Optimal Number Of Wells Research Articles

Numerical approach for the optimal design of dewatering schemes for deep foundation pits

In recent years, underground spaces have expanded widely in the urban zone. The appropriate estimation number of dewatering well with economical costs and securing soil stability at construction sites is challenging in designing pumping schemes. This paper aims to present the numerical approach for the optimal number of wells for designing a dewatering deep foundation pit. First, the estimated hydraulic conductivity was selected among the Theis, Cooper-Jacod, and reverse groundwater modeling methods. The estimated hydraulic conductivity via reverse groundwater modeling shows the lowest error with the monitoring pumping test. Second, hydraulic conductivity was input to groundwater modeling to estimate the groundwater level of four pumping schemes with the same total pumping rate (20 wells, 17 wells, 14 wells, and 13 wells). The number of wells was optimal from four random pumping schemes concerning the cost and the drawdown outside the pit. As a result, the pumping scheme with 16 wells is suitable, satisfying the cost and safety outside the drawdown of the foundation pit. The numerical approach could apply to estimate the number of wells for dewatering projects with economic costs and less impact on surrounding construction sites.

Early field planning using optimisation and considering uncertainties

During early phases of oil field development, field planners must decide upon the optimal number of wells and optimal field plateau rate, usually by performing sensitivity studies. These design choices are then “frozen” in subsequent development stages. However, they often end up being suboptimal when the field is built and produced and the uncertainty is reduced. In this work, we employ non-linear numerical optimisation, latin hypercube sampling and the Schwartz & Smith oil price model to compute probability distributions of the optimal number of wells, plateau rate and project value. We also employ an analytical model to compute production profiles and project value and consider uncertainties in in-place oil volume, well productivity and oil price. Then, we study how do these distributions change from early field planning until when the field is abandoned, when uncertainties are reduced to a minimum. The variation in time of the in-place oil volume uncertainty is modelled with a random walk. The well productivity is a step function altered randomly after production startup. The actual oil price trajectory is picked randomly from possible trajectories computed with the Schwartz and Smith model. The results show that the distributions of the optimal number of wells, plateau rate and project value depend greatly on the uncertainties in the input data. Field designs based on the average of the distributions during the early phase are profitable, but suboptimal. A potential upside of such designs is that they entail less capital investment and therefore less financial risk when compared against the optimal field design. • Robust approach to consider uncertainties when computing optimal field design. • The optimal design strongly depends on the uncertainties in input parameters. • Uncertainties in input parameters are considered to vary during the field’s life. • The value of perfect information is modest for the cases studied in this paper.

Drilling-Campaign Optimization Using Sequential Information and Policy Analytics

SummaryOptimally designed drilling campaigns are essential for improving oil recovery and value creation. They are required at different stages of the hydrocarbon-field life cycle, including exploration, appraisal, development, and infill. A significant fraction of the revenue risk comes from geological uncertainty, and for this reason, subsurface teams are frequently responsible for optimizing campaign parameters such as the number of wells, the corresponding locations, and the drilling sequence. Companies use the information and learning from drilled wells to adapt the remainder of the campaign, but classical optimization methods do not account for such learning and flexibility over time. Accounting for sequential geological information acquisition and decision making in the optimization of drilling campaigns adds value to the project.We propose a method to optimize drilling campaigns under geological uncertainty by using a sequential-decision model to obtain the optimal drilling policy and applying analytics over the policy to obtain the optimal number of wells and corresponding locations. The novel contribution of policy analytics provides better access to information within the complex data structure of the optimal policy, providing decision support for different decision criteria.The method is demonstrated in two different cases. The first case considers a set of eight candidate wells on predefined locations, mimicking the situation where the method is used after a prior subsurface optimization. The second case considers a set of 12 candidate wells regularly scattered in the same area and uses the method as the first optimization approach to filter out less-attractive regions. Exploiting the geological information on a well-by-well basis improved the expected campaign value by 65% in the first case and by 183% in the second case. The value of spatial geological information and value of flexibility from having more drilling candidates are two byproducts of the method application.

