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Abstract In production optimization, we seek to determine the well settings (bottomhole pressures, flow rates) that maximize an objective function such as net present value. In this paper we introduce and apply a new approximate dynamic programming (ADP) algorithm for this optimization problem. ADP aims to approximate the global optimum using limited computational resources via a systematic set of procedures that approximate exact dynamic programming algorithms. The method is able to satisfy general constraints such as maximum watercut and maximum liquid production rate in addition to bound constraints. ADP has been used in many application areas, but it does not appear to have been implemented previously for production optimization. The ADP algorithm is applied to two-dimensional problems involving primary production and water injection. We demonstrate that the algorithm is able to provide clear improvement in the objective function compared to baseline strategies. It is also observed that, in cases where the global optimum is known (or surmised), ADP provides a result within 1-2% of the global optimum. Thus the ADP procedure may be appropriate for practical production optimization problems.
- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (0.34)
Abstract As many fields around the world are reaching maturity, the need to develop new tools that allow reservoir engineers to optimize reservoir performance is becoming more urgent. One of the more challenging and important problems along these lines is the well placement optimization problem. In this problem, there are many variables to consider: geological variables like reservoir architecture, permeability and porosity distributions, and fluid contacts; production variables, such as well placement, well number, well type, and production rate; and economic variables like fluid prices and drilling costs. Furthermore, availability of complex well types, such as multilateral wells (MLWs) and maximum reservoir contact (MRC) wells, aggravate this challenge. All these variables, together with reservoir geological uncertainty, make the determination of an optimum development plan for a given field difficult. The objective of this work was to employ an optimization technique that can efficiently address the aforementioned challenges. Based on the success and versatility of Genetic Algorithms (GAs) in problems of high complexity with high dimensionality and nonlinearity, it is used here as the main optimization engine. Both binary GA (bGA) and continuous GA (cGA) were tested in the optimization of well location and design in terms of well type, number of laterals, and well and lateral trajectories in a channelized synthetic model. Both GA variants showed significant improvement over initial solutions but comparisons between the two types showed that the cGA was more robust for the problem under consideration. The cGA was, thereafter, applied to a real field located in the Middle East to investigate its robustness in optimizing well location and design in more complex reservoir models. The model is an upscaled version for an offshore carbonate reservoir, which is mildly heterogeneous with low and high permeability areas scattered over the field. After choosing the optimization technique to achieve our objective, considerable work was performed to study the sensitivity of the different algorithm parameters on converged solutions. Then, multiple optimization runs were performed to obtain a sound development plan for this field. An attempt was made to quantify how solutions were affected by some of the assumptions and preconditioning steps taken during optimization. Finally, an optimization ran was performed on the fine model using optimized solutions from the coarse model. Results showed that the optimum well configuration for the reservoir model at hand can contain five or more laterals; which shows potential for drilling MRC wells. Other studies comparing results from the fine and coarse reservoir models revealed that the best solutions are different between the two models. In general, solutions from different runs had different well designs due to the stochastic nature of the algorithm but some guidance about preferred well locations could be obtained through this process
- Asia > Middle East > Saudi Arabia (0.68)
- North America > United States > Texas (0.46)
- North America > United States > California (0.46)
- Well Drilling > Drilling Operations > Directional drilling (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization (1.00)
- Data Science & Engineering Analytics > Information Management and Systems > Artificial intelligence (1.00)
