Your ASPEN PLUS system may contain a flow sheet module named Batch-Franc which does a batch distillation. If it isn't appropriate for your system you can construct user defined modules and put the batch fractionation and heat transfer in them. ASPEN offers a different software special for batch distillation, but maybe with a separate license.
I like to write user defined modules in Fortran which is part of ASPEN PLUS, and sometimes develop or modify custom modules in the CUSTOM MODELER which is a separate license. Excel spread sheets can be inserted into ASPEN PLUS but they must be redefined each time an update is applied to Excel or ASPEN.
With a Fortran subroutine calculation you can control the methods and data transfers. The Fortran interpreter is part of ASPEN PLUS and contains nearly every command you need. Occasionally with elaborate data structures your ASPEN run result may ask you to buy the compiler separately, but this can be avoided by minor change of methods in using the interpreter.
Kindly go through the text if it can help. You can use both inbuilt model and the custom model as suggested by the Jerry Decker. In case of for custom modeler you need to have licence and if You don't have licence then can divide your problem in the sub-problem based on the module present the ASPEN which represent the process as desired.
From a mathematical view point, as I guess, the simulation will be based on the solution of ordinary differential equations with given initial conditions. I assume that these equations you have, and you know the value of their coefficients. In this case, you need only procedure code of numerical equations integration. You can do this yourself by writing code in any programming language such as BASIC or FORTRAN. Of course you will need a compiler. Depending on the stiffness of the equations you may use the constant-step e.g Runge Kutta IV or variable-step method e.g Merson - possibly one of the implicit method as Gear method.
All these methods of course you will find in the software Mathematica, MATLAB, CHEMCAD etc.
I advise also try using EXEL. Typing in the first column: time and in subsequent columns: =right side of eqations * delta (t) and multiplying, you get a solution in the simplest method as Euler.
Very simple example: dy/dt = -y, y(0)=1
column A A1: 0, A2: =A1+step, column B B1: 1, B2: = B1+(-B1)*step, and then multiply to required time.
In this case, use a small step-values, eg. 0.01 or 0.001, which of course increases the computation time, but does not require additional software.
Worse, if the calculation of coefficients needs databases use. Then only Aspen or CHEMCAD.
Numerical methods use numbers. It does not matter what the physical quantities we have to deal with. EXEL is easily accessible and convenient for simple problems - a few differential equations, explicit form of their right sides. Euler method suited almost always. Everything depends on the step of integration. It's a convenient alternative, which, however, is no substitute for profesional software. I personally wrote most of the software yourself (in BASIC, FORTRAN and PASCAL). It requires practice, but I knew how and what calculated.
I'm trying to simulate aerobic bio-reaction (enzyme growth) in a batch reactor in ASPEN PLUS. I have read and they suggest ASPEN BEST but don't have it. Any suggestion on which other model I can use in the basic ASPEN PLUS V9?