Differential evolution for early-phase offshore oilfield design considering uncertainties in initial oil-in-place and well productivity

• Differential evolution optimization of number of wells, plateau rate and NPV. • Multi-objective optimization considering ultimate recovery factor and NPV. • The NPV distribution average can be estimated with the average of the variables. • Method provides decision support to field planners in early field development. During the early phases of offshore oil field development, field planners must decide upon general design features such as the required number of wells and maximum oil processing capacity (field plateau rate), usually by performing sensitivity studies. These design choices are then locked in subsequent development stages and often prevent from achieving optimal field designs in later planning stages when more information is available and uncertainties are reduced. In the present study, we propose using numerical optimization of net present value (NPV) to advice field planners when deciding on the appropriate number of wells, maximum oil processing capacity (plateau rate) in a Brazilian offshore oil field. Differential Evolution (DE) is employed for solving the optimization models. The uncertainties considered are well productivity and initial oil-in-place, handled by (1) using the mean of the distributions and (2) Monte Carlo simulation. A multi-objective optimization was also formulated and solved including ultimate recovery factor in addition to net present value. The proposed method successfully computes probability distributions of optimal number of wells, plateau rate and NPV. If one wishes to compute the mean of such distributions only, for most cases it is adequate to run an optimization using the mean of the input values instead of performing Monte Carlo sampling. The multi-objective optimization allows to find field designs with high ultimate recovery factor and high NPV. In this case, the value of NPV is similar to the optimum NPV value when optimizing NPV only. The methods described could provide decision support to field planners in early stages of field development.

Deep Reinforcement Learning for Constrained Field Development Optimization in Subsurface Two-phase Flow

Oil and gas field development optimization, which involves the determination of the optimal number of wells, their drilling sequence and locations while satisfying operational and economic constraints, represents a challenging computational problem. In this work, we present a deep-reinforcement-learning-based artificial intelligence agent that could provide optimized development plans given a basic description of the reservoir and rock/fluid properties with minimal computational cost. This artificial intelligence agent, comprising of a convolutional neural network, provides a mapping from a given state of the reservoir model, constraints, and economic condition to the optimal decision (drill/do not drill and well location) to be taken in the next stage of the defined sequential field development planning process. The state of the reservoir model is defined using parameters that appear in the governing equations of the two-phase flow (such as well index, transmissibility, fluid mobility, and accumulation, etc.,). A feedback loop training process referred to as deep reinforcement learning is used to train an artificial intelligence agent with such a capability. The training entails millions of flow simulations with varying reservoir model descriptions (structural, rock and fluid properties), operational constraints (maximum liquid production, drilling duration, and water-cut limit), and economic conditions. The parameters that define the reservoir model, operational constraints, and economic conditions are randomly sampled from a defined range of applicability. Several algorithmic treatments are introduced to enhance the training of the artificial intelligence agent. After appropriate training, the artificial intelligence agent provides an optimized field development plan instantly for new scenarios within the defined range of applicability. This approach has advantages over traditional optimization algorithms (e.g., particle swarm optimization, genetic algorithm) that are generally used to find a solution for a specific field development scenario and typically not generalizable to different scenarios. The performance of the artificial intelligence agents for two- and three-dimensional subsurface flow are compared to well-pattern agents. Optimization results using the new procedure are shown to significantly outperform those from the well pattern agents.

OPTIMIZATION OF GROUND WATER CUTOFF WITH A SIPHON INTAKE FROM THE DRAIN WELLS (AS IN THE CASE OF KAMYANKA-DNIPROVSKA GROUND WATER CUT-OFF)

