Modeling subroutines

Whatever the code used to solve material and energy balance problems, you must provide certain input information to the code in an acceptable format. All flowsheeting codes require that you convert the information in the flowsheet (see Fig. 5.4) to an information flowsheet as illustrated in Fig. 5.5, or something equivalent. In the information flowsheet, you use the name of the mathematical model (subroutine for modular-based flowsheeting) that will be used for the calculations instead of the name of the process unit. 

This is the standard mixture model subroutine for two populations. 

The coupled differential equations are solved numerically by the BD method implemented in the software LSODE. The main program and the model subroutine written in Fortran 90 for the toluene hydrogenation process are listed below ... 

Batch reactor model subroutine batch(ncom,t,c,dcdt) implicit none... 

Subroutine REGRES. REGRES is the main subroutine responsible for performing the regression. It solves for the parameters in nonlinear models where all the measured variables are subject to error and are related by one or two constraints. It uses subroutines FUNG, FUNDR, SUMSQ, and SYMINV. 

The use of the computer in the design of chemical processes requires a framework for depiction and computation completely different from that of traditional CAD/CAM appHcations. Eor this reason, most practitioners use computer-aided process design to designate those approaches that are used to model the performance of individual unit operations, to compute heat and material balances, and to perform thermodynamic and transport analyses. Typical process simulators have, at their core, techniques for the management of massive arrays of data, computational engines to solve sparse matrices, and unit-operation-specific computational subroutines. 

In this section assume a mathematical model is possible for the problem to be solved. The model may be encoded in a subroutine and be known only imphcitly, or the equations may be known explicitly. A general form for such an optimization problem is... 

Turbulence modeling capability (range of models). Eddy viscosity k-1, k-e, and Reynolds stress. k-e and Algebraic stress. Reynolds stress and renormalization group theory (RNG) V. 4.2 k-e. low Reynolds No.. Algebraic stress. Reynolds stress and Reynolds flux. k- Mixing length (user subroutine) and k-e. 

Non-Newtonian modeling capability Choice of models available, user subroutines. Power law. and difficult to implement user subroutines. Choice of models available. Not available. Power law. Bingham. Generalized power law. and user subroutines. 

This is a subroutine that calculates an evaporation rate from a pool of spilled liquid in presence of wind (ORG-40), or in still air (TP-10). It was developed by the U.S. Array for downwind hazard prediction following release from smoke munitions and chemical agents. The code calculates the evaporation rate of a liquid pool, given the physical stale variables, wind speed, and diameter of pool. ORG-40 and TP-10 models are coded as a Fortran 77 subroutine, EVAP4.FOR, in D2PC. The user s manual is Whiiacre (1987). 

The table below illustrates these issues by comparing how a recursive subroutine must handle data which is available from a database, such as the cost of a raw material, data that is calculated for the formulated product, such as PBR, and data for intermediate products. (The variable names shown in the table are part of the example procedure given in the appendix.) Compare with the previous table for a non-recursive modelling procedure s data structure. 

The program can solve both steady-state problems as well as time-dependent problems, and has provisions for both linear and nonlinear problems. The boundary conditions and material properties can vary with time, temperature, and position. The property variation with position can be a straight line function or or a series of connected straight line functions. User-written Fortran subroutines can be used to implement more exotic changes of boundary conditions, material properties, or to model control systems. The program has been implemented on MS DOS microcomputers, VAX computers, and CRAY supercomputers. The present work used the MS DOS microcomputer implementation. 

Dynamic models expressed in terms of transform functions can be solved by digital simulation by transposing the transfer function into an equivalent set of differential equations, as shown by Ord-Smith and Stephenson (1975) and by Matko et al. (1992). Also some languages include special transfer function subroutines. 

For convenience, only four stages were used in this model. An iterative solution is required for the bubble point calculations and this is based on the half-interval method. A FORTRAN subroutine EQUIL, incorporated in the ISIM program, estimates the equilibrium conditions for each plate. The iteration routine was taken from Luyben and Wenzel (1988). The program runs very slowly. 

Declaration which makes the reserved variable available in subroutine/function. Also makes routine a sub-model. 

WASP/TOXIWASP/WASTOX. The Water Quality Analysis Simulation Program (WASP, 3)is a generalized finite-difference code designed to accept user-specified kinetic models as subroutines. It can be applied to one, two, and three-dimensional descriptions of water bodies, and process models can be structured to include linear and non-linear kinetics. Two versions of WASP designed specifically for synthetic organic chemicals exist at this time. TOXIWASP (54) was developed at the Athens Environmental Research Laboratory of U.S. E.P.A. WASTOX (55) was developed at HydroQual, with participation from the group responsible for WASP. Both codes include process models for hydrolysis, biolysis, oxidations, volatilization, and photolysis. Both treat sorption/desorption as local equilibria. These codes allow the user to specify either constant or time-variable transport and reaction processes. 

The next two steps after the development of a mathematical process model and before its implementation to "real life" applications, are to handle the numerical solution of the model s ode s and to estimate some unknown parameters. The computer program which handles the numerical solution of the present model has been written in a very general way. After inputing concentrations, flowrate data and reaction operating conditions, the user has the options to select from a variety of different modes of reactor operation (batch, semi-batch, single continuous, continuous train, CSTR-tube) or reactor startup conditions (seeded, unseeded, full or half-full of water or emulsion recipe and empty). Then, IMSL subroutine DCEAR handles the numerical integration of the ode s. Parameter estimation of the only two unknown parameters e and Dw has been described and is further discussed in (32). 

The adaptive parameters in the model were estimated by nonlinear and multiresponse regression, performed using the Fortran subroutine BURENL23 based... 

Chapter 8 presented the last of the computational approaches that I find widely useful in the numerical simulation of environmental properties. The routines of Chapter 8 can be applied to systems of several interacting species in a one-dimensional chain of identical reservoirs, whereas the routines of Chapter 7 are a somewhat more efficient approach to that chain of identical reservoirs that can be used when there is only one species to be considered. Chapter 7 also presented subroutines applicable to a generally useful but simple climate model, an energy balance climate model with seasonal change in temperature. Chapter 6 described the peculiar features of equations for changes in isotope ratios that arise because isotope ratios are ratios and not conserved quantities. Calculations of isotope ratios can be based directly on calculations of concentration, with essentially the same sources and sinks, provided that extra terms are included in the equations for rates of change of isotope ratios. These extra terms were derived in Chapter 6. 

Fortran, C/C++, Visual Basic, or Delphi. The user provides the model coded as a corresponding subroutine or function. 

The PARROT programme uses the Poly-3 subroutine in Thermo-Calc to calculate Gibbs energies of the various phases and find the equilibrium state. In such equilibrium calculations the temperature, pressiue and chemical potentials are treated as independent variables, and preselected state variables are used to define the conditions for an equilibrium calculation. The dependent state variables, i.e., the responses to the system, can then be given as a function of the independent state variable and the model parameters. It is thus possible to use almost any type of experimental information in the evaluation of the model parameters. 

By the direct coupling of thermodynamic and kinetic models in a single software package, where the kinetic model can call the thermodynamic calculation part as a subroutine for the calculation of critical input parameters. 

Equations (15)-(23) can be solved numerically using a combination of IMSL and NAG library subroutines. The DIVPAG subroutine of IMSL for ordinary differential equations and the D03PAF subroutine of NAG library for partial differential equations may serve the purpose and we applied this method for simulating the results for ELM extraction of CPC [26] and cephalexin [25]. The agreement between model prediction and experimental data was found to be quite reasonable. 

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