Water Network Optimization with Wastewater Regeneration Models

Abstract

The conventional water network synthesis approach greatly simplifies wastewater treatment units by using fixed recoveries, creating a gap for their applicability to industrial processes. This work describes a unifying approach combining various technologies capable of removing all the major types of contaminants through the use of more realistic models. The following improvements are made over the typical superstructure-based water network models. First, unit-specific shortcut models are developed in place of the fixed contaminant removal model to describe contaminant mass transfer in wastewater treatment units. Shortcut wastewater treatment cost functions are also incorporated into the model. In addition, uncertainty in mass load of contaminants is considered to account for the range of operating conditions. Furthermore, the superstructure is modified to accommodate realistic potential structures. We present a modified Lagrangean-based decomposition algorithm in order to solve the resulting nonconvex mixed-integer nonlinear programming (MINLP) problem efficiently. Several examples are presented to illustrate the effectiveness and limitations of the algorithm for obtaining the global optimal solutions.

Simultaneous Energy and Water Optimisation in Shale Exploration

“…This indicates that the volume of the wastewater tank on each well pad becomes zero at the end of each time point. The concentration of water sent to the treatment unit is given by Equation (14), where c st,ww n is the contaminant concentration in the treatment unit at time point n. The capacity of the treatment wastewater tank v ww n at time point n is bounded by the volume of flowback water f reg n to be treated at time point n, as given in Equation (15). Equations (16)- (18) ensure that the maximum capacity of the tank is not exceeded, where V max and V min are parameters that indicate the maximum and minimum capacity of the wastewater storage tank, respectively.…”

“…The capacity of the treatment wastewater tank w w n v at time point n is bounded by the volume of flowback water re g n f to be treated at time point n, as given in Equation (15). Equations (16)- (18) ensure that the maximum capacity of the tank is not exceeded, where m a x V and m in V are parameters that indicate the maximum and minimum capacity of the wastewater storage tank, respectively.…”

“…Assuming a fixed schedule is a huge drawback, as this has a great effect on the overall profit. In addition, most of the research conducted in this area has represented the wastewater treatment unit as a "black box" which does not give the true cost representation of the project or uses "short cut" regenerator model [15] due to the complexity of the regenerator design.…”

Optimization Models for Process Water Networks and Their Application to Biofuel Processes

“…Based on the superstructure for WN synthesis, Yang et al (2014) presented an approach to incorporate treatment unit models that are common industrial practice to allow for a more thorough understanding of the trade-offs between unit performance and the economics of the WN design. The authors replaced simplified unit models by short-cut models to describe mass transfer in wastewater treatment units.…”

Synthesis of Material Interception Networks with P-Graph

“…The main advantage with mathematical optimization is that, the model may incorporate other considerations that are not readily handled with pinch analysis approaches, such as multiple-contaminant cases (Huang et al 1999), or forbidden recycle (Bagajewicz and Savelski 2001). Later works in this area considered the development of a linear model for global optimum solution (Gabriel and El-Halwagi 2005;Ng et al 2009a, b), detailed modeling for the various source interception units (Yang et al 2014;Mafukidze and Majozi 2016), and extension to property-based network (Ng et al 2009c). The main limitation to these mathematical optimization approaches is that, a single solution is normally reported, unless more constraints are added to the model.…”