Relevance of research.To increase the efficiency and reliability of the territory protection against flooding with the infiltration water of the Kakhovsky Reservoir, it is proposed to replace the low-performance ground water cutoff with an airlift water intake system for the protection of the Kamensky Pod’s area with a groundwater cutoff with a siphon intake system from wells. That will enable to increasesignificantly the efficiency and reliability of the ground water cutoff and greatly reduce the specific costs of water pumping. The reliability of the ground water cutoff with a siphon intake system is achieved by ensuring the reliable sealing of the entire siphon collecting conduit. In case of a slightest damage, there is a loss of sealing of the pipes and the water stops flowing into a drain well.
 The purpose of the research. To determine the best parameters of ground water cutoff with a siphon intake system from the well, in particular: - the optimal number of wells, the distance between them; - estimated depths of each wells connected to the siphon collecting conduit; - estimated water flows from each well and the decrease in the static water table in them taking into account the hydro-geological interaction between them during their collaboration; - optimal pipe diameters on each section of the siphon collecting conduit to ensure the reliability of its operation.
 The research methods. The research involves the use of analytical and mathematical methods, in particular: calculations, iterations, forecasting.
 The research results. New approaches enabling to find an optimal variant of uniform water drawdown in the aquifer along the whole length of the siphon water conduit by reducing the depths of the intake wells towards the intake well. To optimize the ground water cutoff with the siphon intake system from the wells, it is proposed to drill drain wells of different depths and place them at different distances from each other along the entire length of the collecting conduit, determining the required depth of the well depending on its diameters and vacuum value.
 The conducted studies as in the case of calculating the Kamyanka-Dniprovskaground water cutoff showed that the minimum depth of drainage wells depends on the diameter of the well and the vacuum value in it, and the most efficient option of all possible ones is the option when there are drain wells with different depths and they are located at different distances from each other that provides a minimum specific cost for the construction of wells and siphon collecting water conduit.

A Mixed Integer Linear Programming Method for Optimizing Layout of Irrigated Pumping Well in Oasis

Optimization of irrigation well layout plays a vital role in the rational utilization of groundwater and to balance the water–energy nexus, especially in arid irrigation districts. This study proposes the mixed integer linear programming model (MILP) for well layout optimization with minimum well irrigation costs. This model efficiently establishes a link between irrigation area and wells to express the constraints of ensuring that irrigation area can be covered with optimal wells by using grid points to represent the irrigation area. It also uses the special ordered sets (SOS) modeling tool to decompose the mixed integer nonlinear programming into a mixed integer linear programming by assigning SOS-constrained weights to discrete points of a nonlinear function. This method was used in Cele Oasis of the Tarim Basin of the Xinjiang Province, an arid region in northwestern China. Since the original well layout was already established, different economic criteria like implicit cost and explicit cost were considered and two optimization results were yielded. The results showed that (1) the implicit cost optimization (ICO) and explicit cost optimization (ECO) reduced total costs by 7.64% and 3.56% compared with the condition of without optimization; and (2) the ICO and ECO reduced the optimal number of wells by 52.89% and 10.74% compared with the existing number of wells. Based on the analysis of the results, it is suggested that the manager should close uneconomical wells after determining the economic criteria. This method for well layout optimization can assist managers to make more rational plans for irrigation systems to exploit groundwater more efficiently, economically, and in a more environmentally friendly manner.

A simulation study to enhance the gas production rate by nitrogen replacement in the underground gas storage performance

Underground gas storage (henceforth; UGS) is considered as a common method which resolves the seasonality problem of transportation and distribution of gas phase in the oil and gas industries. The main objective of this study is to simulate one of Iranian’s depleted gas condensate reservoir and compare different injectivity scenarios especially nitrogen injection to enhance the gas production. Based on the anticipated target rate performance of UGS with a different scenario that was analyzed the effect of injection gas, finding optimum original reservoir pressure, an optimum number of wells. Moreover, abandonment pressure is one of the main concerns for UGS process in partially depleted reservoirs especially in the depleted reservoir to decrease the ultimate recovery. It contains insufficient base gas reserves, and if it may not meet the target withdrawal rate, the original reservoir pressure has been estimated at 250 bar. Consequently, it found that this problem can be addressed by injecting a higher volume of gas in the first cycle and due to the existence of new wells, the maximum injection rate was obtained about 6.1∗1010m3.

