Equations process simulation programs

The UNIQUAC equation is not given here as its algebraic complexity precludes its use in manual calculations. It would normally be used as a sub-routine in a design or process simulation program. For details of the equation consult the texts by Reid et al. (1987) or Walas (1984). 

Design of extraction processes and equipment is based on mass transfer and thermodynamic data. Among such thermodynamic data, phase equilibrium data for mixtures, that is, the distribution of components between different phases, are among the most important. Equations for the calculations of phase equilibria can be used in process simulation programs like PROCESS and ASPEN. 

Equation (9.1) is the preferred method of describing membrane performance because it separates the two contributions to the membrane flux the membrane contribution, P /C and the driving force contribution, (pio — p,r). Normalizing membrane performance to a membrane permeability allows results obtained under different operating conditions to be compared with the effect of the operating condition removed. To calculate the membrane permeabilities using Equation (9.1), it is necessary to know the partial vapor pressure of the components on both sides of the membrane. The partial pressures on the permeate side of the membrane, p,e and pje, are easily obtained from the total permeate pressure and the permeate composition. However, the partial vapor pressures of components i and j in the feed liquid are less accessible. In the past, such data for common, simple mixtures would have to be found in published tables or calculated from an appropriate equation of state. Now, commercial computer process simulation programs calculate partial pressures automatically for even complex mixtures with reasonable reliability. This makes determination of the feed liquid partial pressures a trivial exercise. 

Close to the critical conditions, these equations should not be used. The procedure for calculation of polytropic work of compression or expansion close to the critical point is more complex (Shultz, 1962), and it is easiest to make such calculations using process simulation programs. 

When there are multiple recycles present, it is sometimes more effective to solve the model in a simultaneous (equation-oriented) mode rather than in a sequential modular mode. If the simulation problem allows simultaneous solution of the equation set, this can be attempted. If the process is known to contain many recycles, then the designer should anticipate convergence problems and should select a process simulation program that can be run in a simultaneous mode. 

As in Example 4, the EXTRACT block in the Aspen Plus process simulation program (version 12.1) is used to model this problem, but any of a number of process simulation programs such as mentioned earlier may be used for this purpose. The first task is to obtain an accurate fit of the liquid-liquid equilibrium (LLE) data with an appropriate model, realizing that liquid-liquid extraction simulations are very sensitive to the quality of the LLE data fit. The NRTL liquid activity-coefficient model [Eq. (15-27)] is utilized for this purpose since it can represent a wide range of LLE systems accurately. The regression of the NRTL binary interaction parameters is performed with the Aspen Plus Data Regression System (DRS) to ensure that the resulting parameters are consistent with the form of the NRTL model equations used within Aspen Plus. 

Use the marginal vapor rate (MV) method to determine a sequence for the separation of light hydrocarbons specified in Figure 7.12a, except (1) remove the propane from the feed, (2) ignore the given temperature and pressure of the feed, and (3) strive for recoveries of 99.9% of the components in each column. Use a process simulation program, with the Soave-Redlich-Kwong equation of state for if-values and enthalpies, to set top and bottom colunm pressures and estimate the reflux ratio with the Underwood equations. 

Process simulation programs are preferred to compute the theoretical and brake horsepower requirements, as well as the exit temperature, of a compressor because the ideal gas law is not usually applicable for pressures above two atmospheres. However, Eq. (16.30) can be used to obtain a preliminary estimate of the brake horsepower. An estimate of the exit temperature, including the effect of compressor efficiency, can be made with the following modification of the equation for the isentropic exit temperature ... 

Initially, most engineers wrote their own programs to solve both the nonlinear algebraic equations that describe the steady-state operation of a distillation column and to numerically integrate the nonlinear ordinary differential equations that describe its dynamic behavior. Many chemical and petroleum companies developed their own in-house steady-state process-simulation programs in which distillation was an important unit operation. Commercial steady-state simulators took over about two decades ago and now dominate the field. 

Chapter 5 gives a comprehensive overview on the most important models and routes for phase equilibrium calculation, including sophisticated phenomena like the pressure dependence of liquid-liquid equilibria. The abilities and weaknesses of both models and equations of state are thoroughly discussed. A special focus is dedicated to the predictive methods for the calculation of phase equilibria, applying the UNIFAC group contribution method and its derivatives, that is, the Mod. UNIFAC method and the PSRK and VTPR group contribution equations of state. Furthermore, in Chapter 6 the calculation of caloric properties and the way they are treated in process simulation programs are explained. 

For process simulation applications, a high accuracy is often required, especially when components with similar vapor pressures have to be separated in distillation columns. When a parameter database is set up. for example, the one in a commercial process simulation program, it cannot be known in advance at which conditions exact vapor pressures will be required. The advantage of the Antoine equation is its simplicity in contrast to many other vapor pressure equations it can easily be converted into a temperature-explicit equation. However, it cannot be applied for the whole temperature range from the triple point to the critical point. In these cases, more capable vapor pressure correlations are recommended, that is, the extended Antoine equation and the Wagner equation. 

Sometimes, users of process simulation programs calculate vapor pressures beyond the critical point, although it is physically meaningless. If the Wagner equation is applied above the critical temperature, it will yield a mathematical error. Therefore, the simulation program must provide an extrapolation function that continues the vapor pressure line with the same slope [26]. 

Nowadays, in modern process simulation programs the possible electrolyte reactions and the equations for equilibrium calculation are generated automatically. The user only has to check the reactions in order to simplify the chemistry as much as possible, that is, to eliminate equilibrium reactions with extremely high or low equilibrium constants, as in these cases the equilibrium will be completely on one side of the reaction. Considering these reactions as equilibrium reactions will often yield to a drastically increased calculation time and has often a bad influence on the convergence. 

E2. Notation of the Wilson, NRTL, and UNIQUAC Equations in Process Simulation Programs... 

For the use in a process simulator. Eq. (C.242) is not appropriate as an expression for the Wilson equation, as the specific volumes have an influence on the activity coefficients. When the binary parameters Akij are stored, they are related to the specific volumes that were used in the parameter regression run. If the pure component values are changed, maybe due to an improved data situation, the binary parameters would have to be refitted, which is usually not considered by the user. In process simulation programs, the Wilson equation is therefore written in a different way which avoids these disadvantages. Starting with Eq. (C.242), we can write... 

In the past, most simulation programs available to designers were of the sequential-modular type. They were simpler to develop than the equation based programs, and required only moderate computing power. The modules are processed sequentially, so essentially only the equations for a particular unit are in the computer memory at one time. Also, the process conditions, temperature, pressure, flow-rate, are fixed in time. 

Write a simulation program (e.g., in Excel) to solve the system of equations. For the nominal geometry and process conditions, plot the pressure and velocity as a function of 6. Explain the results in physical terms. 

To study different operating conditions in the pilot plant, a steady-state process simulator was used. Process simulators solve material- and energy-balance, but they do not generally integrate the equations of motion. The commercially-available program, Aspen Plus Tm, was used in this example. Other steady-state process simulators could be used as well. To describe the C02-solvent system, the predictive PSRK model [11,12], which was found suitable to treat this mixture, was applied. To obtain more reliable information, a model with parameters regressed from experimental data is required. 

The user specified subroutines allow for connections to various other programs such as process simulators and ordinary differential equation solvers. Currently, MINOPT is connected to the DASOLV (Jarvis and Pantelides, 1992) integrator, and can solve MINLP models with differential and algebraic constraints. 

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