Dynamic Optimization for Industrial
Waste Treatment Design
CHI A SHUN SHIH, Research Supervisor
P. KRISHNAN, Project Engineer
Roy F. Weston, Inc.
West Chester, Pennsylvania
INTRODUCTION
The concepts of system analyses and optimization have assumed increased
significance in recent years in various water pollution control activities. System
optimization of wastewater treatment process design has become a very challenging
topic in view of the ever-increasing pollution problem, the rapid development of new
knowledge, and the complexity of the environment.
The purpose of this paper is to present an application of dynamic programming
for the system optimization of an industrial wastewater treatment design. The
optimization procedure for a serial multi-stage system with two-point boundary value
is utilized. The objective of the optimization is to identify the optimum combinations
and efficiencies of various unit processes in a multi-stage treatment plant meeting the
ultimate design requirements.
Designing and optimizing single processes individually has been the basic approach in wastewater treatment process design for many years. This method may
yield the best design for a specific unit process but not necessarily the least-cost design
for the multi-stage system. In addition, new treatment alternatives are now available
for many of the unit processes involved. Thus, a proper optimization analysis must
be applied to secure the optimal selection of process and equipment in terms ot meeting design requirements with minimum costs.
The principles of dynamic programming are reviewed briefly. Then, based on
the wastewater treatment design principles, the economic optimization scheme for
the plant design is formulated with the integration of dynamic programming techniques. A specific case in pulp and paper wastewater treatment is presented for
illustration; the cost functions used in the example are compiled on the basis of
process design and engineering evaluations.
DYNAMIC PROGRAMMING
Dynamic programming is a computation technique based on Bellman's
Principle of Optimality (1). The principle states that an optimal policy has the
property that, whatever the initial state and initial decision, the remaining decisions must constitute an optimal policy with respect to the state resulting from the
initial decision of the system. In contrast to linear programming, there is no
standard formulation of a specific dynamic programming problem. However,
dynamic programming provides a general systematic procedure for the determination
of optimal decisions in solving the problem. The particular equations must be developed for each individual situation (2).
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