Abstract Field development optimization is a computationally intensive task due to the large number of reservoir simulation runs required. These simulations can be expensive, especially for large and complex reservoir models. Proxies can be used to efficiently estimate the objective function value for new scenarios and can act to reduce the number of simulations required. Thus they can be very useful for speeding up field development optimization. In this paper a procedure that combines an optimization algorithm (in this case a genetic algorithm or GA) and a new statistical proxy is described. The statistical proxy has the following key elements. First, a new selection procedure called individual-based selection is applied to decide which individuals (scenarios) are to be simulated. Second, the new approach uses multiple proxies for optimization problems involving multiple reservoir models, which are needed to account for geological uncertainty. Third, the statistical proxy is modified to work efficiently in distributed computing environments. Finally, the proxy procedure is successfully incorporated into an existing general field development optimization package (Williams et al., 2004; Litvak et al., 2007a). In the individual-based selection method, for each scenario the proxy estimate of the objective function is compared to a threshold. If the estimate exceeds the threshold, then the case is simulated (otherwise it is not simulated). The threshold corresponds to a specified percentile of the cumulative distribution function constructed from previously simulated cases and therefore changes during the course of the optimization. In cases with multiple reservoir models, each model has its own corresponding proxy. This eliminates the problem of duplicate objective function estimates for different reservoir models, which may occur with previous proxy-based methods. The individual-based selection method is shown to perform better for a particular example than the population-based method published previously. The overall procedure is applied to the optimization of infill drilling where we maximize the incremental net present value (NPV) by optimizing new well locations, well type and rig schedule, subject to field development constraints. We demonstrate the capabilities of the proxy using synthetic reservoir models and a real field in the Gulf of Mexico. In the first example, two optimization cases are considered, corresponding to the use of single and multiple reservoir models. In the case with one reservoir model, the hybrid procedure found the same field development scenario compared to GA only, and required 85% fewer simulations. In the case with multiple reservoir models, the hybrid procedure found a slightly different field development scenario than the pure GA approach, though the NPV from the hybrid procedure was within 1% of that using only GA. The hybrid approach, however, required 91% fewer simulations for this case. In the field application, a better field development scenario with 45% fewer simulations was found using the hybrid algorithm (GA and proxy) compared to using only GA. These examples clearly demonstrate the effectiveness of the statistical proxy procedure for accelerating field development optimization.
Summary The general petroleum-production optimization problem falls into the category of optimal control problems with nonlinear control-state path inequality constraints (i.e., constraints that must be satisfied at every time step), and it is acknowledged that such path constraints involving state variables can be difficult to handle. Currently, one category of methods implicitly incorporates the constraints into the forward and adjoint equations to address this issue. However, these methods either are impractical for the production optimization problem or require complicated modifications to the forward-model equations (the simulator). Therefore, the usual approach is to formulate this problem as a constrained nonlinear-programming (NLP) problem in which the constraints are calculated explicitly after the dynamic system is solved. The most popular of this category of methods for optimal control problems has been the penalty-function method and its variants, which are, however, extremely inefficient. All other constrained NLP algorithms require a gradient for each constraint, which is impractical for an optimal control problem with path constraints because one adjoint must be solved for each constraint at each time step in every iteration. The authors propose an approximate feasible-direction NLP algorithm based on the objective-function gradient and a combined gradient for the active constraints. This approximate feasible direction is then converted into a true feasible direction by projecting it onto the active constraints and solving the constraints during the forward-model evaluation itself. The approach has various advantages. First, only two adjoint evaluations are required in each iteration. Second, the solutions obtained are feasible (within a specified tolerance) because feasibility is maintained by the forward model itself, implying that any solution can be considered a useful solution. Third, large step sizes are possible during the line search, which may lead to significant reductions in the number of forward- and adjoint-model evaluations and large reductions in the magnitude of the objective function. Through two examples, the authors demonstrate that this algorithm provides a practical and efficient strategy for production optimization with nonlinear path constraints. Introduction One of the primary goals of the reservoir modeling and management process is to enable decisions that maximize the production potential of the reservoir. Among the various existing approaches to accomplish this, real-time model-based reservoir