Dr. Elkamel Research Group

Process Planning and Scheduling

Our goal in this area is to develop effective discrete optimization models and solution strategies that exploit the structure of the planning/scheduling problem and processing facilities. In addition, we are concerned with scheduling of start-ups, shut downs, and maintenance of facilities.

In a real processing plant, there is always an uncertainty factor associated with various parameters such as market demand, processing time, and resource availability. We are taking two complementary approaches for handling uncertainties in process operations. First, the models must be formulated to be robust (stable) under variations. Stabilized formulations that are able to absorb disturbances are being considered and performance robustness criteria are being defined. The second approach we are taking for handling uncertainties is the development of a reactive strategy that is able to recommend new plans/schedules while keeping the original decisions intact as much as possible. The problem is addressed as a multi-objective optimization problem involving due dates, relative customer importance, and production cost considerations.

Representative Publications:

• "Multisite Facility Network Integration Design and Coordination: An Application to the Refining Industry" Computers and Chemical Engineering, 45 pages, in press.
• "An Optimization Approach for Integrating Planning and CO2 Emission Reduction in the Petroleum Refining Industry", Industrial & Engineering Chemistry Research, in press.
• "Two-Stage Stochastic Programming with Fixed Recourse via Scenario Planning with Financial and Operational Risk Management for Petroleum Refinery Planning under Uncertainty", Chemical Engineering and Processing, 63 pages, in press, 2007.
• “Enhancing CO2 Conversion Using Dynamic Optimization Applied on Shell Temperature and Inlet Hydrogen During 4 years Operation of Methanol Plant”, Energy Sources, 29, 1385-1396, (2007).
• "An Order-Specific Algorithm for the Determination of Representative Demand Curves", Computers and Chemical Engineering, 27 pages, in press (2007).
• “Decision Making for Petrochemical Planning Using Multi-Objective and Strategic Tools”, Trans. I. Chem. E, Part A, Chemical Engineering Research and Design, 84(A11):1019-1030, November (2006).
• “An Optimization Model for Energy Planning with CO2 Emission Considerations”, Industrial & Engineering Chemistry Research, 44, 879-890, (2005).
• “Modeling and Identification of Economic Disturbances in the Planning of the Petrochemical Industry”, invited paper, Industrial & Engineering Chemistry Research, A Special William L. Luyben Issue, 42, 4678-4688, (2003).
• “Planning an Integrated Petrochemical Business Portfolio for Long-Range Financial Stability ”, Industrial & Engineering Chemistry Research, 41 (11): 2798-2804, May 29, (2002).
• “Planning an Integrated Petrochemical Industry with an Environmental Objective”, Industrial & Engineering Chemistry Research, 40 (9), 2103-2111, (2001).
• "A Decomposition Heuristic for Scheduling the General Batch Chemical Plant", Engineering Optimization, Vol. 28, pp 299-330 (1997).
• "A Language for Describing Process Scheduling Problems", Computers and Chemical Engineering, Rippin Memorial Issue, Vol. 22, No. 1-2, pp. 125-145 (1998).
• “Structured Valid Inequalities and Separation in Optimal Scheduling of the Resource-Constrained Batch Chemical Plant”, Mathematical Engineering in Industry, Vol. 6, No. 4, pp. 291 – 318, (1998).
• “A Rolling Horizon Heuristic for Reactive Scheduling of Batch Process Operations”, Accepted for publication in Engineering Optimization (1998).
• “Heuristic Algorithm for Scheduling Batch and Semi-Continuous Plants with Production Deadlines, Intermediate Storage Limitations, and Equipment Changeover Costs", Computers and Chemical Engineering, Vol. 18, No. 9, pp 859-875 (1994).

Energy Planning

Capture, Storage, and Mitigation

Here we seek new solutions to one of the grand challenges of this century: supplying energy to a growing population while reducing greenhouse gas emissions. Since no single technology is likely to be able to meet this ultimate energy challenge of the future on its own, it is essential to use a systems approach that can provide insight and data on how viable a technology can be. Our long term vision is to propose optimal solutions to effectively manage carbon dioxide reduction, capture, and sequestration while meeting growing energy demands. These carbon management solutions shall include physical and natural processes associated with decarbonization; carbon dioxide capture, transport, and sequestration; the use of new and/or improved fuel sources (nuclear, fossil fuels, hydrogen energy, renewables, etc.); improved efficiency of energy conversion and utilization; economic and market analysis; and alternative energy policy options.

The novelty in this research is that it represents a multi-region, multi-technology decision framework that will provide provincial and national strategies for the effective reduction of carbon dioxide. It is based upon a bottom-up view of industrial activities and a top-down view of energy and other product demands. The framework will also account for the predictable trends and interactions that occur in a dynamic setting of a metropolitan region or a country as a whole. Included within this last category will be factors of regional growth, technological development, availability and limitations on resources, and interrelationships between different industrial sectors. One major contribution from this research will be the development of a decision support system that can aid management and policy makers in constructing equitable comparisons among different carbon dioxide abatement proposals. This will permit the selection of the least cost solutions from among a series of alternate carbon dioxide reduction schemes.

