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Inconsistent or Ill-Defined Equation Sets


EES users may occasionally encounter the following error message:




or the following warning message:



In order to see the above warning, warnings must be enabled.  This can be done with the $Warning directive or with the Display Warning Messages checkbox in the Options tab of the Preferences dialog must be selected.  


These messages can result in several ways.  One cause is an ill-defined equation set.  A simple example of an ill-defined equation set is:





It is easy to see in this case that the first and second equations are really the same and thus there is only one equation with two unknowns.  EES will issue an error message for this set of equations.   Although this problem commonly occurs, it is rarely so easy to identify.  A more complicated example of an ill-defined equation set is.







EES will likely issue the warning in this case.  


An ill-defined equation set will occur when the user enters a mass or energy balance for each component in a system and then also enters an overall mass or energy balance, which results in a redundancy. An example of a redundancy is demonstrated in the following two equations:


h=enthalpy(Steam,T=T, P=100 [kPa])

T=temperature(Steam, h=h, P=100 [kPa])


The above two equations are redundant since there is only one relation between T and h at P=100 [kPa] for steam, regardless of how it is expressed.  Unfortunately, EES will likely not issue an error message for this situation because the tolerances associated with finding the property data disguise the underlying problem.  


If EES encounters equation sets similar to those above, it may issue an error or warning.  It is also possible that, depending on the guess values, limits, and tolerances, EES will find a solution for the problem that satisfies all of the equations to within the tolerances set in the Stop Criteria dialog.


In some cases, a warning or error can occur when the equations are well-defined, but the guess values do not permit a solution using the numerical methods in EES.  There are several ways to deal with this situation.  The most straightforward way is to change the guess values and/or variable limits using the Variable Information command or the $VarInfo directive and then try to solve the equations again. Viewing the Residuals window may be helpful to see which equations are involved and to see how EES is solving the problem.   


If the block that identified in the error message contains an equation-based Integral, a possible cause of the error message is that the lower or upper limit of the integral is not determined and EES is trying to solve for the limit.   The numerical procedures in EES are not able to solve for the lower or upper limit of an integral.  There are, however, ways to do this as explained in the online help under Finding a Limit of Integration.