management, also known as the "closed-loop" approach, has recently generated significant interest. This methodology entails model-based optimization of reservoir performance under geological uncertainty while also incorporating dynamic information in real time, which acts to reduce model uncertainty. For such schemes to be practically applicable, a number of algorithmic advances are required. Some earlier papers by the authors (Sarma et al. 2006b; Sarma et al. 2005b) and also papers by other authors such as Brouwer et al. (2004) have discussed efficient algorithms for such closed-loop production optimization problems. This paper, however, focuses only on the optimization component of the closed-loop process, which is essentially a large-scale optimal control problem. A large variety of methods for solving discrete-time optimal control problems now exist in the control-theory literature, including dynamic programming, neighboring extremal methods, and gradient-based nonlinear-programming (NLP) methods. These are discussed in detail in Stengel (1985) and Bryson and Ho (1975). Of these approaches, the NLP method combined with the Maximum Principle (Bryson and Ho 1975) (adjoint models) generates a class of NLP methods in which only the control variables are the decision variables and the state variables are obtained from the dynamic equations. These algorithms are generally considered more efficient compared to the other methods. Furthermore, within this class of NLP methods, there are many existing techniques available for handling nonlinear control-state path inequality constraints (Bryson and Ho 1975; Mehra and Davis 1972; Feehery 1998; Fisher and Jennings 1992). However, as will be discussed later, these techniques are either impractical for the production-optimization problem or difficult to implement with existing reservoir simulator codes. In the petroleum-engineering literature, papers by various authors such as Asheim (1988), Vironovsky (1991), Brouwer and Jansen (2004) have discussed in significant detail the application of adjoint models and gradient techniques to the production-optimization problem. However, an important element that is missing from most of these papers is an effective treatment of nonlinear control-state path inequality constraints (for example, a maximum water-injection-rate constraint). Such constraints are always present in practical production-optimization problems, and therefore appropriate treatments are essential for such algorithms to be useful. In an earlier paper by the authors (Sarma et al. 2005a), two methods to handle such constraints were discussed; however, they either do not satisfy the constraints exactly or are applicable only for small problems. Zakirov et al. (1996) also discussed an approach to implementing path constraints; there are, however, certain issues with this approach, as discussed in a later section. It should be noted that adjoints and gradient methods have also been applied to the history-matching problem. Such approaches were pioneered by Chen et al. (1974) and Chavent et al. (1975) and have more recently been applied by Wu et al. (1999), Li et al. (2001), and Zhang et al. (2005), among others. However, the problem of nonlinear path constraints usually does not appear in the history-matching problem. In this paper, an approximate feasible-direction optimization algorithm is proposed, suitable for large-scale optimal control problems, that is able to handle nonlinear inequality path constraints effectively while maintaining feasibility within a specified tolerance. Other advantages of this approach are that only two adjoint simulations are required for each iteration and that large step sizes are possible during the line search in each iteration, potentially leading to large reductions in the magnitude of the objective function. This method belongs to the class of NLP methods combined with the Maximum Principle (adjoint models) discussed previously. Although the algorithmic components implemented here have been applied previously in various contexts, to the authors' knowledge this is the first integration of a feasible-direction algorithm, constraint lumping (with the particular lumping function used), and a feasible-line search algorithm. Thus the resulting feasible-direction optimization algorithm can be considered to be a new treatment for an important problem. This paper proceeds with a brief description of the mathematical formulation of the problem and the application of adjoint models for efficient calculation of objective-function gradients with respect to the controls. This is followed by a discussion of existing methods for handling nonlinear path constraints for optimal control problems. The next section discusses the traditional feasible-direction optimization algorithm, which is the basis of the proposed algorithm. This is followed by detailed discussions of the proposed approximate feasible-direction and feasible-line search algorithms. The validity and effectiveness of the approach for handling nonlinear path inequality constraints is demonstrated through two examples, one with a maximum water-injection constraint, and the other with a maximum liquid-production constraint (both of these are nonlinear with respect to the BHP controls).