In general terms, the carbon management problem involves energy conservation, process efficiency, fuel switching, and the capture, transportation and storage of CO2. For instance, different processes can be used to effectively capture CO2 (e.g., absorption, adsorption, membrane separation, cryogenic separation). Depending on the nature of the gas stream and the method of capture used, additional treatments might be required to render the stream appropriate to the anticipated mode of transportation and intended storage site in terms of purity, pressure and temperature. These additional treatments can involve purification, pressurization and/or cooling. A number of choices are also available for CO2 transportation, ranging from truck and rail to pipeline or ship. If transportation by pipeline is chosen, as is often the case for relatively large quantities of CO2, a decision must be made on the optimal pipeline network that has to be built along with decisions on which CO2 sources should supply which storage site. Different types of CO2 storage can be considered: oil and gas reservoirs, coal beds, deep saline aquifers, salt domes, and rock caverns, or even in forests. There are also a number of constraints that have to be taken into consideration to be able to successfully formulate a carbon management plan or framework. Among these are the physical constraints imposed by the CO2 production capacities of the CO2 sources and the storage capacities of the geological formations into which the CO2 is to be injected. In situations involving deep water, transportation by ship may be the only option. There are also a number of economic constraints. The economically ideal CO2 source is a single, stationary point that generates a large volume of relatively pure CO2 and which is close to the point of storage. On the other hand, an economically ideal storage site for CO2 is a single point of large storage capacity that generates revenues and which is close to the source(s) of CO2.

The above discussion clearly illustrates the complexity of the carbon management problem and the immense potential utility of the framework that we are developing and undertaking. Only a systems engineering approach can take into account all the interactions among the subproblems and the associated solution alternatives, and can therefore lead to a successful solution. Success will be measured by attaining a least cost solution that is safe, feasible, and yet comprehensive.

We have already started working on a small prototype that involves carbon management decisions for the power generation industry in Ontario. Ontario Power Generation or OPG produces 70 percent of Ontario's electricity source, with approximately 28.5 percent produced through the combustion of fossil fuels, 27 pecent from hydroelectric, 44 percent from nuclear, and the remaining 0.7 percent from renewable or other energy sources such as wind turbine. At peak levels, OPG generates 25,000 MW or 210,900,000 MWh/yr electricity and injects it into the electricity grid. Currently, no CO2 capture processes exist at any of OPG's power plants, and as a result, about 38.6 million tonnes (Mt) of CO2 was emitted in 2001, mainly from fossil fuel-based power plants. There are several possible ways to reduce the amount of CO2 emitted from fossil fuel power plants, for which we have constructed a superstructure that embeds all possible decision alternatives and have developed mixed-integer programming models that provide crucial information in discovering which technologies and solutions may be most promising and how we might improve upon solutions that are presently in use.

Planning for Oil Production

Due to the large scale of oil production operations, even a small improvement in production efficiency can lead to a significant impact on profitability. The aim of our work in this area is to arrive at an optimum development policy for oil production.

A planning model for oil recovery needs to be furnished with recovery predictions continuously before being able to determine the optimal plan of operation. Convergence to an optimal solution might be obtained only after hundreds of iterations. For each iteration, the recovery is calculated as a function of the conditions and parameters of the reservoir. If only a reservoir simulator is available to perform these predictions, the computational expenses become prohibitively large. We therefore decided to prepare replacement tools in terms of Artificial Neural Networks (ANNs) that are able to furnish predictions about reservoir performance quickly. The appropriate development of such networks required a detailed investigation of the scaling groups affecting both miscible and immiscible processes.

In addition to furnishing predictions quickly and accurately, we have shown that ANN models can be used to optimize a given oil recovery process by invoking their inverse property. This finding has great implications in the design of oil recovery processes. Once the optimum values for the different manipulated reservoir conditions are obtained, a second inverse problem must be solved to determine the physical conditions leading to them. For instance in order to attain high break-through oil recoveries, the interfacial tension (IFT) between the water phase and the oil phase must be reduced. However, IFT is a function of several factors such as salinity, type and concentration of surfactant, pH, and the type and concentration of co-surfactants. Therefore, in order to set the IFT to a desired value, the above parameters must be appropriately selected. In order to do this successfully, a functional relationship for IFT must be known. To prepare such relationship, we have planned an experimental approach to study the variations of IFT at various conditions. We are also planning such work for the case of mobility control by adjusting the viscosity of the displacing fluid in polymer flooding. Future work will also consider the optimal design of combined polymer-surfactant flooding.

