Modeling and Control Simulation for a Condensate Distillation Column

The separation process requires three things. Firstly, a second phase must be formed so that both liquid and vapor phases are present and can contact each other on each stage within a separation column. Secondly, the components have different volatilities so that they will partition between the two phases to a different extent. Lastly, the two phases can be separated by gravity or other mechanical means.


Introduction
Distillation is a process that separates two or more components into an overhead distillate and a bottoms product.The bottoms product is almost exclusively liquid, while the distillate may be liquid or a vapor or both.
The separation process requires three things.Firstly, a second phase must be formed so that both liquid and vapor phases are present and can contact each other on each stage within a separation column.Secondly, the components have different volatilities so that they will partition between the two phases to a different extent.Lastly, the two phases can be separated by gravity or other mechanical means.
Calculation of the distillation column in this chapter is based on a real petroleum project to build a gas processing plant to raise the utility value of condensate.The nominal capacity of the plant is 130,000 tons of raw condensate per year based on 24 operating hours per day and 350 working days per year.The quality of the output products is the purity of the distillate, x D , higher than or equal to 98% and the impurity of the bottoms, x B , may be less/equal than 2%.The basic feed stock data and its actual compositions are based on the other literature (PetroVietnam Gas Company,1999).
The distillation column contains one feed component, F x .The product stream exiting the top has a composition of D x of the light component.The product stream leaving the bottom contains a composition of B x of the light component.The column is broken in two sections.The top section is referred to as the rectifying section.The bottom section is known as the stripping section as shown in Figure 1.1.
The top product stream passes through a total condenser.This effectively condenses all of the vapor distillate to liquid.The bottom product stream uses a partial re-boiler.This allows for the input of energy into the column.Distillation of condensate (or natural gasoline) is cutting off light components as propane and butane to ensure the saturated vapor pressure and volatility of the final product.
The goals of this chapter are twofold: first, to present a theoretical calculation procedure of a condensate column for simulation and analysis as an initial step of a project feasibility study, and second, for the controller design: a reduced-order linear model is derived such that it best reflects the dynamics of the distillation process and used as the reference model Fig. 1.1.Distillation Flow-sheet for a model-reference adaptive control (MRAC) system to verify the ability of a conventional adaptive controller for a distillation process dealing with the disturbance and the plantmodel mismatch as the influence of the feed disturbances.
In this study, the system identification is not employed since experiments requiring a real distillation column is still not implemented.So that a process model based on experimentation on a real process cannot be done.A mathematical modeling based on physical laws is performed instead.Further, the MRAC controller model is not suitable for handling the process constraints on inputs and outputs as discussed in other literature (Marie, E. et al., 2008) for a coordinator model predictive control (MPC).In this chapter, the calculations and simulations are implemented by using MATLAB (version 7.0) software package.

Fundamental variables for composition control
The purity of distillate or the bottoms product is affected by two fundamental variables: feed split (or cutting point) and fractionation.The feed split variable refers to the fraction of the feed that is taken overhead or out the bottom.The fractionation variable refers to the energy that is put into the column to accomplish the separation.Both of these fundamental variables affect both product compositions but in different ways and with different sensitivities.a. Feed Split: Taking more distillate tends to decrease the purity of the distillate and increase the purity of the bottoms.Taking more bottoms tends to increase distillate purity and decrease bottoms product purity.
b. Fractionation: Increasing the reflux ratio (or boil-up rate) will reduce the impurities in both distillate and the bottoms product.
Feed split usually has a much stronger effect on product compositions than does fractionation.One of the important consequences of the overwhelming effect of feed split is that it is usually impossible to control any composition (or temperature) in a column if the feed split is fixed (i.e. the distillate or the bottoms product flows are held constant).Any small changes in feed rate or feed composition will drastically affect the compositions of both products, and will not be possible to change fractionation enough to counter this effect.