- Europe (0.93)
- North America > United States > California (0.46)
- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (0.75)
- Asia > Middle East > Saudi Arabia > Eastern Province > Al-Ahsa Governorate > Arabian Basin > Widyan Basin > Ghawar Field > Lower Fadhili Formation (0.99)
- Asia > Middle East > Saudi Arabia > Eastern Province > Al-Ahsa Governorate > Arabian Basin > Widyan Basin > Ghawar Field > Khuff D Formation (0.99)
- Asia > Middle East > Saudi Arabia > Eastern Province > Al-Ahsa Governorate > Arabian Basin > Widyan Basin > Ghawar Field > Khuff C Formation (0.99)
- (4 more...)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Waterflooding (1.00)
- Production and Well Operations > Well Operations and Optimization (1.00)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)
Abstract Efficient history matching of geologically complex reservoirs is important in many applications, but it is central in closed-loop reservoir modeling, in which real-time model updating is required. Within the context of closed-loop reservoir modeling, the two approaches receiving the most attention to date are ensemble Kalman filtering and gradient-based methods using Karhunen-Loeve representations (eigen-decomposition) of the permeability field. Both of these procedures are technically appropriate only for random fields (e.g., permeability) characterized by two-point geostatistics (multi-Gaussian random fields). Realistic systems are much better described by multipoint geostatistics, which is capable of representing key geological structures such as channels. History matching algorithms that are able to reproduce realistic geology provide enhanced predictive capacity and are therefore more suitable for use with field optimization. In this work, we apply a new parameterization, referred to as a kernel principal component analysis (kernel PCA or KPCA) representation, to model permeability fields characterized by multipoint geostatistics. Kernel PCA enables preserving arbitrarily high order statistics of random fields, thereby providing the capability to reproduce complex geology. The KPCA representation is then combined with an efficient gradient-based history matching technique. The linkage of KPCA for modeling geology with gradient-based history matching is very natural as the KPCA representation is differentiable and gradients with respect to geological parameters can be readily computed. The overall procedure is then applied to several example cases, including synthetic models and a model of a real reservoir. The approach is shown to better reproduce complex geology, which leads to improved history matches and better predictions, while retaining reasonable computational requirements. Introduction History matching is a key component of closed-loop reservoir modeling. In this procedure, real-time surface and downhole production data provide continuous input to the history matching algorithm. Although history matching has been investigated actively within the petroleum engineering community for the last three or more decades, and numerous algorithms have been developed, in practice most history matching is still performed manually or at best with assisted history matching techniques (Milliken et al., 2000). This suggests that new developments are still required in order to provide a robust, efficient and reliable history matching capability that can be used for closed-loop applications. It is well known that, because history matching is an ill-posed problem with non-unique solutions, additional prior information in the form of geostatistical constraints is required to obtain geologically realistic history matched models that have good predictive capability (Caers, 2003a). In essence, the goal is to integrate and preserve all available qualitative and quantitative data during the process of creating the history matched model, thereby maximizing the reduction of uncertainty and thus leading to better predictions. Existing history matching algorithms can be broadly classified into four general categories: stochastic algorithms, gradient-based methods, streamline-based techniques, and Kalman filter approaches. Within the category of stochastic algorithms, the probability perturbation method (Caers, 2003a) and the gradual deformation method and its extensions (Hu et al., 2001, 2005) are popular methods that have been widely applied. A definite advantage of these algorithms is that they are able to easily honor complex geological constraints by preserving multipoint statistics present in the prior geological model. Furthermore, they are quite easy to implement as they treat the simulator as a "black box." These algorithms are also claimed to be globally convergent due to their stochastic nature. A disadvantage of these approaches is their inefficiency, as they require numerous simulations for convergence (Wu, 2001, Liu et al., 2004). This is particularly of concern in closed-loop reservoir management (Jansen et al., 2005, Sarma et al., 2006a), which requires continuous real-time use of history matching algorithms.
