Study And Application On The Nonlinear Improvement Of P-graph Theory In Process Routes Selection

P-graph theory, based on graph theory, is a high efficient tool of process network synthesis. The advantage of P-graph theory includes:rigorous superstructure generation with axiom, logic constraint support, redundant structures elimination with algorithm, friendly modelling process etc. So P-graph theory is designed to deal with complicated process network synthesis which includes many sub-structures and their combinations. However, nonlinear constraints are not supported in the inner layer of P-graph theory by far and further application of this theory is restricted. This work provides a methodology to add nonlinear constraints into inner layer of P-graph theory by using Lagrangian linear interpolation. And a biomass energy synthesis case study is introduced into this paper to prove the validation of the nonlinear improvement.A nonlinear improvement based on Lagrangian linear interpolation is provided in the second chapter. Firstly, the modelling framework, mathematical definition and axiom constraints of P-graph theory are reviewed. And an equivalent mathematical programming form of P-graph is presented. Secondly, based on the engineering background of P-graph theory, two kinds of nonlinear constraints are put forward and the corresponding method based on Lagrangian linear interpolation is presented. Thirdly, an improved P-graph theory modelling framework is developed. The algorithm module is programmed by Python and pns_solver is invoked to finish the solving process. The method dealing with nonlinear constraint in P-graph can be packaged as an extended module and integrated into P-graph modelling framework to enlarge the application scope of P-graph theory.A industrial case study of biomass energy synthesis which contains nonlinear constrints is presented in the third chapter.Firstly, the modelling construction process is presented with P-graph tool and the optimized result is pursued in P-graph Studio to determine the most profitable process route. Secondly, in the calculation.of equipment cost, production scale index method is adopted. The nonlinear model is processed with the method presented in the second chapter and a 10%-50% production cost can be saved by choosing the appropriate equipment size. Furthermore, environment impact is also taken into consideration. A dual objective P-graph model is constructed and a series of candidate solutions are obtained with the help of the character of maintaining the feasible solutions in P-graph Studio. An economy-environment dual objective curve is diagramed to assist the engineering decision with the environmental assessment.An extended application of P-graph theory about technical parameter selection is presented in the last chapter. In the real engineering process design, technical parameter selection optimization is part of process routes selection. In this chapter, the process of light hydrocarbon recovery is introduced. And the area of membrane and the number of distillation plates can be varied simultaneously. With the help of the combination character of P-graph theory, tedious repeatable work is eliminated. With the help of logic constraint, the number of combination is reduced from 137 to 45 and a set of minimum cost process parameters is obtained. Furthermore, this extended application can be used in other process parameter selection.