In this thesis we optimize the drilling location and operational controls of wells in a joint manner to improve the overall development strategy for a petroleum field. In particular, in this thesis we treat the integrated problem of searching for an improved well placement configuration while also taking into account the control settings of the production and/or injector wells planned for the development of the hydrocarbon asset. In oil field development, the well placement and well control problems are commonly performed in a sequential manner. However, this type of sequential approach cannot be expected to yield optimal solutions because it relies on handling well production controls using heuristic techniques during the well placement part of the procedure. In this work, we develop a nested (joint) optimization approach that seeks to capture the interdependency between the well configuration and the associated controls during the optimization search.This thesis summarizes the development of the joint approach; from establishing the methodology while using relatively simple cases and performing thorough comparisons against sequential approaches, to further extending and finally testing the methodology using a real field case model. This progression naturally divides the work in this thesis into two parts with different research focus. The first part of this work (Chapter 2) focuses chiefly on creating proper definitions and on establishing the proposed methodology against common approaches. The second part of this thesis (Chapters 3 and 4), on the other hand, focuses mainly on applying the developed methodology within a real field case scenario involving the North Sea Martin Linge oil reservoir. The dual aim of this application work is both to further develop the methodology, and to produce and test optimization solutions that may serve as decision-support to engineering efforts within the development work process of the Martin Linge field.Chapter 2 establishes the core of the methodology followed in this thesis. This chapter introduces the joint and sequential approaches as different ways to solve for the coupled well placement and control problem. The joint approach embeds the well control optimization within the search for optimum well placement configurations. Derivativefree methods based on pattern search are used to solve for the well-positioning part of the problem, while the well control optimization is solved by sequential quadratic programming using gradients efficiently computed through adjoints. Compared to reasonable sequential approaches, the joint optimization yields a significant increase in net present value of up to 20%. Compared to the sequential procedures, though, the joint approach requires about an order of magnitude increase in the total number of reservoir simulations performed during optimization. This increase, however, is somewhat mitigated by i the parallel implementation of some of the pattern search algorithms used in this work.Chapter 3 focuses on extending and applying ...

No abstract

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. This paper was prepared for the 49th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Texas, Oct. 6–9, 1974. Permission to copy is restricted to an abstract of not more than 300 words. illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract A study has been made of the flow behavior of fractured oil reservoirs produced by water displacement. A two-dimensional numerical model capable of simulating flow of water and oil in the matrix blocks as well as in the fractures has been developed. The validity of the model has been cheeked against data from a laboratory experiment involving a matrix-fracture system. Good agreement was observed between the laboratory and simulation results. By means of numerical simulation, the effects of production rate and fracture flow capacity on the production history and ultimate oil recovery of a fractured system have been evaluated. Results are presented for a single matrix-block system where the block is surrounded by horizontal and vertical fractures. Production rates ranging from 0.05 to 5 times Production rates ranging from 0.05 to 5 times the gravity reference rate of the matrix, and fracture flow capacities ranging from 0.1 to 10 times the flow capacity of the matrix are included in the investigation. At production rates much lower than the gravity reference rat the system behaves essentially as a nonfractured reservoir. It is also observed that for fracture flow capacities of the order of one-tenth of the matrix flow capacity, the effect of the fractures is negligible. At higher fracture flow capacities the water-oil ratio performance of the system becomes increasingly more sensitive to production rate. Water production starts much earlier with high fracture flow capacities and high production rates than it does from a nonfractured reservoir, and a large portion of the oil is produced at high water-oil portion of the oil is produced at high water-oil ratios. However, if the additional water can be handled economically, no oil is lost by high rate production. It is demonstrated that for a given fracture flow capacity, the producing water-oil ratio is a unique function of oil remaining in place and present producing rate. Thus, a reservoir can be produced at a high rate until the water-oil ratio becomes too high to handle. Then, reducing the rate causes the water-oil ratio to decrease to the value it would have had if all the oil had been produced at this lower rate. Introduction A significant number of petroleum reservoirs exist where discontinuities such as fractures or joints in the porous rock matrix are the main paths for transmitting fluids to the producing wells. In naturally fractured producing wells. In naturally fractured reservoirs, the matrix rock generally has a low permeability and one or more well-developed permeability and one or more well-developed fracture systems are present.