Representative Publications:

• "An Optimization Approach for Integrating Planning and CO2 Emission Reduction in the Petroleum Refining Industry", Industrial & Engineering Chemistry Research, in press.
• "Modeling the Energy Demands and Greenhouse Gas Emissions of the Canadian Oil Sands Industry" , Energy and Fuels, 21, 2098-2111, 2007.
• "Dynamic Optimization Strategies of a Heterogeneous Reactor for CO2 Conversion to Methanol", Energy and Fuels, 21, 2977-2983, 2007.
• "Enhancing CO2 Conversion Using Dynamic Optimization Applied on Shell Temperature and Inlet Hydrogen During 4 years Operation of Methanol Plant", Energy Sources, 29, 1385-1396, (2007).
• "A Mixed-Integer Nonlinear Programming Model for CO2 Emission Reduction in the Power Generation Sector", International Journal of Environment and Pollution, Vol. 29, Nos. 1/2/3, 254-273, (2007).
• "An Optimization Model for Energy Planning with CO2 Emission Considerations", Industrial & Engineering Chemistry Research, 44, 879-890, (2005).
• "Modeling the Energy Demands and Greenhouse Gas Emissions of the Canadian Oil Sands Industry" , Energy and Fuels, 21, 2098-2111, 2007.
• "Building an Inferential Estimator for Modeling Product Quality in a Crude Oil Desalting and Dehydration Process", Chemical Engineering and Processing, 45 (7): 568-577, JUL (2006).
• "Numerical Characterization of Distributed Dynamic Systems Using Tools of Intelligent Computing and Generalized Dimensional Analysis", Applied Mathematics and Computation, 182, 1021-1039, (2006).
• "A Computational Intelligence Based Approach for the Analysis and Optimization of a Crude Oil Desalting and Dehydration Process", Energy & Fuel, 19 (6): 2526-2534 NOV-DEC (2005).
• "An Artificial Neural Network for the Prediction of Immiscible Flood Performance", Energy & Fuels, 9, 894-900 (1995).
• "Scaling Miscible Fluid Displacements in Porous Media", Energy & Fuels, 12, 801-811, (1998).
• "An Artificial Neural Network for Predicting and Optimizing Immiscible Flood Performance in Heterogeneous Reservoirs", Computers and Chemical Engineering, Vol. 22, No. 11, pp. 1699-1709, (1998).
• "Flow Properties of weathered crude Oils and their Emulsions" Journal of Dispersion Science and Technology, 20(3), 857-882, (1999).
• "The Accuracy of Predicting Compressibility Factor for Sour Natural Gases", Petroleum Science and Technology, 19 (5-6):711-731, (2001).
• "Producing Ultra Low Interfacial Tension at the Oil/Brine Interface", Petroleum Science and Technology, 20 (7-8): 773-788, (2002).
• "Studying the Interactions Between Kuwaiti Oils and Alkaline Solutions", Petroleum Science and Technology, 2 (7-8 789-7, (2002).
• "An Experimental Investigation of Crude Oil Desalting/Dehydration Process", Journal of Chemical Engineering Communications, 190 (1): 65-82 Jan, (2003).

Optimization

Mixed-Integer Programming

Integer and mixed integer programs (MIP) can be used to model a wide variety of problems encountered in many areas including plant layout and design, process scheduling, pollution prevention, and even molecular simulation and design. The general MIP is, however, known to belong to the class NP-complete or hard combinatorial optimization problems and no technically good algorithm is known to be available for its solution. Our aim is to develop novel model representations and novel solution methods for these problems.

We have incorporated propositional calculus in expressing a logical expression in an equivalent mathematical formula. The models developed in this fashion, and as in the case of process scheduling, exhibited tighter linear programming relaxations leading to a tremendous enhancement of the performance of the standard branch-and-bound technique for solving MILP problems. We have also developed systematic ways to reduce the size of MILP problems. These are based on graph theoretic properties to exploit problem structure.

Currently, we are generating a new class of heuristic procedures that combine the advantages of rule-based heuristics and mathematical programming algorithms; we call them mathematical programming based heuristics. These heuristics use a mathematical programming formulation of the problem and are based on employing different modifications to the exact solution procedure to efficiently obtain sub-optimal solutions. All of these heuristics exploit problem structure and consist of an initial phase that identifies a feasible solution and a final phase that improves upon this solution. These heuristics will play a pivotal role in obtaining an effective exact algorithm. Apart from being able to provide sub-optimal solutions quickly, they can be used to fathom vertices in the search space of the optimal solution.

