Material balance algebraic techniques

Step 8 Solve the Equations. Many material balances can be stated in terms of simple algebraic expressions. For complex processes, matrix-theory techniques and extensive computer calculations will be needed, especially if there are a large number of equations and parameters, and/or chemical reactions and phase changes involved. 

Block 6 solves the 5 overall tray material balances and 5 tray energy balances. These are linear coupled algebraic equations that can be conveniently solved simultaneously by matrix techniques. 

Material and energy balances are the primary tools of chemical engineers. Such balances applied to multistage or multicomponent processes result in sets of equations that can be either differential or algebraic. Often the systems under analysis are nonlinear, thus resulting in sets of nonlinear equations. However, many procedures have been developed that linearize the equations and apply iterative convergence techniques to arrive at the solution of the nonlinear systems. 

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