Equation-Oriented Architectures

To construct equation-oriented models for an entire process, it becomes important to identify specifications that are consistent, avoiding overspecifying or underspecifying subsets of the equations. When convergence is not achieved, facilities are provided to examine the values of selected variables and the residuals of selected equations. This requires well-designed programs that can display subsets of variables and equation residuals. 

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In the period 1970-80 s the major engineering bureaus, as well as some large manufacturing companies in refining and petrochemical industries developed in-house flowsheeting programs. Mostly adopted the modular sequential architecture. However, some were based on the equations oriented approach, as SPEEDUP at Imperial College in London (UK) and TISFLO at DSM in The Netherlands. 

In Simultaneous-Modular approach the solution strategy is a combination of Sequential-Modular and Equation-Oriented approaches. Rigorous models are used at units level, which are solved sequentially, while linear models are used at flowsheet level, solved globally. The linear models are updated based on results obtained with rigorous models. This architecture has been experimented in some academic products. 

In Equation-Oriented (EO) approach the software architecture is close to a solver of equations. EO is more suited for dynamic simulation since this can be modelled by a system of differential-algebraic equations (DAE) of the form ... 

Figure 2.9 Software architecture of an Equation-Oriented simulator...

Flowsheeting is still dominated by the Sequential-Modular architecture, but incorporates increasingly features of the Equation-Oriented solution mode. A limited number of systems can offer both steady state and dynamic flowsheeting simulators. 

The algorithmic treatment depends on the architecture of the flowsheeting system. In Equation-Oriented mode, the approach consists of solving all the equations describing the problem simultaneously. In Sequential-Modular approach the mathematical solution must take into account the convergence of units and tear streams, as well as of all design specifications. Supplementary equations must be added, so that the general formulation of the optimisation problem (3.10) becomes ... 

This equation cannot be reduced further unless we assume some specific gel architecture and some rule on how DNA distributes in the pores. For instance, with a distribution of pore sizes, one has since the field-induced orientation of a tube section of length a. is expected to be proportional to qE, the electric force on the end-segment that created this tube section. Therefore, Eq. (10) cannot be treated easily in general. 

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