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In this work, we address the optimal water management strategies and fair cost distribution among various shale gas companies placed in the same play. A mixed integer non-linear programming (MINLP) formulation with the objective of maximizing the Nash product is presented including the analysis of different policies to determine the most appropriate transportation cost distribution. As a result of Nash product maximization and transfer cost designation formulation, the problem includes non-linearities in the objective function which hinders its resolution. Therefore, to solve the model effectively, we apply logarithmic operation and separable programming approach to reformulate the Nash product and Glover's linearization to reformulate the bilinear terms appearing in the transfer cost designation. Finally, the applicability of the proposed approach is illustrated in a case study comprising 4 companies. Then, an example comprising 10 shale gas companies is performed to analyse the behaviour of the proposed formulation considering a larger problem.

Under the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach.

In this article, we introduce a novel framework for the design of multi set-point nonlinear explicit controllers for process systems engineering problems where the set-points are treated as uncertain parameters simultaneously with the initial state of the dynamical system at each sampling instance. To this end, an algorithm for a special class of multi-parametric nonlinear programming problems with uncertain parameters on the right-hand side of the constraints and the cost coefficients of the objective function is presented. The algorithm is based on computed algebra methods for symbolic manipulation that enable an analytical solution of the optimality conditions of the underlying multi-parametric nonlinear program. A notable property of the presented algorithm is the computation of exact, in general nonconvex, critical regions that results in potentially great computational savings through a reduction in the number of convex approximate critical regions.

A large power generation facility is a complex multi-criteria system associated with multivariate couplings, high dependency, and non-linearity among the operating variables which present a major challenge to ensure efficient power production. In this research, an integrated artificial intelligence (AI) and response surface methodology (AI-RSM) framework to achieve the efficient power production operation of a 660 MW coal power plant is presented. Two AI algorithms, i.e., extreme learning machine (ELM) and support vector machine (SVM) are trained comprehensively on the power plant's operational data and are validated as well. Full factorial design of experiments on the three levels of the operating parameters are constructed and simulated from the better performing AI model which is an effective non-linear representation of the complex power plant operation. RSM analysis is carried out under three power generation scenarios to simulate the effective values of the operating variables which are tested on the power plant's operation and a reasonable agreement is found with the experimental observations. The notable improvement in fuel consumption rate, thermal efficiency, and heat rate of the power plant under Half Load, Mid Load, and Full Load capacity of the power plant is achieved by the AI-RSM framework enabled analyses. It is estimated that annual reduction in CO2, CH4 and Hg emissions measuring 210 kg tons per year (kt/y), 23.8 t/y and 2.7 kg/y, respectively can be obtained corresponding to Mid Load operating state of the power plant. The research presents the reliable and robust utilization of AI-RSM framework for simulating the effective operating conditions for the fossil-based power plants’ operation with an eventual goal to improve the techno-environmental performance which is expected to contribute to net-zero emissions goal from the energy sector.

This work presents a study that aims to compare two discretization methods for solving parameter estimation using multiparametric programming. In our earlier work, parameter estimation using multiparametric programming was presented where model parameters were obtained as an explicit function of measurements. In this method, the nonlinear ordinary equations (ODEs) model was discretized by using explicit Euler’s method to obtain algebraic equations. Then, a square system of parametric nonlinear algebraic equations was obtained by formulating optimality condition. These equations were then solved symbolically to obtain model parameters as an explicit function of measurements. Thus, the online computation burden of solving optimization problems for parameter estimation is replaced by simple function evaluations. In this work, we use implicit Euler’s method for discretization of nonlinear ODEs model and compare with the explicit Euler’s method for parameter estimation using multiparametric programming. Complexity of explicit parametric functions, accuracy of parameter estimates and effect of step size are discussed.

Advanced decision making in the process industries requires efficient use of information available at different decision levels. Traditionally, planning, scheduling, and optimal control problems are solved in a decoupled way, neglecting their strong interdependence. Integrated planning, scheduling and optimal control (iPSC) aims to address this issue. Formulating the iPSC, results in a large scale nonconvex mixed integer nonlinear programming problem. In the present work, we propose a new approach for the iPSC of continuous processes aiming to reduce model and computational complexity. For the planning and scheduling, a Traveling Salesman Problem-based formulation is employed, where the planning periods are modeled in discrete time while the scheduling within each week is in continuous time. Another feature of the proposed iPSC framework is that backlog, idle production time, and multiple customers are introduced. The resulting problem is a mixed integer programming problem and different solution strategi...

Fault detection has become increasingly important for improving the reliability and safety of process systems. This paper presents a model-based fault detection methodology for nonlinear process systems. The objective of this work is to detect faults by estimating the model parameters using multiparametric programming. The parameter estimates are obtained as an explicit function of the measurements by using multiparametric programming. The diagnosis of fault is carried out by monitoring the changes in the residual of model parameters. Case studies of fault detection for a single stage evaporator system and quadruple tank system are presented. A number of faulty and fault-free scenarios are considered to show the effectiveness of the presented approach. The proposed approach successfully estimates the model parameters and detects the faults through a simple function evaluation of explicit functions.

Multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side remains limited and as a result, hybrid, or approximate solution strategies have been proposed in the literature. In this work, a new algorithm is introduced for the exact solution of multi-parametric linear programming problems with simultaneous variations in the objective function's coefficients, the right-hand side and the left-hand side of the constraints. The proposed methodology is based on the analytical solution of the system of equations derived from the first order Karush–Kuhn–Tucker conditions for general linear programming problems using symbolic manipulation. Emphasis is given on the ability of the proposed methodology to handle efficiently the LHS uncertainty by computing exactly the corresponding nonconvex critical regions while numerical studies underline further the advantages of the proposed methodology, when compared to existing algorithms.

Process and energy models provide an invaluable tool for design, analysis and optimisation. These models are usually based upon a number of assumptions, simplifications and approximations, thereby introducing uncertainty in the model predictions. Making model based optimal decisions under uncertainty is therefore a challenging task. This issue is further exacerbated when more than one objective is to be optimised simultaneously, resulting in a Multi-Objective Optimisation (MO2MO2) problem. Even though, some methods have been proposed for MO2MO2 problems under uncertainty, two separate optimisation techniques are employed; one to address the multi-objective aspect and another to take into account uncertainty. In the present work, we propose a unified optimisation framework for linear MO2MO2 problems, in which the uncertainty and the multiple objectives are modelled as varying parameters. The MO2MO2 under uncertainty problem (MO2U2)(MO2U2) is thus reformulated and solved as a multi-parametric programming problem. The solution of the multi-parametric programming problem provides the optimal solution as a set of parametric profiles.

Development of fast, robust and reliable computational tools capable of addressing the process management under uncertain conditions, is an active topic in the current process systems engineering literature. In fact, scenario reduction strategies (for example SCENRED and OSCAR) have acquired a lot of attention to overcome the traditional issues associated to large-scale scenario-based problems. Thus, this work proposes a novel scenario-reduction alternative (henceforth known as SCANCODE approach) by combining Graph Theory to construct a network and community detection methods to identify the clusters within the network. The capabilities and limitations of the proposed approach were tested through the two-stage MILP optimisation of a bio-based energy network under raw material availability and energy demand uncertainties. For comparison purposes, the same problem was solved using the sets of scenarios obtained with SCENRED and OSCAR. This comparison demonstrates the quality of SCANCODE approach while states the potential benefits of the proposed approach over the current alternatives.

Haemodialysis is a blood treatment technique used for patients whose kidneys are not working normally. A number of Linear Model Predictive Control (LMPC) formulations for controlling haemodialysis have been proposed in the literature. In this paper, a Nonlinear Model Predictive Control (NMPC) formulation is proposed that instead of using an approximated linear model takes into account the nonlinear model for haemodialysis. One of the key advantages of the NMPC formulation is that it gives more comprehensive control of the haemodialysis process. Four manipulated variables are considered: the blood flow out of the body, the blood flow returned from the dialysis machine to the body, the dialysate rate and the sodium concentration of the inlet blood flow. By manipulating these variables, the fluid volumes and the toxin clearance are monitored and controlled. The results show that a better control performance for the blood volumes and toxin clearance is obtained while the blood and dialysate flow rates are held at a relatively low level, which is expected to reduce the risk of adverse reactions for the patients.

In this work, a methodology for fault detection in wastewater treatment systems, based on parameter estimation, using multiparametric programming is presented. The main idea is to detect faults by estimating model parameters, and monitoring the changes in residuals of model parameters. In the proposed methodology, a nonlinear dynamic model of wastewater treatment was discretized to algebraic equations using Euler’s method. A parameter estimation problem was then formulated and transformed into a square system of parametric nonlinear algebraic equations by writing the optimality conditions. The parametric nonlinear algebraic equations were then solved symbolically to obtain the concentration of substrate in the inflow, , inhibition coefficient, , and specific growth rate, , as an explicit function of state variables (concentration of biomass, concentration of organic matter, concentration of dissolved oxygen, and volume, ). The estimated model parameter values were compared with values from the normal operation. If the residual of model parameters exceeds a certain threshold value, a fault is detected. The application demonstrates the viability of the approach, and highlights its ability to detect faults in wastewater treatment systems by providing quick and accurate parameter estimates using the evaluation of explicit parametric functions.

In this work we investigate the integrated planning, scheduling and control (iPSC) of process systems under uncertain conditions throughout the three levels of decision making. The planning problem is explored in a rolling horizon fashion coupled with demand forecasts. Proactive and reactive approaches are employed to handle the effect of stochastic variations. Depending on the nature of the uncertain parameters robust optimisation and chance constrained programming are employed. For the closed-loop implementation of the control, novel multi-parametric controllers are designed. The proposed framework is tested on the iPSC of a polymerisation process. Finally, Monte Carlo simulations are conducted to highlight the benefits of the “uncertainty-aware” solutions when compared to the deterministic ones.