Closed-loop field development with multipoint geostatistics and statistical performance assessment

Closed-loop field development (CLFD) optimization is a comprehensive framework for optimal development of subsurface resources. CLFD involves three major steps: 1) optimization of full development plan based on current set of models, 2) drilling new wells and collecting new spatial and temporal (production) data, 3) model calibration based on all data. This process is repeated until the optimal number of wells is drilled. This work introduces a new CLFD implementation for complex systems described by multipoint geostatistics (MPS). Model calibration is accomplished in two steps: conditioning to spatial data by a geostatistical simulation method, and conditioning to production data by optimization-based PCA. A statistical procedure (TruMAP) is presented to assess the performance of CLFD. For performance assessment by TruMAP, the methodology is applied to an oil reservoir example for 25 different true-model cases. Application of a single-step of CLFD, improved the true NPV in 64%–80% of cases. The full CLFD procedure (with three steps) improved the true NPV in 96% of cases, with an average improvement of 37%. These results indicate that probability of improving true NPV increases with closed-loop step. This massive computational experiment involved about 9.5 million reservoir simulation runs that took about 320,000 CPU hours.

A new method to determine reasonable well pattern density in low-permeability gas reservoirs

The productivity evaluation of gas reservoirs is used to determine the optimal number of well pattern, which is an important part of the preparation of gas reservoir development plan. Using integral transformation and asymptotic analyses to solve the pseudo steady-state flow model in closed rectangular gas reservoir of constant thickness, analytic solution of pressure distribution of eccentric well can be obtained. This paper presents mathematical model of multiple wells producing from a closed gas reservoir by applying the principle of pressure superposition. The pseudo steady-state dimensionless production index is introduced to solve the multiple well mathematical models under the constant pressure, and the number of production wells and cumulative production in different production interval are obtained. The results of the calculation shows that the curve of the cumulative production and economic benefits have a maximum value when the producing time, gas price, and drilling costs are given, so it can determine the optimal number of wells and provide the basis for making gas reservoir development plan.

Influence of available data on the geostatistical-based design of optimal spatiotemporal groundwater-level-monitoring networks

Several methodologies exist for the design of optimal groundwater monitoring networks. Those that employ geostatistical techniques are usually dependent on a variogram. In practice, different variograms for an environmental variable can be fitted depending on the number of available data, their spatial distribution, and their variability. For this reason, in most cases, it is difficult to get an adequate variogram. This report evaluates the influence of the groundwater level data available in the construction of a product-sum spatiotemporal variogram model and its consequences on a geostatistical-based methodology that uses the Kalman filter for the design of optimal spatiotemporal monitoring networks. Additionally, a sensitivity analysis is carried out to determine the variations in the optimal number of wells and monitoring frequency for the monitoring network, depending on the selected spatiotemporal variogram model. The results show the importance of getting a good quality spatiotemporal variogram when designing optimal groundwater-level monitoring networks using geostatistical-based methodologies.

Use of Dynamic Data and a New Material-Balance Equation for Estimating Average Reservoir Pressure, Original Gas in Place, and Optimal Well Spacing in Shale Gas Reservoirs

Summary The average reservoir pressure is a key parameter in material-balance calculations, but its determination is challenging when dealing with shales because of their low and ultralow permeabilities. This paper presents an easy-to-reproduce methodology for calculating the average reservoir pressure from flowing data, and its use in a new material-balance equation (MBE) that considers the simultaneous contribution of free, adsorbed, and dissolved gas. The procedure developed in this paper uses a modified gas-compressibility factor (Z′) introduced in the new MBE. Because Z′ accounts for the combined effect of free, adsorbed, and dissolved gas, then total original gas in place (OGIP) can be determined from extrapolation of the MBE straight line to an average reservoir pressure equal to zero. Drainage area can be estimated on the basis of calculated OGIP and volumetric equations. As such, the methodology offers the potential to help improve well spacing in shale gas reservoirs in such a way that no stranded gas is left in the reservoir, or that excess wells are not drilled in the field. This can help to improve recoveries from shales by assisting in the determination of the optimal number of wells needed to drain a given play efficiently. In conventional reservoirs, a well is shut in, and the average reservoir pressure is determined from the corresponding pressure-buildup test. But, for the case of unconventional shale gas reservoirs, shutting the wells in is unacceptable because of the long time it would require for estimating average reservoir pressure. The methodology developed in this paper for shale gas reservoirs circumvents this problem by using dynamic data. Production data from multistage hydraulically fractured horizontal wells completed in a Canadian shale gas reservoir are used for testing the effectiveness of the new methodology. Comparison of typical well-spacing values vs. the drainage area calculated with the new methodology leads to the conclusion that, probably, only 40% of the gas is being drained efficiently. The novelty of this work relies on the development of a methodology for calculating average reservoir pressure, OGIP, drainage area, and optimal well spacing in shale reservoirs through the combination of dynamic data and a new MBE that considers simultaneously the effects of free, adsorbed, and dissolved gas.