- Europe (0.68)
- North America > United States > Texas > Harris County > Houston (0.28)
- Research Report > New Finding (0.46)
- Overview > Innovation (0.40)
- North America > United States > Texas > Permian Basin > Midland Basin > University Field > Wolfcamp Formation (0.98)
- North America > United States > Arkansas > Smart Field (0.98)
Abstract The general petroleum production optimization problem falls under the category of optimal control problems with nonlinear control-state path inequality constraints (i.e. constraints that have to be satisfied at every time step), and it is acknowledged that such path constraints involving state variables are particularly difficult to handle. Currently, one category of methods implicitly incorporates the constraints into the forward and adjoint equations to tackle this issue. However, these are either impractical for the production optimization problem, or require complicated modifications to forward model equations (simulator). Thus, the usual approach is to formulate the above problem as a constrained nonlinear programming problem (NLP) where the constraints are calculated explicitly after the dynamic system is solved. The most popular of this category of methods (for optimal control problems) has been the penalty function method and its variants, which are, however, extremely inefficient. All other constrained NLP algorithms require the gradient of each constraint, which is impractical for an optimal control problem with path constraints, as one adjoint has to be solved for each constraint at each time step at every iteration. We propose an approximate feasible direction NLP algorithm based on the objective function gradient and a combined gradient of the active constraints. This approximate feasible direction is then converted into a true feasible direction by projecting it onto the active constraints by solving the constraints during the forward model evaluation itself. The approach has various advantages. Firstly, only two adjoint evaluations are required at each iteration. Secondly, all iterates obtained are always feasible, as feasibility is maintained by the forward model itself, implying that any iterate can be considered a useful solution. Thirdly, large step sizes are possible during the line search, which can lead to significant reductions in forward and adjoint model evaluations and large reductions in the objective function. Through two examples, we demonstrate that the algorithm provides a practical and efficient strategy for production optimization with nonlinear path constraints. Introduction One of the primary goals of the reservoir modeling and management process is to enable decisions that maximize the production potential of the reservoir. Among the various existing approaches to accomplish this, real-time model-based reservoir management, also known as the "closed-loop" approach, has recently generated significant interest. This methodology entails model-based optimization of reservoir performance under geological uncertainty, while also incorporating dynamic information in real-time, which acts to reduce model uncertainty (see Figure 1). For such schemes to be practically applicable, a number of algorithmic advances are required. Some of our earlier papers [1,2], and also papers by other authors such as Brouwer et al. [3] have discussed efficient algorithms for such closed-loop production optimization. This paper, however, is only focused on the optimization component of the closed-loop process, which is essentially a large-scale optimal control problem. A large variety of methods for solving discrete-time optimal control problems now exist in control theory literature, including dynamic programming, neighboring extremal methods, gradient-based nonlinear programming methods (NLP), etc. These are discussed in detail in Stengel [4] and Bryson and Ho [5]. Of these approaches, the NLP method combined with the Maximum Principle [5] (adjoint models) generates a class of NLP methods in which only the control variables are the decision variables and the state variables are obtained from the dynamic equations. These algorithms are generally considered more efficient compared to the other methods. Further, within this class of NLP methods, there are many existing techniques available for handling nonlinear control-state path inequality constraints [5,6,7,8]. However, as will be discussed later, these are either not practical for the production optimization problem or are difficult to implement with existing reservoir simulator codes.
- Europe (0.93)
- North America > United States (0.68)
- Asia > Middle East > Saudi Arabia (0.28)
- Asia > Middle East > Saudi Arabia > Eastern Province > Al-Ahsa Governorate > Arabian Basin > Widyan Basin > Ghawar Field > Lower Fadhili Formation (0.99)
- Asia > Middle East > Saudi Arabia > Eastern Province > Al-Ahsa Governorate > Arabian Basin > Widyan Basin > Ghawar Field > Khuff D Formation (0.99)
- Asia > Middle East > Saudi Arabia > Eastern Province > Al-Ahsa Governorate > Arabian Basin > Widyan Basin > Ghawar Field > Khuff C Formation (0.99)
- (4 more...)
