HEAT AND MASS BALANCE USING CONSTRAINT EQUATIONS, A SPREADSHEET, AND THE NEWTON-RAPHSON TECHNIQUE
R. C. Loubser · 2005
To work out a balance problem in a factory, two simple rules are applied. Firstly, a steady state condition applies. This gives rise to the second rule: what goes in must come out. Based on these rules, the equations for heat and mass balances can be derived. There are several packages available to solve these rules or constraints. The choices include Simulink and Sugars. The use of these packages would require the ownership of a software licence. Often it is not cost effective to purchase the licence for a single project. This leaves the choice of solving the problem using a spreadsheet. Once the equations are expressed in terms of brix, fibre, etc, the equations become non-linear, and linear methods of solution such as Gauss-Jordan row reduction are no longer possible. Traditionally, the equations are then manipulated to isolate terms and thereby extract a solution. This approach fails when there are numerous return streams. In this case, the iteration facility of the spreadsheet is used in an attempt to resolve the values that could not be solved explicitly. This paper describes a technique where the constraint equations are entered into the spreadsheet for each point of mixing or separation in the system. The Jacobian matrix can then be constructed using some elementary rules. Thereafter, the power of the spreadsheet matrix functions can be employed to iterate simply to a solution using the Newton-Raphson (or any other applicable) technique. This process eliminates the need to manipulate the constraints to isolate variables, and ensures that the iteration can be handled in an orderly manner.