Stochastic Resource Allocation for Well Control With Digital Oil Field Infrastructure

To investigate the flux patterns for a digital oil field system, the modeling and analysis need to include waterflood optimization, which is generated to maintain pressure and sweep oil to production. In this paper, a life-cycle well control optimization is integrated with proactive resource allocation to increase computational efficiency of mature fields. Based on a noninvasive and derivative-free approach, the combinatorial model is developed to address geological uncertainty by modifying injection and production rates at individual wells. With the derived model, the joint well control and field development algorithm is proposed based on their influence on the control variables. The possible benefits from the hybrid method and heuristics are clarified. In addition, the Benders decomposition method is adopted considering the computation burden with the optimal number of wells in a distributed manner at the cost of iteration. With the relaxation technique and acceleration technique, the optimal solutions are achieved to strengthen the cuts generated and to find better feasible solutions in less time. Simulation and experimental results are presented to verify the achievements of the proposed methods.

Determination of vertical/horizontal well type from generalized field development optimization

Field development planning entails determination of the optimal number of wells (horizontal/vertical), well types (producer/injector), well locations, and well controls. The numerous variables to be estimated and the reservoir geological uncertainty complicate the problem of determining the optimal development plan. The improvements in computational science have advanced the use of automated optimization for field development decisions.In this paper, we present a generalized field development optimization methodology for estimating vertical and horizontal well-types in developing a hydrocarbon reservoir. Two approaches for the generalized field development optimization are presented. One approach is based on the well control zonation (WCZ) procedure; the other is based on the mixed integer non-linear programming (MINLP) procedure. In the WCZ procedure, five zones were identified, each signifying a region of either horizontal injection wells, vertical injection wells, no wells, vertical production wells or horizontal production wells. In the MINLP approach, separate variables were defined for the determination of the well type. Additionally, we present an efficient method to constrain the minimum well spacing of the horizontal and vertical wells to predetermined parameters. The aim was to optimize the number of wells, the well types, the well locations and the well controls (production rates). These operational variables were estimated simultaneously. Particle swarm optimization (PSO) algorithm was used as an optimizer to determine the optimal parameter values.The WCZ and MINLP approaches were tested with two examples to determine which methodology was more effective. The results indicated that both methods could successfully determine the optimal parameters while satisfying the spacing constraints imposed by the user. The comparison of the results showed that the WCZ approach was more effective than the MINLP approach.

Application of DOE and metaheuristic bat algorithm for well placement and individual well controls optimization

The design of an optimal gas field development and production management is a complicating task because of influencing various factors on decision-making process. Typical factors include number and type of wells, well locations, and production constraints, economic factors of capital expenditure, operating costs, gas sale price, and different engineering and geological parameters. The situation is further complicated due to uncertainty associated with the nonlinear problem of field development optimization.In this study, first, design of experiment (DOE) techniques including uniform design (UD) and Box-Behnken design (BBD) are used for performance prediction of water drive gas reservoirs. Next, a new metaheuristic bat inspired algorithm (BA) will be applied in optimization process of objective function. Undiscounted net present value (UNPV) is used as an objective function for the determination of optimal number of wells (N), individual well locations (I and J), production rate (Qg), perforation thickness (Hp) and the limit of tubing head pressure (THP) for different average reservoir permeability (KG) and permeability anisotropy (Kv/Kh). In this regard, part of gas reservoir with an active bottom aquifer based on actual data is simulated in order to predict gas recovery factor and cumulative water production data that are necessary for performing production optimization.The results show that reducing gas production rate increases the UNPV. Reducing production rate increases ultimate recovery factor and decreases cumulative water production. However, considering time value of money, it is favorable to produce with high rates and consequently deplete the reservoir over short time scales in order to compensate the reduction of profit.