Abstract This paper discusses new techniques for the modeling and simulation of naturally fractured reservoirs with dual porosity models. Most of the existing dual porosity models idealize matrix-fracture interaction by assuming orthogonal fracture systems (parallelepiped matrix blocks) and pseudo-steady state flow. More importantly, a direct generalization of single-phase flow equations is used to model multi-phase flow, which can lead to significant inaccuracies in multiphase flow behavior predictions. In this work, many of these existing limitations are removed in order to arrive at a transfer function more representative of real reservoirs. Firstly, combining the differential form of the single-phase transfer function with analytical solutions of the pressure diffusion equation, an analytical form for a shape factor for transient pressure diffusion is derived to corroborate its time dependence. Further, a pseudo-steady shape factor for rhombic fracture systems is also derived and its effect on matrix-fracture mass transfer demonstrated. Finally, a general numerical technique to calculate the shape factor for any arbitrary shape of the matrix block (i.e. non-orthogonal fractures) is proposed. This technique also accounts for both transient and pseudo-steady state pressure behavior. The results were verified against fine-grid single porosity models and were found to be in excellent agreement. Secondly, it is shown that the current form of the transfer function used in reservoir simulators does not fully account for the main mechanisms governing multiphase flow. A complete definition of the differential form of the transfer function for two-phase flow is derived and combined with the governing equations for pressure and saturation diffusion to arrive at a modified form of the transfer function for two-phase flow. The new transfer function accurately takes into account pressure diffusion (fluid expansion) and saturation diffusion (imbibition), which are the two main mechanisms driving multiphase matrix-fracture mass transfer. New shape factors for saturation diffusion are defined. It is shown that the prediction of wetting phase imbibition using the current form of the transfer function can be quite inaccurate, which might have significant consequences from the perspective of reservoir management. Fine grid single porosity models are used to verify the validity of the new transfer function. The results from single block dual porosity models and the corresponding single porosity fine grid models were in good agreement. Introduction A naturally fractured reservoir (NFR) can be defined as a reservoir that contains a connected network of fractures (planar discontinuities) created by natural processes like diastrophism and volume shrinkage (Ordonez et al., 2001). Fractured petroleum reservoirs represent over 20% of the world's oil and gas reserves (Saidi, 1983), but are however amongst the most complicated class of reservoirs. A typical example is the Circle Ridge fractured reservoir located on the Wind River Reservation in Wyoming, USA. This reservoir has been in production for more than 50 years but the total oil recovery until now has been less than 15% (, 2000). It is undeniable that reservoir characterization, modeling and simulation of naturally fractured reservoirs present unique challenges that differentiate them from conventional, single porosity reservoirs. Not only do the intrinsic characteristics of the fractures, as well as the matrix, have to be characterized, but the interaction between matrix blocks and surrounding fractures must also be modeled accurately. Further, most of the major NFRs have active aquifers associated with them, or would eventually be subjected to some kind of secondary recovery process such as waterflooding (German, 2002), implying that it is essential to have a good understanding of the physics of multiphase flow for such reservoirs. This complexity of naturally fractured reservoirs necessitates the need for their accurate representation from a modeling and simulation perspective, such that production and recovery from such reservoirs be predicted and optimized.
