uses matrix representation to solve the
flowsheet by solving each set of equations for
each unit in order of which they appear in the
flowsheet.
1. Guess values for stream 4
2. Using these values, solve for streams 2, 3, 5 and new set of
values for stream 4
3. Modify the guessed values for stream 4
4. Redo the flowsheet calculations until calculated values are
equal to the guessed values for stream 4
5. When the two values are essentially the same, the procedure is
said to have converged
What is essentially equal? When comparing the guessed value and calculated value for stream 4, a
‘tolerance’ or ‘ԑ’ value may be set as an acceptable accuracy (10-3 , 10-7 etc.)
Successive substitution
ADV: simple, easy to implement
DIS: may diverge (unlikely), very
slow rate of convergence
Convergence acceleration techniques
ADV: faster convergence
DIS: possible divergence,
more complex
implementation
Equation
Oriented
uses matrix representation of material and
energy balance problems to solve the flowsheet.
It solves the equations simultaneously.
occurrence matrix
When the matrix is square, the degree of freedom
is zero – this means the number of equations is
equal to the number of variables, hence a solution
can be sought.
Jacobian matrix (refer to slides on equation solving methods) to find a solution.