Degrees of freedom of the distillation process
The degrees of freedom of a process system are the independent variables that must be specified in order to define the process completely.Consequently, the desired control of a process will be achieved when and only when all degrees of freedom have been specified.The mathematical approach to determine the degrees of freedom of any process (George, S., 1986) is to sum up all the variables and subtract the number of independent equations.However, there is a much easier approach developed by Waller, V. (1992): There are five control valves as shown in Figure 1.2, one on each of the following streams: distillate, reflux, coolant, bottoms and heating medium.The feed stream is considered being set by the upstream process.So this column has five degrees of freedom.Inventories in any process must be always controlled.Inventory loops involve liquid levels and pressures.This means that the liquid level in the reflux drum, the liquid level in the column base, and the column pressure must be controlled.
If we subtract the three variables that must be controlled from five, we end up with two degrees of freedom.Thus, there are two and only two additional variables that can (and must) be controlled in the distillation column.Notice that we have made no assumptions about the number or type of chemical components being distilled.Therefore a simple, ideal, binary system has two degrees of freedom; a complex, multi-component system also has two degrees of freedom.


Local perspective considering the dynamic characteristics of the column.


Global perspective considering the interaction of the column with other unit operations in the plant.

Energy balance control structure (L-V)
The L-V control structure, which is called energy balance structure, can be viewed as the standard control structure for dual composition control of distillation.In this control structure, the reflux flow rate L and the boil-up flow rate V are used to control the "primary" outputs associated with the product specifications.The liquid holdups in the drum and in the column base (the "secondary" outputs) are usually controlled by distillate flow rate D and the bottoms flow rate B.

Material balance control structure (D-V) and (L-B)
Two other frequently used control structures are the material balance structures (D-V) and (L-B).The (D-V) structure seems very similar to the (L-V) structure.The only difference between the (L-V) and the (D-V) structures is that the roles of L and D are switched.

Preparation for initial data
The plant nominal capacity is 130,000 tons of raw condensate per year based on 24 operating hours per day and 350 working days per year.The plant equipment is specified with a design margin of 10% above the nominal capacity and turndown ratio of 50% The feed is considered as a pseudo binary mixture of Ligas (iso-butane, n-butane and propane) and Naphthas (iso-pentane, n-pentane, and heavier components).The column is designed with N=14 trays.The model is simplified by lumping some components together (pseudocomponents) and modeling of the c o l u m n d y n a m i c s i s b a s e d o n t h e s e pseudocomponents only (Kehlen, H. & Ratzsch, M., 1987).Depending on the feed composition fluctuation, the properties of pseudo components are allowed to change within the range as shown in the Table 2.4.

Relative volatility:
Relative volatility is a measure of the differences in volatility between two components, and hence their boiling points.It indicates how easy or difficult a particular separation will be.Checking the data in the handbook (Perry, R. & Green, D., 1984) for the operating range of temperature and pressure, the relative volatility is calculated as:   5.68 .

Correlation between TBP and Equilibrium Flash Vaporization (EFV):
The EFV curve is converted from the TBP data according to (Luyben, W., 1990)

Calculation for feed section
The feed is in liquid-gas equilibrium with gas percentage of 38% volume.However it is usual to deeply cut 4% of the unexpected heavy components, which will be condensed and refluxed to the columnmore bottom.Thus there are two equilibrium phase flows: vapor V F =38+4=42% and liquid L F =100-42=58%.
Operating temperature: Consulting the EFV curve (4.6 atm) of feed section, the required feed temperature is 118 0 C corresponding to 42% volume point.
The phase equilibrium is shown in the Figure 2.2.The heavy fraction flow L f dissolved an amount of light components is descending to the column bottom.These undesirable light components shall be caught by the vapor flow V f arising to the top column.V f , which can be calculated by empirical method, is equal to 28% vol.The bottoms product flow B is determined by yield curve as 62% vol.Hence, the internal reflux across the feed section can be computed as: Material balances for the feed section is shown in the Table 2.6.The calculation based on the raw condensate feed rate for the plant: 15.4762 tons/hour.

Calculation for stripping section
In the stripping section, liquid flows, which are descending from the feed section, include the equilibrium phase flow L F , and the internal reflux flow L f .They are contacting with the arising vapor flow V f for heat transfer and mass transfer.This process is accomplished with the aid of heat flow supplied by the re-boiler.
Main parameters to be determined are the bottoms product temperature and the re-boiler duty Q B .The column base pressure is approximately the pressure at the feed section because pressure drop across this section is negligible.Consulting the EFV curve of stripping section and the Cox chart, the equilibrium temperature at this section is 144 °C.The re-boiler duty is equal to heat input in order to generate boil-up of stripping section an increment of 144-118=26 °C.

