Subroutine form

The FCC simulator program was converted to subroutine form a few years ago and incorporated into a nonlinear programming model representing a complex of process units in the Toledo refinery. It is this subroutine version which has been linked with the LP preprocessor. 

The hydrocracker simulator was also converted to subroutine form for inclusion in the nonlinear programming model of the Toledo process complex. The subroutine was considerably simplified, however, to save computer time and memory. The major differences are (1) the fractionation section is represented by correlations instead of by a multi-stage separation model, (2) high pressure flash calculations use fixed equilibrium K-values instead of re-evaluating them as a function of composition, and (3) the beds in each reactor are treated as one isothermal bed, eliminating the need for heat balance equations. 

The reformer simulator was converted to subroutine form for inclusion in nonlinear programming models of two refinery complexes. To save computer time and memory, the subroutine uses a linearized version of the original kinetic model, with 28 components and 33 reactions. Instead of numerical integration, the linearized model is solved analytically at constant temperature, pressure, and total mols using special subroutines to find the eigenvalues and eigenvectors of the reaction rate constant matrix. 

The calculation of vapor and liquid fugacities in multi-component systems has been implemented by a set of computer programs in the form of FORTRAN IV subroutines. These are applicable to systems of up to twenty components, and operate on a thermodynamic data base including parameters for 92 compounds. The set includes subroutines for evaluation of vapor-phase fugacity... 

Subroutine REFUG. This subroutine calculates the liquid reference fugacities. Three options are possible. First, an equation of the form... 

Input and output subroutines to read and echo print data, allocate and initiahze working arrays, and output the final results generally in a form that a post processor can use for graphical representations. 

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... 

The most successful and user-friendly approach, which is now adopted by virtually all commercial systems, is the fill-in-the-forms or table-driven process control languages (PCLs). The core of these languages is a number of basic functional blocks or software modules. AU modules are defined as database points. Using a module is analogous to calhng a subroutine in conventional programs. 

Figure 8 depicts our view of an ideal structure for an applications program. The boxes with the heavy borders represent those functions that are problem specific, while the light-border boxes represent those functions that can be relegated to problem-independent software. This structure is well-suited to problems that are mathematically either systems of nonlinear algebraic equations, ordinary differential equation initial or boundary value problems, or parabolic partial differential equations. In these cases the problem-independent mathematical software is usually written in the form of a subroutine that in turn calls a user-supplied subroutine to define the system of equations. Of course, the user must write the subroutine that defines his particular system of equations. However, that subroutine should be able to make calls to problem-independent software to return many of the components that are needed to assemble the governing equations. Specifically, such software could be called to return in-... 

Perhaps the most important thing to notice is that there is really no need to convert to flowchart form as we did once one gets the "hang" of it, the verificatior can be done directly for the Fortran subroutine. 

This illustrates that the CO2 in solution is predominately in the form of carbamate ion and as CO2 concentration is increased we finally reach a point where sufficient aqueous CO2 is present for the CO2 vapor pressure to increase markedly with fraction of total CO2 in solution. Similar input can be used to create subroutines for a fractionator program and this system is described for such a case in a recent paper (12). 

Table 16.1 gives a FORTRAN program which generates the multivariable Nyquist plot for the Wood and Berry column. The subroutines given in Chap. 15 are used for manipulating the matrices with complex elements. The subroutines PROCTF and FEEDBC calculate the and complex numbers at each value of frequency. A general process transfer function is used for each of the elements in the matrix that has the form... 

EXMATH - An Expert System for Pattern Recognition. A prototype expert system for pattern recognition and data analysis, EXMATH, has been developed to embed a chemometrician s expertise into an accessible form for researchers. The selected library of subroutines developed over the past ten years comprise a portion of the EXMATH program to permit an integrated expert systems approach (Figures 5 and 6). 

The first three subroutines, bubpt, dewpt, and isovfl, are very similar in form. Using an estimated temperature, 2(Ax), 2(i//A), or 2(Uy/ya88umed) together with 2(Z/X/Las,umed) is calculated. This (or these) summation must be within bdferb of unity if not, the temperature is moved by tint (10° originally) in the correct direction until the summation crosses unity. The correct temperature is then estimated by inter-... 

The PFT NMR spectrum can then be recorded in analog or digital form by a plotter controlled by the computer. If the computer core memory allows, additional subroutines may be stored which automatically compute signal intensities and positions (in ppm values relative to some standard or in Hz) and outputs them to the printer. 

The process model is given in Leversund et al. (1993). As the polymer product forms a separate solid phase, this was not included in the process model. The model includes mass and energy balances, column holdup and phase equilibria and results in a set of DAEs. All thermodynamic, physical properties are calculated from library subroutines. The column description and data for the process are given in Table 9.6. 

With this change to the Jacobian generator and a user supplied routine to evaluate the extents of reaction and at the user s option the partial derivatives 3r/3x, 3r/3l, and 3R/3T along with the ECES generated subroutines, this form of process can be successfully modeled. This type of model has been successfully used to simulate proprietary processes developed by our clients. 

Some constraints, such as < >2 use stream variables to describe the thermodynamic state of the working fluid. Numerical values for steam properties are generated using a computer subroutine called STEAM (14). Thus not all constraint equations are in analytical form. 

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