- North America > United States > California > Dixon Field (0.89)
- North America > Canada > Manitoba > Williston Basin > Pierson Field (0.89)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Naturally-fractured reservoirs (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management (1.00)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)
Abstract For some petroleum fields, optimization of production operations can be a major factor for increasing production rates and reducing production costs. While for single wells or other small systems simple nodal analysis can be adequate, large complex systems demand a much more sophisticated approach. Many mature fields are produced by gas-lift under multiple constraints imposed by the field handling capacity of the system. In this paper we present an optimization technique for allocating production rates and lift-gas rates to wells of large fields subject to multiple flow rate and pressure constraints. The well rate and lift-gas rate allocation problem has been addressed in the literature. However, existing methods are either inefficient or make significant simplifications. This often leads to suboptimal operations. This paper proposes a new formulation of the problem that is able to handle flow interactions among wells and can be applied to a variety of problems of varying complexities. We show that the proper formulation of the optimization problem is important in the practical use of modern optimization techniques. Once formulated, the optimization problem is solved by a sequential quadratic programming algorithm. Our results show that the procedure developed in this paper is capable of handling complex oil production problems. Introduction In petroleum fields, hydrocarbon production is often constrained by reservoir conditions, deliverability of the pipeline network, fluid handling capacity of surface facilities, safety and economic considerations, or a combination of these considerations. While production can be controlled by adjusting well production rates, allocating lift-gas rates, and in some fields, by switching well connections from one flowline to another flowline, implementation of these controls in an optimal manner is not easy. The objective of dynamic production optimization is to find the best operational settings at a given time, subject to all constraints, to achieve certain operational goals. These goals can vary from field to field and with time. Typically one may wish to maximize daily oil rates or minimize production costs. Various aspects of production optimization have been addressed in the literature. For example, several researchers have studied the problem of allocating limited amount of available gas to specified wells for continuous gas-lift. Fang and Lo proposed a linear programming technique to allocate lift-gas and well rates subject to multiple flow rate constraints. Barnes et al. developed an optimization technique for a portion of the Prudhoe Bay field in Alaska. This model maximizes oil production while minimizing the need for gas processing. Several papers have reported results for the production optimization of the Kuparuk River field in Alaska. The techniques published so far either addressed only a part of the optimization problem of interest to us or made significant simplifications during the optimization process. In most commercial reservoir simulators, flow rate constraints on facilities are handled sequentially by ad hoc rules. In addition, gas-lift optimization is done separately from the allocation of well rates. Because of the nonlinear nature of the optimization problem and complex interactions, results from such procedures can be unsatisfactory. In a companion paper Wang et al. presented a procedure for the simultaneous optimization of well rates, lift-gas rates, and well connections subject to multiple pressure, flow rate, and velocity constraints. While this approach was successful, it was limited in its ability to handle flow interactions among wells when allocating well rates and lift-gas rates. Here we extend the work of Wang et al. and propose a new formulation for the problem of simultaneously optimizing the allocation of well rates and lift-gas rates. The optimization problem is solved by a sequential quadratic programming algorithm, which is a derivative-based nonlinear optimization algorithm. The proposed method is tested on several examples. Results show that the method is capable of handling flow interactions among wells and can be applied to a variety of problems of varying complexities and sizes.