Generalized field-development optimization with well-control zonation

Of concern in the development of oil fields is the problem of determining the optimal locations of wells and the optimal controls to place on the wells. Extraction of hydrocarbon resources from petroleum reservoirs in a cost-effective manner requires that the producers and injectors be placed at optimal locations and that optimal controls be imposed on the wells. While the optimization of well locations and well controls plays an important role in ensuring that the net present value of the project is maximized, optimization of other factors such as well type and number of wells also plays important roles in increasing the profitability of investments. Until very recently, improving the net worth of hydrocarbon assets has been focused primarily on optimizing the well locations or well controls, mostly manually. In recent times, automatic optimization using either gradient-based algorithms or stochastic (global) optimization algorithms has become increasingly popular. A well-control zonation (WCZ) approach to estimating optimal well locations, well rates, well type, and well number is proposed. Our approach uses a set of well coordinates and a set of well-control variables as the optimization parameters. However, one of the well-control variables has its search range extended to cover three parts, one part denoting the region where the well is an injector, a second part denoting the region where there is no well, and a third part denoting the region where the well is a producer. By this, the optimization algorithm is able to match every member in the set of well coordinates to three possibilities within the search space of well controls: an injector, a no-well situation, or a producer. The optimization was performed using differential evolution, and two sample applications were presented to show the effectiveness of the method. Results obtained show that the method is able to reduce the number of optimization variables needed and also to identify simultaneously, optimal well locations, optimal well controls, optimal well type, and the optimum number of wells. Also, comparison of results with the mixed integer nonlinear linear programming (MINLP) approach shows that the WCZ approach mostly outperformed the MINLP approach.

Optimization of pumping policy using coupled finite element-particle swarm optimization modelling

An optimal pumping policy during groundwater extraction ensures the sustainability of groundwater resources. In this paper, a coupled finite element-particle swarm simulation–optimization model is implemented to assess the optimal pumping policy in a confined heterogeneous anisotropic synthetic aquifer. Pumping wells are set up in the aquifer to meet a specified water demand. The objective is to find the optimum number and pumping discharges of these wells such that their collective drawdown is minimized while meeting the demand at a reasonable cost. Constraints on the maximum allowable pumping discharge and the location of the wells are also imposed. After analysing the aquifer behaviour in the presence of 8, 9 and 10 pumping wells, the optimal number of wells is selected. The coupled FEM-PSO model also predicts the spatial distribution of the wells that incur the minimum cost for installation and pumping to a specified storage location. Adequate tuning of the PSO parameters involving population size, inertia weight, acceleration constants and number of iterations is performed to arrive at their optimal values.

Effects of Directional Permeability Anisotropy on Sweep Efficiency for Five-Spot and Nine-Spot Pattern Flood

Water flooding is the dominant fluid injection technique and is frequently applied worldwide secondary recovery process, which involves water injection in the oil formation under high pressure through an injection well to enhance oil recovery of the well(s) of interest. In order to plan implement successful water flooding optimum number of wells and location must be selected. This involves successful and judicious selection of water flood pattern to increase the reserves. This study emphasizes on important and effect of water flood pattern on oil recovery. This paper will also address the effect of the directional permeability on Cartesian and uniform grid. The patterns studied were fivespot and nine-spot pattern and by ignoring the gravity and capillary pressure the designed model will calculate the pressure and the water saturation for all nodes in five and nine spots scheme. The work shows that both pattern schemes produce almost the same tertiary oil under identical reservoir conditions. The nine point’s scheme showed smooth pressure and water distribution compared to five point’s scheme. A breakthrough time was earlier by 40-50 days for the nine spot patterns as compared to five spots pattern.

