Optimization of wastewater treatment design under uncertainty and variability

by Jr. Doby, Troy Alvin

DOBY, JR., TROY ALVIN. Optimization of Wastewater Treatment Design under Uncertainty and Variability. (Under the direction of John W. Baugh, Jr.) The objective in domestic wastewater treatment is to provide a low cost process that is reliable meeting effluent quality standards. Designers using traditional steadystate design and modeling of domestic wastewater treatment plants use scalar values as inputs. The inputs are typically of two types – (1) design loadings based on historical data and (2) stoichiometric and kinetic parameters based on literature values. Using the traditional design approach, there is no way of knowing a priori the reliability of the design or whether the design is least cost. Designers using deterministic optimization and modeling of domestic wastewater treatment plants also use the two types of scalar inputs as with traditional design. While the designer may now know that the design is least cost given the inputs, there is no way of knowing a priori whether the design is the most reliable for the cost. It is possible to take an existing design – whether obtained by traditional design methods, deterministic optimization, or by any other design method – and determine the reliability of the design. To do so, however, requires characterization of both uncertainty and variability of the data. Uncertainty arises because of a lack of knowledge about an input value and its statistical distribution. Variability arises because of the heterogeneity of the processes determining the input value and its statistical distribution. In a case study developed herein, the historical input loadings are presented and the variability is characterized. The characterization of the load variability is then used for future predictions of behavior. The stoichiometric and kinetic parameter values for the particular case are not typically known and thus are uncertain. An approach to quantifying the uncertainty of these values is proposed. Different loading criteria (based on percentiles of historical flow and waste concentration data) are used in deterministic optimization. It is determined that the higher the flow percentile, the more expensive the design. However, a more reliable design could be found at a lower cost and at a lower flow percentile. A different design procedure using stochastic programming is illustrated taking both cost and reliability into account during the design procedure. As a result, a reliability-cost tradeoff curve is generated. This curve is characterized by (1) a steep portion where slight increases in cost lead to large improvements in reliability; and (2) a flat portion where large increases in cost lead to small improvements in reliability. This design procedure also allows determination of the value of an experimental program characterizing the uncertainty and variability of the stoichiometric and kinetic parameters and their statistical distribution. This proposed methodology allows the designer to choose for a level of uncertainty in stoichiometric and kinetic parameter the design values with an optimum cost-reliability tradeoff. This proposed methodology also shows the value to the owner of reducing the uncertainty level by experimentally determining the stoichiometric and kinetic parameter values. Optimization of Wastewater Treatment Design under Uncertainty and Variability by Troy Alvin Doby, Jr. A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Department of Civil Engineering Raleigh 2004 Approved By: Dr. J. W. Baugh, Jr. Chair of Advisory Committee Dr. F. L. de los Reyes, III Dr. S. R. Ranjithan Dr. E. D. Brill, Jr. Dr. D. H. Loughlin Dr. S. K. Liehr