Stream
The material and energy balances for stripping section is displayed in the

Calculation for rectifying section
The overhead vapor flow, which includes V F from feed section and V f from stripping section, passes through the condenser (to remove heat) and then enter into the reflux drum.
There exists two equilibrium phases: liquid (butane as major amount) and vapor (butane vapor, uncondensed gas -dry gas: C 1 , C 2 , e.g.).The liquid from the reflux drum is partly pumped back into the top tray as reflux flow L and partly removed as distillate flow D. The top pressure is 4 atm due to pressure drop across the rectifying section.The dew point of distillate is correspondingly the point 100% of the EFV curve of rectifying section.Also consulting the Cox chart, the top section temperature is determined as 46 °C .
The equilibrium phase flows at the rectifying sections are displayed in the

Latent heat and boil-up flow rate
The heat input of Q B (re-boiler duty) to the reboiler is to increase the temperature of stripping section and to generate boil-up V 0 as (Franks, R., 1972):    Total mass balance: Component balance: Energy balance: (3.9)

Reflux drum and condenser
Total mass balance:  ()

Re-boiler and Column Bottoms (stage n=1)
The base of the column has some particular characteristics as follows:  There is re-boiler heat flux B Q establishing the boil-up vapor flow B V .


The holdup is variable and changes in sensible heat cannot be neglected.


The outflow of liquid from the bottoms B is determined externally to be controlled by a bottoms level controller.Total mass balance: Component balance: Energy balance: When all the modeling equations above are resolved, we find out how the flow rate and concentrations of the two product streams (distillate product and bottoms product) change with time, in the presence of changes in the various input variables.

Simplified model
To simplify the model, we make the following assumption (Papadouratis, A. et al. 1989):


The relative volatility  is constant throughout the column.This means the vapor- liquid equilibrium relationship can be expressed by where n x : liquid composition on n th stage; n y : vapor composition on n th stage; and  : relative volatility.


The overhead vapor is totally condensed in a condenser.


The The column is numbered from bottom (n=1 for the re-boiler, n=2 for the first tray, n=f for the feed tray, for the top tray and n=N+2 for the condenser).
Under these assumptions, the dynamic model can be expressed by (George, S., 1986): x in the liquid and F y in the vapor phase of the feed are obtained by solving the flash equations: where,  is the relative volatility.
Although the model order is reduced, the representation of the distillation system is still nonlinear due to the vapor-liquid equilibrium relationship in equation (3.25).

www.intechopen.com
Distillation -Advances from Modeling to Applications 20

Model dynamic equations
In the process data calculation, we have calculated for the distillation column with 14 trays with the following initial data -equations ( 2

Simulation with 10% decreasing and increasing feed flow rate
When decreasing the feed flow rate by 10%, the quality of the distillate product will get worse while the quality of the bottoms product will get better: the purity of the distillate product reduces from 96.54% to 90.23% while the impurity of the bottoms product reduces from 3.75% to 0.66%.
In contrast, when increasing the feed flow rate by 10%, the quality of the distillate product will be better while the quality of the bottoms product will be worse: the purity of the distillate product increases from 96.54% to 97.30% while the impurity of the bottoms product increases from 3.75% to 11.66%.(See  When the input flow rate fluctuates in sine wave by 5% (see Figure 4.3), the purity of the distillate product and the impurity of the bottoms product will also fluctuate in a sine wave (see Figure 4.4 and Table 4.4).In order to obtain a linear mathematical model for a nonlinear system, it is assumed that the variables deviate only slightly from some operating condition (Ogata, K., 2001).If the normal operating condition corresponds to n x and n y , then equation (5.1) can be expanded into a Taylor's series as: ... Substituting equation (5.4) into equation (5.5), the following expression is obtained: In order to obtain a linear approximation to this nonlinear system, this equation may be expanded into a Taylor series about the normal operating point from equation (5.3), and the linear approximation equations for general trays are obtained: (5.6) Linearization for special trays: Tray above the feed flow (n=f+1): and the linear approximation equations for the tray above the feed flow: (5.7) Tray below the feed flow (n=f): and the linear approximation equations for the tray above the feed flow:   The matrix B elements:

