Flowsheeting optimisation

Chen, C.L., A Class of Successive Quadratic Programming Methods for Flowsheet Optimisation. PhD Thesis, (Imperial College, London, 1988). 

Optimisation in flowsheeting implies by principle several variables, because a mono-variable optimisation can be solved easily by a sensitivity study. A flowsheeting optimisation problem is always constraint. Firstly, there are equality constraints, as for example the material and heat balances, but also phase equilibrium conditions, as the equality of component fligacities. Secondly, there are inequality constraints. Usually these consist of bounds on temperatures, pressures, flow rates, and concentrations, but they can express also performance limits, as minimum reflux ratio, temperature approach in heat exchangers, etc. 

The description of the optimisation techniques is outside the scope of this work. An excellent introductory tutorial can be found in the book of Biegler, Grossmann and Westerberg (1997). As a general reference we recommend the work of Himmelblau and Edgar (1988). Here we only mention that the most efficient algorithm in flowsheet optimisation is based on Successive Quadratic Programming (SQP). 

Flowsheet optimisation can provide significantly better designs at modest cost during the early stages of design. Modular flowsheeting systems dominate the market and are used by much of the design community. 

Schmid, C. and Biegler, L.T., 1994, A simultaneous approach for flowsheet optimisation with existing modelling procedures. Trans. IchemE, 72, 382-388. 

The book begins in Chapter 1 with the cornerstone of any process design, the development of mass and energy balances, based on the simple conservation principle. From such balances a chemical engineer will then go on to add more detail in order to come up with a fully optimised process flowsheet, providing the most efficient, safe and economic route to the production of the specified chemicals within the constraints of thermodynamics, material properties and environmental regulations. All chemical processes are dynamic in nature, involving the... 

The two last years was marked by working diagram, the initial benchmark flowsheet. This result will enable the technological teams (chemical engineering at Marcoule, energy at Cadarache and materials at Saclay and Grenoble) to start working in on the optimisation of systems and components. 

In the past, the development of a new process has been described often as a kind of art . The strategy, called sometimes the engineering method, consisted of sketching a simple but Inspired flowsheet, and improving it by successive layers of refinements, up to final optimisation. The experience of the designer, the expertise of the company, and the availability of pilot data were crucial. 

IPD consists of developing alternatives rather than a unique flowsheet. The selected solution fulfils at best the optimisation criteria and the environment of constraints. 

Process synthesis by superstructure optimisation consists of the identification of the best flowsheet from a superstructure that considers many possible alternatives, including the optimal one. Set in this term, the approach seems extremely complicated. An obvious theoretical advantage would be that allows the designer to consider simultaneously the synthesis and integration problems. Another practical advantage is the automation of the design process. However, there are two major difficulties ... 

Flowsheeting analysis tools enable to get more value from the simulation results. The most used is the sensitivity analysis. This consists usually of recording the variation of some sampled variables as function of manipulated variables. The interpretation of results can be exploited directly, as trends, correlation or pre-optimisation. Case studies can be employed to investigate combinations (scenarios) of several flowsheet variables. Finally, the simulation work may be refined by multi-variable optimisation. 

It may be concluded that Sequential-Modular approach keeps a dominant position in steady state simulation. The Equation-Oriented approach has proved its potential in dynamic simulation, and real time optimisation. The solution for the future generations of flowsheeting software seems to be a fusion of these strategies. The release 11.1 of Aspen Plus (2002) incorporates for the first time EO features in the environment of a SM simulator. 

In Computer Aided Operation we can mention the real time monitoring of material and energy balance, managed nowadays by means of data reconciliation programs. The plant operation can be adapted and optimised in real time by means of computerised tools based on dynamic flowsheeting. Other advanced applications are simulators for safety studies and operator training. 

Optimisation is an advanced feature in flowsheeting. The first step is the formulation of an objective function, which may be of technical or economic nature. In the first category we may cite the yield of transformation of raw materials in products, the energy consumed or saved in a process, the amount of emissions or impurities, etc. An economic function can be the total operation cost, the profit, or a measure of profitability, as the rate of return on investment (see Chapter 15). 

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 ... 

Figure 3.41 illustrates the optimisation of a flowsheeting problem in a two dimensional space. Contours of the objective function F are plotted, where the two variables x, and Xj are bounded by upper and lower values. The overall heat and... 

We conclude this section with some remarks concerning the optimisation of a flowsheeting problem ... 

Optimisation of the flowsheet is the ultimate goal. This task is difficult, and should be preceded by careful analysis regarding the definition of the objective function and its sensitivity to different variables. 

Assembly the final flowsheet from the partial separations. Optimise the design. 

The key result of the Hierarchical Approach is the development of the basic flowsheet structure, formed by Reactor-Separations-Recycles. This structure defines the material balance envelope. In this respect of highest importance is the behaviour of the reaction system, which should deliver a realistic image of the reaction mixture. Other constraints regarding the reactor operation, as molar ratio of reactants, or safety requirements, are determinant for the structure of recycles. Optimal conversion represents a complex optimisation problem between the valorisation of raw materials and the cost of reactor, separators and recycles. 

From competing alternatives select a good base case and improve it by using the techniques of Process Integration. Determine targets for utilities, process water and mass separation agents, as well as for the equipment design. Optimise the final flowsheet. 

Grossmann IE. A modelling decomposition strategy for MINLP optimisation of process flowsheets. Comput Chem Eng 1989 13 797. 

Equation 4 was discretised by a 5-point central difference formula and thereafter first-order differential equations 1, 2, 4 and 6 were solved by a backward difference method. Apparent reaction rate was solved by summing the average rates of each discretisation piece of equation 4. The reactor model was integrated in a FLOWBAT flowsheet simulator [12], which included a databank of thermodynamic properties as well as VLE calculation procedures and mathematical solvers. The parameter estimation was performed by minimising the sum of squares for errors in the mole fractions of naphthalene, tetralin and the sum of decalins. Octalins were excluded from the estimation because their content was low (<0.15 mol-%). Optimisation was done by the method of Levenberg-Marquard. 

Figure 5.1 Simplified flowsheet showing the role of computer software and simulations in the selection, sizing and optimisation of solid/liquid separation equipment.

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