A new method for construction of hysteresis capillary pressure relationships for use in reservoir simulation models is presented. The method is based on the experimental drainage-imbibition bounding curves and the history of the saturation changes. By scaling of the measured drainage and imbibition bounding curves into the saturation ranges in question for hysteresis scanning loops, any family of hysteresis curves may be constructed. The method is well suited for use in reservoir simulation models. Results of highly accurate laboratory measurements of capillary pressures on a gas-oil system including re-imbibition and re-drainage are presented. Predictions of hysteresis behavior of the laboratory system by the new method show satisfactory agreement with the experiments, while prediction by the much used Killough's method fail to match the experiment, primarily because it does not scale saturations. It is also observed that the commonly used Land equation for prediction of residual saturations is not representative for the system under investigation. Since the Land equation do not distinguish between rock types, it is not recommended used unless experimental support of its applicability exists. Our results show that the relationship between the residual saturation and the initial saturation for a hysteresis imbibition process is approximately linear. Introduction In a paper published in 1965, Morrow and Harris presented experimental results and a comprehensive discussion of capillary behavior of porous materials. They show that a hysteresis curve departing from one of the bounding drainage or imbibition curves is uniquely defined by the departing point on the curve. By the same token, virtually an infinite number of families of hysteresis curves may result from saturation reversals, and each branch is defined by the departing point and the history of saturation reversals. In order to define an imbibition hysteresis curve, the residual saturation in addition to the departing point must be known. Commonly used for prediction of residual saturation is the semi-empirical relation presented by Land based on matching of experimental data. He found that for a given sand the difference in reciprocals of residual and initial saturations remains constant. Several authors have discussed hysteresis behavior of porous media. Of particular interest is representation of hysteresis in reservoir simulation. Model input data normally includes complete drainage and imbibition curves. The simulation model then applies some method to predict hysteresis residual saturations and hysteresis capillary pressures and relative permeabilities. Both Killough and Carlson presented methods for predicting hysteresis in relative permeability. For prediction of hysteresis in capillary pressures, the method presented by Killough is frequently employed. His method computes hysteresis capillary pressures by weighting of the complete drainage and imbibition curves. However, as pointed out by Tan, Killough's method was specially formulated for the case where the drainage and imbibition curves meet at the residual saturation. Because of that, the method is often inadequate. Recently, very accurate laboratory measurements of gas-oil capillary hysteresis have been made in the laboratories of IFP in a cooperation with Total and Elf Aquitaine. Measurements of capillary pressures including complete drainage and imbibition curves and intermediate drainage-imbibition and drainage-imbibition-drainage loops were made. The results are presented in this paper and used for evaluation of hysteresis prediction methods. Experiment Gas-oil drainage and imbibition capillary pressure cycles were measured using the Porous Plate Method. A schematic of the laboratory setup is shown in Fig. 1. The laboratory setup includes: P. 597^

The process of conditioning the geological or the static model to production data is typically known as history matching (HM). The economic viability of a petroleum recovery project is greatly influenced by the reservoir production performance under the current and future operating conditions. Therefore evaluation of the past and present reservoir performance and forecast of its future are essential in reservoir management process. At this point history matching plays a very important role in model updating and hence optimum forecasting, researchers are looking for new techniques, methods and algorithms to improve it. This paper therefore reviews HM and its advancements to date including time-lapse seismic data integration. The paper covers manual and automatic HM, minimization algorithms including gradient and non gradient methods. It reviews the advantages and disadvantages of using one method over the other. Gradient methods covered include conjugate gradient, steepest descent, Gauss-Newton and Quasi-Newton. Non-gradient methods covered includes evolutionary strategies, genetic algorithm and Kalman filter (ensemble Kalman filter).It also addresses re-parameterization techniques including principal component analysis (PCA) and discrete cosine transforms (DCT). The methods are evaluated using a data set based on data from the Norne Field in the Norwegian Sea provided by Statoil and its partners to the Center of Integrated in Petroleum Industry (IO Center) at the Norwegian University of Science and Technology (NTNU).