Reduced-order linear model
The full-order linear model in equation 5-11, which represents a 2 input -2 output plant can be expressed in the S domain as: (5.12) where  c is the time constant and (0) G is the steady state gain The steady state gain can be directly calculated: The time constant  c can be calculated based on some specified assumptions (Skogestad, S.,  & Morari, M., 1987).The linearized value of  c is given by:

Control simulation with MRAC
The reduced-order linear model is then used as the reference model for a model-reference adaptive control (MRAC) system to verify the applicable ability of a conventional adaptive controller for a distillation column dealing with the disturbance and the model-plant mismatch as the influence of the plant feed disturbances.
Adaptive control system is the ability of a controller which can adjust its parameters in such a way as to compensate for the variations in the characteristics of the process.Adaptive control is widely applied in petroleum industries because of the two main reasons: Firstly, most processes are nonlinear and the linearized models are used to design the controllers, so that the controller must change and adapt to the model-plant mismatch; Secondly, most of the processes are non-stationary or their characteristics are changed with time, this leads again to adapt the changing control parameters.
The general form of a MRAC is based on an inner-loop Linear Model Reference Controller (LMRC) and an outer adaptive loop shown in Fig. 6.1.In order to eliminate errors between the model, the plant and the controller is asymptotically stable, MRAC will calculate online the adjustment parameters in gains L and M by  () L t and  () M t as detected state error () et when changing A , B in the process plant.where  is an adaptive gain and P is a Lyapunov matrix.) amid the disturbances and the plant-model mismatches as the influence of the feed stock disturbances.

Derivative Calculation of
The design of a new adaptive controller is shown in Figure 6.2 where we install an MRAC and a closed-loop PID (Proportional, Integral, Derivative) controller to eliminate the errors between the reference set-points and the outputs.

Conclusion
A procedure has been introduced to build up a mathematical model and simulation for a condensate distillation column based on the energy balance (L-V) structure.The mathematical modeling simulation is accomplished over three phases: the basic nonlinear model, the full order linearized model and the reduced order linear model.Results from the simulations and analysis are helpful for initial steps of a petroleum project feasibility study and design.

Fig. 2
Fig. 2.2.The Equilibrium phase flows at the feed section Where, V F : Vapor phase rate in the feed flow; L F : Liquid phase rate in the feed flow; V f : Vapor flow arising from the stripping section; L f : Internal reflux descending across the feed section.

Fig
Fig. 3.1.A General n th Tray Total mass balance:

Fig. 4
Fig. 4.2.Product qualities depending on change of feed rate

Fig. 6
Fig. 6.1.MRAC block diagram Simulation program is constructed using Maltab Simulink with the following data: Process Plant:

Table 2
.1.Manipulated variables and controlled variables of a distillation column Selecting a control structure is a complex problem with many facets.It requires looking at the column control problem from several perspectives:Local perspective considering the steady state characteristics of the column.
The relative volatility of component i with respect to component j is defined as:

Table 2
.7.Material and Energy Balances for Stripping Section

Table 2
Table 2.8.Material and Energy Balances for Rectifying Section Calculate the internal reflux flow L 0 : Energy balance, INLET=OUTLET: Total light fraction + L 14.047 (ton/h) LL L Calculate the external reflux flow L: Enthalpy data of reflux flow L looked up the experimental chart for petroleum enthalpy are corresponding to the liquid state of 40 °C (liquid inlet at the top tray) and the vapor state of 46 °C (vapor outlet at the column top).L inlet at 40 °C: H liquid(inlet) = 22 kcal/kg; L outlet at 46 °C: H vapor(outlet) = 106 kcal/kg.Then, liquid holdups on each tray, condenser, and the re-boiler are constant and perfectly mixed (i.e.immediate liquid response, ( N LLL . The steady-state solution is determined with dynamic simulation.Figure4.1 displays the concentration of the light component x n at each tray and Table4.2shows the steady state values of concentration of x n on each tray.

Lyapunov Matrix:
It is assumed that the reduced-order linear model in equation (11) can also maintain the similar steady state outputs as the basic nonlinear model.Now this model is used as an MRAC to take the process plant from these steady state outputs (  0.9654 Bx