Applications of P-Graphs for Enhancing Sustainability of Industrial Plants

The consideration of sustainability in the design and operation of industrial processes is becoming a key issue of process systems engineering. There are Mathematical Programming (MP) tools for designing chemical processes by both maximizing the profit and minimizing the costs. These MP formulations are usually highly complex in solving practical problems. Therefore, the original problems are usually decomposed into smaller ones, solved sequentially.

Unfortunately, these MP-based approaches cannot be adopted for designing sustainable processes for at least two reasons: (i) the consideration of sustainability makes the originally complex problem even more complex; (ii) the decomposition of the model (and problem) may produce inadequate results. Therefore, for designing sustainable processes, the methodology must be highly effective and capable of integrating the subproblems of the overall design problem.

The issue of complexity

The complexity of synthesizing process systems and those for energy recovery in particular, in the form of flowsheets, arises from the simultaneous involvement of continuous as well as discrete entities. The combinatorial complexity increases exponentially with the number of candidate operating units. The larger the number of candidate units for the system, the greater the number of possible combinations. MP has achieved only moderate success in reducing the search space, and therefore, the deployment of the approach based on MP becomes increasingly difficult as the size of problems enlarges: (i) as the size of an algebraic optimization problem grows, it is destined to become impossible for any available solver to examine the combinations of the values of integer variables from the topological point of view; and (ii) an enormous number of topological options makes it rather difficult to build the superstructures necessary for solving the problem. Consequently, practical problems are too complex to be solved. If the problem is excessively simplified so that it is solvable by MP, the resultant problem may no longer adequately represent the original one.

Process optimization applications - energy conversion and recovery

The extent of climate change depends on the concentrations of CO₂ and other greenhouse gases in the atmosphere. From the energy perspective, therefore, the enhancement of the industry's sustainability mainly necessitates the reduction of CO₂ in terms of emission from manufacturing. Three major means are available for reducing CO₂ emissions. These include improving energy conversion efficiency, increasing the CO₂ recycling via the use of biofuels, and CO₂ sequestration (Kleme? et al., 2007; Varbanov et al., 2008).

The first area of interest is elevating the efficiency for power generation, especially through combined heat and power (CHP) generation. This can be achieved by incorporating fuel cells in combined (hybrid) cycles. The fuel cells play the role of the topping cycle, whereas the bottoming cycles can be steam or gas turbine subsystems. Various operating modes are possible to achieve increased energy conversion efficiency as well as wide ranging power-to-heat ratios.

The second area of interest is the design of energy efficient processes. Many processes, e.g., distillation and evaporation often constituting the core of any process system, are energy intensive, thus requiring large amounts of energy. Heat integration has been the preferred method of achieving savings of utilities in addition to the reduction in the energy intensity of the core processes.

The classes of problems in the two areas, mentioned above, lead to process-synthesis formulations involving network optimization, which is characterized by significant combinatorial complexity. Initial systematic approaches to circumventing such complexity resorted to a combination of thermodynamic targeting and a heuristic design procedure by means of Process Integration (PI) or Mathematical Programming (MP). The latter represents the selection of the operating units via integer variables. Flexibility requirements have been added to the design problems by recognizing the inherently time-varying nature of process operation due to changing ambient conditions, worker shifts, and market supply-demand balances. The multi-period optimization paradigm has emerged from the methodologies for synthesizing flexible HENs based on an MILP model; see Floudas and Grossmann (1986). MP has also been applied to this problem by Aaltola (2002). Ahmad et al. (2008) have adopted Simulated Annealing.

P-graph framework

The P-graph framework has been developed for systematic design of industrial processes (Friedler et al., 1992, 1995, 1996) to maximize the profit or minimize the costs. This approach proved to be effective in solving industrial-scale problems. Later, it has been extended to the simultaneous solution of formerly sequentially solved problems, e.g. simultaneous synthesis of a process and its heat exchanger network (Nagy et al., 2003), and simultaneous synthesis of separation and heat exchanger networks (Heckl et al., 2005). In the present work the P-graph framework has been extended to consider sustainability indicators in designing industrial processes.

Major challenges and limitations of MP for multi-period HEN synthesis can be effectively overcome by resorting to P-graphs (process graphs). The present work explores the application of an advanced approach to the HEN synthesis based on hP-graphs rooted in the P-graph framework. This framework offers a highly viable alternative to the MP framework in circumventing the combinatorial complexity of the problems by judiciously exploiting their network characteristics.

References

Aaltola J., 2002. Simultaneous synthesis of flexible heat exchanger networks. Appl Therm Engng, 22(8):907?918.

Ahmad M.I., Chen L., Jobson M., Zhang N., 2008. Synthesis and optimisation of heat exchanger networks for multi-period operation by simulated annealing. Proceedings of PRES2008/CHISA2008, Prague, 4:1200

Floudas C.A., Grossmann I.E., 1986. Synthesis of Flexible Heat Exchanger Networks for Multiperiod Operation. Comp Chem Engng, 10(2):153-168.

Friedler F., Tarjan K., Huang Y.W., Fan L.T., 1992. Graph-Theoretical Approach to Process Synthesis: Axioms and Theorems. Chem. Eng. Sci., 47(8):1972-1988.

Friedler F., Varga J.B., Fan L.T., 1995. Decision-Mapping: A Tool for Consistent and Complete Decisions in Process Synthesis. Chem. Eng. Sci., 50, 1755-1768.

Friedler F., Varga J.B., Fehér E., Fan L.T., 1996. Combinatorially Accelerated Branch-and-Bound Method for Solving the MIP Model of Process Network Synthesis. In State of the Art in Global Optimization, Ed. Floudas, C.A. and Pardalos, P.M., Kluwer Academic Publishers, Boston, Mass, 609-626.

Heckl I., Friedler F., Fan L.T., 2005. Integrated Synthesis of Optimal Separation and Heat Exchanger Networks Involving Separations Based on Various Properties, Heat Transfer Engineering, 26(5), 25-41.

Kleme? J.; Bulatov I., Cockeril T., 2007. Techno-Economic Modelling and Cost Functions of CO2 Capture Processes. Computers & Chemical Engineering, 31(5-6):445-455.

Nagy A.B., Adonyi R., Halasz L., Friedler F., Fan L.T., 2001. Integrated Synthesis of Process and Heat Exchanger Networks: Algorithmic Approach. Appl. Therm. Engng, 21:1407?1427.

Varbanov P., Friedler F., 2008. P-graph Methodology for Cost-Effective Reduction of Carbon Emissions Involving Fuel Cell Combined Cycles. Applied Thermal Engineering, 28(16): 2020-2029.