Zohreh Fathi

Optimal Injection Policies for Enhanced Oil Recovery: Part 2-Surfactant Flooding

The optimal control theory of distributed-parameter systems has been applied to the problem of determining the best injection policy of a surfactant slug for a tertiary oil recovery chemical flood. The optimization criterion is to maximize the amount of oil recovered while minimizing the chemical cost. A steepest-descent gradient method was used as the computational approach to the solution of this dynamic optimization problem. The performance of the algorithm was examined for the surfactant injection in a one-dimensional flooding problem. Two types of interfacial tension (IFT) behavior were considered. These are a Type A system where the IFT is a monotonically decreasing function with solute concentration and a Type B system where a minimum IFT occurs at a nominal surfactant concentration. For a Type A system, the shape of the optimal injection strategy was not unique; however, there is a unique optimum for the amount of surfactant needed. For a Type B system, the shape of the optimal injection as well as the amount injected was unique.

Optimal Injection Policies for Enhanced Oil Recovery: Part 1 Theory and Computational Strategies

The theory of optimal control of distributed-parameter systems is presented for determining the best possible injection policies for EOR processes. The optimization criterion is to maximize the amount of oil recovered at minimum injection costs. Necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagins weak minimum principle. A gradient method is proposed for the computation of optimal injection policies.

Use of optimal control theory for computing optimal injection policies for enhanced oil recovery

Abstract The theory of optimal control of distributed parameter systems has been applied to the problem of determining an optimum injection policy for a chemical flooding enhanced oil recovery process. The optimization criterion is to maximize the difference between gross revenue and cost of chemicals injected. Necessary conditions for optimality are obtained through application of the calculus of variations and the distributed weak minimum principle. A gradient method is used for the computation of optimal injection policies. The performance of the algorithm was examined for the surfactant injection in a one-dimensional flooding problem. Two types of interfacial tension behaviour were considered: a type ‘A’ system in which the interfacial tension is a monotically decreasing function with solute concentration and a type ‘B’ system in which a minimum in the interfacial tension occurs at a nominal surfactant concentration. Different initial values were used in order to establish the convergence of the computational algorithm. For a type ‘A’ system, the shape of the optimum injection strategy was not unique; however, there is a unique optimum for the amount of surfactant needed. For a type ‘B’ system, the shape of the optimum injection was unique as well as the amount injected. The results of this work show that given the properties of an oil reservoir and the properties of a surfactant solution, an optimum injection policy which minimizes a specific economic objective functional can be obtained using distributed parameter control theory.

Optimization of an enhanced oil recovery process with boundary controls- A large-scale non-linear maximization

Abstract The problem of optimally determining the injected concentration histories for a micellar/polymer flooding enhanced oil recovery (EOR) system so as to maximize the net profitability of the project is considered. The state dynamics are described by a set of highly non-linear partial differential equations with boundary control inputs. The theoretical characterization of the optimal control policy is obtained using both a continuous and a discrete variational formulation. The numerical optimum-seeking algorithm is formulated based on generating a maximizing sequence which converges to the optimum control policy. This sequence is generated by employing gradient or conjugate directions of search on the performance measure. Numerical calculations are presented to illustrate optimal policies. Specific results depend on the physical chemistry as well as on reservoir parameters. The method has been tested on the realistic linear core experiments used to design the Sloss field test of Amoco. The optimization studies yield optimum injection strategies which improve the core flood performance by over 21%. The optimum value of the performance measure is about 81% of the greatest attainable economic value which corresponds to complete oil recovery at no chemical cost. This paper emphasizes the applicability of optimal control theory to a problem which is highly non-linear, mathematically complex and extensively large. The effectiveness of the approach has been established by numerical results.

State estimation schemes for fault detection and diagnosis in dynamic systems

Abstract The state estimation problem for dynamic systems is one of the fundamental problems in the fields of modelling, optimal control, and fault detection and diagnosis. Linear and non-linear state estimation has been a very active research field during the last 30 years. The purpose of this paper is to give a brief review of the basic fault detection and diagnosis methods based upon the analytical and knowledge-based redundancy. The main emphasis is placed upon estimation methods that are widely applied for fault detection. The advantages and disadvantages of these methods also are discussed both in general and in diagnostic applications.

