/12392/images/7282_n.png",biography:"Alex Lazinica is the founder and CEO of IntechOpen. 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. Today his focus is on defining the growth and development strategy for the company.",institutionString:null,institution:{name:"TU Wien",country:{name:"Austria"}}},{id:"19816",title:"Prof.",name:"Alexander",middleName:null,surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/19816/images/1607_n.jpg",biography:"Alexander I. Kokorin: born: 1947, Moscow; DSc., PhD; Principal Research Fellow (Research Professor) of Department of Kinetics and Catalysis, N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow.\r\nArea of research interests: physical chemistry of complex-organized molecular and nanosized systems, including polymer-metal complexes; the surface of doped oxide semiconductors. He is an expert in structural, absorptive, catalytic and photocatalytic properties, in structural organization and dynamic features of ionic liquids, in magnetic interactions between paramagnetic centers. The author or co-author of 3 books, over 200 articles and reviews in scientific journals and books. He is an actual member of the International EPR/ESR Society, European Society on Quantum Solar Energy Conversion, Moscow House of Scientists, of the Board of Moscow Physical Society.",institutionString:null,institution:{name:"Semenov Institute of Chemical Physics",country:{name:"Russia"}}},{id:"62389",title:"PhD.",name:"Ali Demir",middleName:null,surname:"Sezer",slug:"ali-demir-sezer",fullName:"Ali Demir Sezer",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/62389/images/3413_n.jpg",biography:"Dr. Ali Demir Sezer has a Ph.D. from Pharmaceutical Biotechnology at the Faculty of Pharmacy, University of Marmara (Turkey). 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. I had been a visiting research student at Faculty of Computer Science, University of Murcia, Murcia, Spain for three months.\n\nI have published over 40 papers during 5 years in refereed journals, books, and conference proceedings in the areas of electro-physiological signals processing and classification, notably EMG and EOG signals, fractal analysis, wavelet analysis, texture analysis, feature extraction and machine learning algorithms, and assistive and rehabilitative devices. I have several computer programming language certificates, i.e. Sun Certified Programmer for the Java 2 Platform 1.4 (SCJP), Microsoft Certified Professional Developer, Web Developer (MCPD), Microsoft Certified Technology Specialist, .NET Framework 2.0 Web (MCTS). 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