- Research Report > New Finding (0.88)
- Research Report > Experimental Study (0.54)
- North America > United States > Alaska > North Slope Basin > Prudhoe Bay Field (0.99)
- North America > United States > Alaska > North Slope Basin > Kuparuk River Field (0.99)
- Asia > Middle East > Israel > Mediterranean Sea > Southern Levant Basin > Or Field (0.99)
Abstract In many mature fields, the production of oil, gas, and water is facility constrained. For such fields, optimal use of existing surface facilities is the key to increasing well rates and/or reducing production costs. Here we propose solution procedures for such nonlinearly constrained production optimization problems. The objective function of the optimization problem is oil or gas production from the field. Production is subject to multiple flow rate constraints at separators, pressure constraints at specific nodes of the gathering system, total gas-lift volumes, and maximum velocity constraints for pipelines. The control variables are the well rates, gas-lift rates, and well allocations to flow lines. The problem is formulated as a mixed integer nonlinear optimization problem and is solved by a heuristic nonlinear optimization method. The optimization algorithm is coupled with models for multiphase fluid flow in the reservoir and surface pipeline network in a commercial reservoir simulator+. The proposed procedure was tested in a Gulf of Mexico oil field and a published example, and then applied to the Prudhoe Bay field in the North Slope of Alaska. Results demonstrate the effectiveness and business value of the developed tools. Introduction In some mature fields, oil production is constrained by the gas and/or liquid handling capacities of surface facilities. While facility expansion may be an option to increase rates, it may not be the optimal choice. An economic alternative is to make optimal use of existing production facilities. In this study, we address the following operational decisions to enhance production:How to control well rates with chokes? How to distribute available lift-gas among specified wells? How to route fluids by switching well connections to flow lines? These operational decisions are constrained by multiple capacity constraints in production facilities and wells, along with velocity constraints in flow lines to avoid excessive corrosion/erosion. Various aspects of the gas-lift optimization problem have been studied by Kanu et al.1, Buitrago et al.2, Nishikiori et al.3, and Martinez et al.4 using various optimization techniques, i.e., the equal-slope method, a Quasi-Newton method, and a genetic algorithm. Fang and Lo5 proposed a linear programming model to optimize lift-gas subject to multiple nonlinear flow rate constraints. In these studies various gas injection scenarios were evaluated using gas-lift performance curves for individual wells, ignoring interactions among wells. Dutta-Roy et al.6 analysed a gas-lift optimization problem with two wells sharing a common flow line. They pointed out that when flow interactions among wells are significant, nonlinear optimization tools are needed. They applied a Sequential BLOCK 1 - - FORUM 4 337 OPTIMIZATION OF PRODUCTION FROM MATURE FIELDS Quad
- North America > United States > Alaska > North Slope Basin > Prudhoe Bay Field (0.99)
- North America > United States > Texas > Permian Basin > Midland Basin > University Field > Wolfcamp Formation (0.98)
Abstract Three-phase flow is present in many oil recovery processes of interest to the oil industry. It occurs in processes such as primary production below bubble point pressure in reservoirs with water drive, in gas or water alternating gas (WAG) injection into waterflooded reservoirs, in thermal oil recovery, and in surfactant flooding. Despite its common occurrence, our ability to reliably model three-phase flow using numerical simulation is questionable. This paper shows the importance of three-phase flow at typical oil field conditions. It also shows the uncertainties in the predictions of oil recovery due to the three-phase relative permeability model. Numerical simulations of immiscible gas and WAG injection into a waterflooded one eighth of a five-spot were performed to determine the importance of the three-phase flow at conditions that are of interest to the oil industry. Consistent oil-water imbibition and oil-gas drainage relative permeability and capillary pressure were derived for this purpose, including a new form for imbibition capillary pressure. Dimensionless scaling groups for three-dimensional three-phase flow in porous media were developed. The scaling groups were used to design simulations at various conditions of gravity, viscous and capillary force interactions. In addition, several simulations were made to determine the uncertainty of the results due to the model for three-phase relative permeabilities. The results of this study show that there is a significant uncertainty associated with the selection of the three-phase relative permeability model for field scale simulations of gas and WAG injections. This uncertainty is translated into doubtful sirnulation results in terms of distribution of the fluids inside large volumes of the reservoir, total oil recovery, and fluids production rates. It is shown that additional oil recovery due to gas injection after a waterflood can be different by a factor of two depending on the model for three-phase relative permeability. It is also shown that the producing gas oil ratio (GOR) varies considerably depending on the model for three-phase relative permeability, while maintaining the same two-phase relative permeabilities. Accurate predictions of oil recovery in processes that exhibit three-phase flow need more rigorous models for three-phase relative permeability. Large three-phase flow regions were present for most of the conditions simulated. The size of the three-phase flow regions ranged from 20% to 80% of the volume of the reservoir. The size of the three-phase flow region was a strong function of the kro model used. Thus, an argument asserting that only a small part of the reservoir is affected by the uncertainties in the three-phase relative permeability model is not supported by these results.