Design and control degrees of freedom

One oft,he central problems in developing a steady-state process flowsheet is finding the number of variables that must be specified to completely define the process. This number is called the design degrees of freedom. Once this number has been found, the number of design optimization variables can be calculated by subtracting all variables that are set by specifications on production rate, product qualities, safety constraints, and environmental limitations. In principle, the design degrees of freedom are easily calculated by simply subtracting the number of equations from the number of variables. However, for typically complex industrial processes, there are many hundreds of variables and equations, and it is not a trivial job to make sure that the correct variables and equations have been defined. in addition, this conventional variables-minus-equations approach requires that. a detailed model of the process be available. Once the plant has been specified, the design of a control structure requires that the control degrees of freedom be known. This is the number of variables that can be controlled. It is very easy to calculate this number, even for quite complex processes, because it is equal to the number of manipulated variables (the number of control valves in the process). These variables are different than the design optimization variables. This paper illustrates that the number of design degrees of freedom is equal to the number of control degrees of freedom for an important class of processes. For a much broader class of processes a slight modification of this equality must be used. Several progressively more complex recycle process case studies are used to demonstrate these results. The practical significance of this approach is that we do not need a model and we can avoid the tedious and error-prone procedure of accounting for all variables and equations.