# (620c) A Mathematical Programming Formulation for the Synthesis of Property-Based of Batch Water Network

- Conference: AIChE Annual Meeting
- Year: 2011
- Proceeding: 2011 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Wednesday, October 19, 2011 - 6:00pm-8:00pm

The search for the efficient utilization of natural resources has driven to the development of new strategies that are focused in solving problems that arise in chemical process industry; some of these strategies that have received considerable attention are the mass integration strategies. Usually, mass integration strategies aim to optimize the allocation, transformation, and separation of species and streams. An important class of mass integration problems deals with the synthesis of networks that allow the recycle and reuse of process sources to minimize the consumption of fresh sources and waste discharges, the mass integration techniques for recycle/reuse can be classified into two categories, methodologies that use the principles of pinch analysis and methods based on mathematical programming, it should be noted that in many of the reported methods based on mathematical programming, the model formulation for the synthesis of recycle/reuse networks have ignored the fact that environmental and process constraints do not depend only on compositions and flows of the streams, but also on properties such as pH, density, viscosity, toxicity, color, and theoretical oxygen demand. Recently there has been some research works based on mass and property integration, however, the vast majority has been devoted to processes that operate under a continuous regime leaving aside processes that can be classified as batch processes.

This work presents a mathematical programming model for the synthesis of a property-based regeneration batch water network. The batch network is represented as a state-task network with a stated horizon time over which states and tasks are allocated, states are represented by buffer tanks whereas property interceptor units are tasks. The model includes mass and property balances in process sinks (process equipment), waste disposal (discharges to environment) and it is based on mass and property integration. In addition, mass balances in states throughout the horizon time are formulated, which take into account mass retention in current and previous periods of time, the model is also formulated in such way that both process and environmental constraints imposed by process sinks and environmental regulations respectively are met, properties constrained by sinks include composition, density, viscosity, pH, on the other hand properties constrained by the environment include composition for hazardous materials, toxicity, chemical oxygen demand. The objective function consists in the minimization of the total annual cost for the batch water network, which includes: Cost of fresh sources, cost of the units for treatment of properties, cost of the buffer tanks, cost of buffering in tanks during periods throughout the horizon time and cost of treatment of properties in the treatment units. To ensure an optimal solution in the objective function of the mathematical model formulation, this is based on a new superstructure that eliminates most of the non convex terms. The solution provides an optimal planning of tasks in the batch network, and the results show that the strategy of property-based regeneration water networks applied to the treatment of properties in continuous processes can be extended to processes that operate under a batch regime without problems.