The most critical factor for successfully solving MIP problems is the quality of the lower bounds. When the lower bounding techniques provide weak bounds, the number of search tree nodes that must be explicitly considered grows rapidly with problem size. While the MIP formulations developed from propositional calculus proved to exhibit tight linear programming relaxations, the most efficient branch-and-bound algorithms must take advantage of the best bounding techniques. One common approach of improving MIP relaxations is to add new valid inequality constraints to the model. An inequality is called a valid inequality of an MIP if it is satisfied by every feasible solution to the MIP. Technically, all the original constraints of the MIP are valid inequalities. But this term refers to added constraints that improve the relaxation but are not needed in the original problem formulation. Useful "strong" inequalities are usually developed based on exploiting the structure of the problem. The development of such inequalities in this fashion is more of an art than a formal methodology. We have successfully derived such inequalities for the process scheduling problem. Separation heuristics that detect which of the inequalities are violated in order to use them as cuts were also developed. We plan to extend this development to other MIP problems such as the pollution control selection problem and the molecular design and product formulation problem.

Uncertainty in Optimization

The applications discussed thus far illustrate clearly the utility of optimization models in improving productivity, profitability, and even in preventing pollution. However, the presence of various uncertainties (uncertainty in price, production rates and costs, labor, demand, raw material availability, etc.) complicates the optimization process. Traditionally, the treatment of uncertainty is realized by the use of a stochastic optimization approach. This approach recognizes the presence of multiple data instances that might be potentially realized in the future. The optimization will then attempt to generate a decision that maximizes (or minimizes) an expected performance measure, where the expectation is taken over the assumed probability distribution. In many cases, when multiple uncertain factors exist in the input data, assumptions of distributional independence among factors are made. After possible data instances (scenarios) or probability distributions are fed into a model, a stochastically optimal solution is generated.

There are multiple drawbacks of the stochastic approach in handling uncertainty. First of all, a decision has to be made on probabilities to the various data instances (future scenarios) or probability distributions for the different uncertain factors. Assigning such probabilities is far from a trivial exercise for many decision makers. Another more important drawback is that every decision has associated with it a whole distribution of outcomes, depending on what data scenario is actually realized. Decision makers are interested in having information about the whole distribution of outcomes. They are reasonably more interested in hedging against the risk of poor system performance than in optimizing expected system performance over all potential scenarios. Clearly, a more robust approach is needed.

Representative Publications:

• "Multisite Facility Network Integration Design and Coordination: An Application to the Refining Industry" Computers and Chemical Engineering, 45 pages, in press.
• Optimal Design of Reverse-Osmosis Networks for Wastewater Treatment" 44 pages, Chemical Engineering & Processing, in press.
• "A Heuristic Optimization Approach for Air Quality Monitoring Network Design with the Simultaneous Consideration of Multiple Pollutants", Journal of Environmental Management, 29 pages, in press (2007).
• "Two-Stage Stochastic Programming with Fixed Recourse via Scenario Planning with Financial and Operational Risk Management for Petroleum Refinery Planning under Uncertainty", Chemical Engineering and Processing, 63 pages, in press, 2007.
• "A Mixed-Integer Nonlinear Programming Model for CO2 Emission Reduction in the Power Generation Sector", International Journal of Environment and Pollution, Vol. 29, Nos. 1/2/3, 254-273, (2007).
• "Decision Making for Petrochemical Planning Using Multi-Objective and Strategic Tools", Trans. I. Chem. E, Part A, Chemical Engineering Research and Design, 84(A11):1019-1030, November (2006).
• "Modeling and Optimization of a Multistage Flash Desalination Process", Engineering Optimization, Volume 37, Number 6, 591-607, (2005).
• "An Optimization Model for Energy Planning with CO2 Emission Considerations", Industrial & Engineering Chemistry Research, 44, 879-890, (2005).
• "Modeling and Identification of Economic Disturbances in the Planning of the Petrochemical Industry", invited paper, Industrial & Engineering Chemistry Research, A Special William L. Luyben Issue, 42, 4678-4688, (2003).
• "Planning an Integrated Petrochemical Business Portfolio for Long-Range Financial Stability", Industrial & Engineering Chemistry Research, 41 (11): 2798-2804, (2002).
• "Mathematical Programming Based Heuristic for Scheduling the General Batch Plant", INVITED PAPER, Proceedings of the American Control Conference, San Francisco, California, pp. 2552-2556 (1993).
• "A Decomposition Heuristic for Scheduling the General Batch Chemical Plant", Engineering Optimization, Vol. 28, pp 299-330 (1997).
• "Optimal Scheduling of the Resource Constrained Batch and Semicontinuous Chemical Plant", TIMS/ORSA Joint National Meeting, Chicago - USA, May (1993).
• "A Mixed Integer Linear Programming Model for Air Pollution Control Decision Making", AIChE's Spring 1995 National Meeting, New Orleans - USA (1996)
• "Structured Valid Inequalities and Separation in Optimal Scheduling of the Resource-Constrained Batch Chemical Plant", Mathematical Engineering in Industry, Vol. 6, No. 4, pp. 291 - 318, (1998).