Optimal Injection Policies for Enhanced Oil Recovery

Abstract The theory of optimal control of distributed parameter systems is presented for determining the best possible injection policies for enhanced oil recovery processes. The optimization criterion is to maximize the amount of oil recovered while minimizing injection costs. Necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagins Weak Minimum Principle . A gradient method is used for the computation of optimal injection policies. The perforrnance of the algorithm was examined for the surfactant injection in a one di mensional flooding problem. Two types of interfacial tension behavior were cons idered: a type “A” system in which the interfacial tension is a monotically decreasing function with solute concentration and a type “B” system in which a minimurn in the in terfacial tension occurs at a nominal surfactant concentration. For a type “A” system, the shape of the optimum injection strateay was not unique, however, there is a unique optimum for the amount of surfacta nt needed. For a type “B” system, the shape of the optimum injection was unique as well as the amount injected. The results of this work show that given the properties of an oil reservoir and the properties of a surfactant solution, an optimum injection policy can be obtained using distributed parameter control theory.

A Knowledge-Based System with Embedded Estimation Components for Fault Detection and Isolation in Process Plants

Abstract Fault diagnosis in the area of process operations is critical for modern production and is receiving increasing theoretical and practical attention. In spite of many research and practical attempts, process fault diagnosis remains a rather complex task. In this work, we present a diagnostic methodology in which the symbolic reasoning of knowledge-based systems techniques is integrated with quantitative analysis of analytical redundancy methods. The system first performs a diagnosis by means of a compiled knowledge structure, and then attempts to build a detailed explanation by using proper fault models (adaptive filters). It also performs various statistical analyses to determine the process condition and check the validity of models. This unified approach increases the completeness and reliability of the diagnostic system.

Symbolic reasoning and quantitative analysis for fault detection and isolation in process plants

Abstract Fault diagnosis in the area of process operations is critical for modern production and is receiving increasing theoretical and practical attention. In spite of many research and practical attempts, process fault diagnosis remains a rather complex task. This work presents a diagnostic methodology in which the symbolic reasoning of knowledge-based systems techniques is integrated with quantitative analysis of analytical redundancy methods. The system first performs a diagnosis by means of a compiled knowledge structure, and then attempts to build a detailed explanation by using proper fault models. It also performs various statistical analyses to determine the process condition and check the validity of models (adaptive filters). This unified approach increases the completeness and reliability of the diagnostic system.

An Integrated Diagnostic System using Analytical Redundancy and Artificial Intelligence for Coal-Fired Power Plants

Abstract The increasing complexity of process plants and their reliability has encouraged industry to look for new approaches for detecting and diagnosing process abnormalities. One such approach is the use of knowledge-based system techniques. On the contrary to many recent attempts using this technology where diagnostic analysis is based solely on measurable and observable data, in this work we consider the adaptive inclusion of a state and/or parameter estimation module in the diagnostic reasoning loop, in addition to employing information based on measurable data. The design methodology is a new layered knowledge base that houses compiled/qualitative knowledge in the high-levels and process-general estimation knowledge in the low-levels of a hierarchical knowledge structure. The compiled knowledge is used to narrow the diagnostic search space and provide an effective way of employing estimation modules. The purpose of this paper is to present the failure detection issues for the deaerator control subsystem of a coal fired power plant. The main emphasis is placed upon the model-based redundancy methods which create the low-levels of the hierarchical knowledge base. Due to the highly-nonlinear and mixed-mode nature of the power plant dynamics, the modified extended Kalman filter is used in designing the local detection filters.

Optimization of an Enhanced Oil Recovery Process with Boundary Controls

Abstract We consider the problem of optimally determining the injected concentration histories for a micellar/polymer flooding enhanced oil recovery (EOR) system, so as to maximize the net profitability of the project. The state dynamics are described by a set of highly nonlinear partial differential equations with boundary control inputs. The theoretical characterization of the optimal control policy is obtained using a discrete variational formulation. The numerical optimum-seeking algorithm is formulated based on generating a maximizing sequence which converges to the optimum control policy. This sequence is generated by employing gradient or conjugate directions of search on the performance measure. Numerical calculations are presented to illustrate optimal policies. Specific results depend upon the physical chemistry as well as reservoir parameters. The method has been tested on the realistic linear core experiment used to design the Sloss field test of Amoco. Our optimization studies yield optimum injection strategies which improve the core flood performance by over 21%. The optimum value of the performance measure is about 81% of the greatest attainable economic value which corresponds to complete oil recovery at no chemical cost. This paper emphasizes the applicability of optimal control theory to a problem which is highly nonlinear, mathematically complex, and extensively large. The effectiveness of the approach has been established by numerical results.