Effects of Infill- and Offset-Drilling Patterns on Field Development for Shale Wells

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 165722, ’An Examination of Infill- and Offset-Drilling Patterns in Field Development for Shale Wells,’ by Vivek Sahai, SPE, Greg Jackson, SPE, Farshad Lalehrokh, SPE, and Rakesh Rai, SPE, Weatherford, prepared for the 2013 SPE Eastern Regional Meeting, Pittsburgh, Pennsylvania, USA, 20-22 August. Delaying the start of new wells is understood to reduce the net present value (NPV) of a section, but variations in the arrangement of infill wells have not been examined thoroughly. In this paper, the effect of timing and pattern of well placement on NPV is studied. Three scenarios were evaluated: an infill scheme in which future wells are drilled between existing wells, a linear scheme in which future wells are immediate offsets of existing wells, and a hybrid scheme that is a combination of the infill and linear schemes. Introduction All previously published work using reservoir modeling to ascertain optimal well density assumes idealized conditions: zero well-to-well interference through fracture communication and simultaneous production initiation for all wells. Previous work postulated how infill-well drilling can improve cumulative recovery from shale-gas reservoirs because the distance between wells and the type of completion technique affect the amount of additional possible recovery. NPV considerations are important when operators consider either infill drilling or enhanced recovery methods to improve cumulative recovery from reservoirs that have gone through primary recovery. Reservoir simulation can help determine areas where depletion has not occurred and thus are optimal for potential infill-well development. The base case was chosen to be five wells per section (1,056 ft between wellbores) because of previous work. This paper determined how the economic results vary for three different field-development schemes for this optimal-well-spacing scenario. Basis of Modeling The numerical reservoir simulations used in this study capture flow from the stimulated reservoir volume (SRV) and external reservoir volume (XRV) within the drainage volume, as shown in Fig. 1. Average reservoir properties for the models are given in Table 1. The properties were averaged across 160 wells in a shale play in North America. The completed well length was the same for all cases, 3,840 ft, and the lateral was placed in the middle of the pay. The base case had a matrix permeability of 50 nd, a fracture spacing of 80 ft (which corresponds to 48 fractures on the 3,840-ft lateral), and a fracture half-length of 500 ft. The gas-production rate for each well in the section was 3,000 Mscf/D. Base Case The base case, described in earlier work, is shown in Fig. 2. The optimal number of wells per section is determined using normalized incremental cumulative recovery, which is defined as the number of wells beyond which any additional well provides a recovery factor less than 50% of that of the first well. Thus, the optimal number of wells per section for the base case is five wells, as confirmed by the peak in NPV. In this paper, all sections are assumed to require five wells for optimal development, on the basis of Fig. 2.

A derivative-free methodology with local and global search for the constrained joint optimization of well locations and controls

In oil field development, the optimal location for a new well depends on how it is to be operated. Thus, it is generally suboptimal to treat the well location and well control optimization problems separately. Rather, they should be considered simultaneously as a joint problem. In this work, we present noninvasive, derivative-free, easily parallelizable procedures to solve this joint optimization problem. Specifically, we consider Particle Swarm Optimization (PSO), a global stochastic search algorithm; Mesh Adaptive Direct Search (MADS), a local search procedure; and a hybrid PSO–MADS technique that combines the advantages of both methods. Nonlinear constraints are handled through use of filter-based treatments that seek to minimize both the objective function and constraint violation. We also introduce a formulation to determine the optimal number of wells, in addition to their locations and controls, by associating a binary variable (drill/do not drill) with each well. Example cases of varying complexity, which include bound constraints, nonlinear constraints, and the determination of the number of wells, are presented. The PSO–MADS hybrid procedure is shown to consistently outperform both stand-alone PSO and MADS when solving the joint problem. The joint approach is also observed to provide superior performance relative to a sequential procedure.