Hybrid differential evolution and particle swarm optimization for optimal well placement

There is no gainsaying that determining the optimal number, type, and location of hydrocarbon reservoir wells is a very important aspect of field development planning. The reason behind this fact is not farfetched—the objective of any field development exercise is to maximize the total hydrocarbon recovery, which for all intents and purposes, can be measured by an economic criterion such as the net present value of the reservoir during its estimated operational life-cycle. Since the cost of drilling and completion of wells can be significantly high (millions of dollars), there is need for some form of operational and economic justification of potential well configuration, so that the ultimate purpose of maximizing production and asset value is not defeated in the long run. The problem, however, is that well optimization problems are by no means trivial. Inherent drawbacks include the associated computational cost of evaluating the objective function, the high dimensionality of the search space, and the effects of a continuous range of geological uncertainty. In this paper, the differential evolution (DE) and the particle swarm optimization (PSO) algorithms are applied to well placement problems. The results emanating from both algorithms are compared with results obtained by applying a third algorithm called hybrid particle swarm differential evolution (HPSDE)—a product of the hybridization of DE and PSO algorithms. Three cases involving the placement of vertical wells in 2-D and 3-D reservoir models are considered. In two of the three cases, a max-mean objective robust optimization was performed to address geological uncertainty arising from the mismatch between real physical reservoir and the reservoir model. We demonstrate that the performance of DE and PSO algorithms is dependent on the total number of function evaluations performed; importantly, we show that in all cases, HPSDE algorithm outperforms both DE and PSO algorithms. Based on the evidence of these findings, we hold the view that hybridized metaheuristic optimization algorithms (such as HPSDE) are applicable in this problem domain and could be potentially useful in other reservoir engineering problems.     

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.     

Simultaneous and sequential approaches to joint optimization of well placement and control

Determining optimal well placement and control is essential to maximizing production from an oil field. Most academic literature to date has treated optimal placement and control as two separate problems; well placement problems, in particular, are often solved assuming some fixed flow rate or bottom-hole pressure at injection and production wells. Optimal placement of wells, however, does depend on the control strategy being employed. Determining a truly optimal configuration of wells thus requires that the control parameters be allowed to vary as well. This presents a challenging optimization problem, since well location and control parameters have different properties from one another. In this paper, we address the placement and control optimization problem jointly using approaches that combine a global search strategy (particle swarm optimization, or PSO) with a local generalized pattern search (GPS) strategy. Using PSO promotes a full, semi-random exploration of the search space, while GPS allows us to locally optimize parameters in a systematic way. We focus primarily on two approaches combining these two algorithms. The first is to hybridize them into a single algorithm that acts on all variables simultaneously, while the second is to apply them sequentially to decoupled well placement and well control problems. We find that although the best method for a given problem is context-specific, decoupling the problem may provide benefits over a fully simultaneous approach.     

Well placement optimization with the covariance matrix adaptation evolution strategy and meta-models

The amount of hydrocarbon recovered can be considerably increased by finding optimal placement of non-conventional wells. For that purpose, the use of optimization algorithms, where the objective function is evaluated using a reservoir simulator, is needed. Furthermore, for complex reservoir geologies with high heterogeneities, the optimization problem requires algorithms able to cope with the non-regularity of the objective function. In this paper, we propose an optimization methodology for determining optimal well locations and trajectories based on the covariance matrix adaptation evolution strategy (CMA-ES) which is recognized as one of the most powerful derivative-free optimizers for continuous optimization. In addition, to improve the optimization procedure, two new techniques are proposed: (a) adaptive penalization with rejection in order to handle well placement constraints and (b) incorporation of a meta-model, based on locally weighted regression, into CMA-ES, using an approximate stochastic ranking procedure, in order to reduce the number of reservoir simulations required to evaluate the objective function. The approach is applied to the PUNQ-S3 case and compared with a genetic algorithm (GA) incorporating the Genocop III technique for handling constraints. To allow a fair comparison, both algorithms are used without parameter tuning on the problem, and standard settings are used for the GA and default settings for CMA-ES. It is shown that our new approach outperforms the genetic algorithm: It leads in general to both a higher net present value and a significant reduction in the number of reservoir simulations needed to reach a good well configuration. Moreover, coupling CMA-ES with a meta-model leads to further improvement, which was around 20% for the synthetic case in this study.     

Well placement optimization subject to realistic field development constraints

This work considers the well placement problem in reservoir management and field development optimization. In particular, it emphasizes embedding realistic and practical constraints into a mathematical optimization formulation. Such constraints are a prerequisite for the wider use of mathematical optimization techniques in well placement problems, since constraints are a way to incorporate reservoir engineering knowledge into the problem formulation. There are important design limitations that are used by the field development team when treating the well placement problem, and these limitations need to be articulated and eventually formalized within the problem before conducting the search for optimal well placements. In addition, these design limitations may be explicit or implicit. In this work, various design limitations pertaining to well locations have been developed in close collaboration with a field operator on the Norwegian Continental Shelf. Moreover, this work focuses on developing constraint-handling capability to enforce these various considerations during optimization. In particular, the Particle Swarm Optimization (PSO) algorithm is applied to optimize for the well locations, and various practical well placement constraints are incorporated into the PSO algorithm using two different constraint-handling techniques: a decoder procedure and the penalty method. The decoder procedure maps the feasible search space onto a cube and has the advantage of not requiring parameter tuning. The penalty method converts the constrained optimization problem into an unconstrained one by introducing an additional term, which is called a penalty function, to the objective function. In contrast to the penalty method, only feasible solutions are evaluated in the decoder method. Through numerical simulations, a comparison between the penalty method and the decoder technique is performed for two cases. We show that the decoder technique can easily be implemented for the well placement problem, and furthermore, that it performs better than the penalty method in most of the cases.     

双种群进化粒子群算法求解地下水管理模型

为避免粒子群算法(PSO)早熟的缺点,设计了一种双种群进化粒子群算法(DE-PSO)。DE-PSO是基于PSO,引入选择、交叉及差分变异操作,并结合合理有效的粒子评价方法及越界处理方法之后形成的。将DE-PSO应用于两个地下水管理模型算例,第一个算例DE-PSO解的总抽水量分别比遗传算法(GA)、模拟退火算法(SA)和PSO减少了64、256、207 m3/d,第二个算例DE-PSO解的总治理成本分别比GA、SA和PSO减少了57.74、151.93、76.59万元。两个算例中DE-PSO都表现出稳定的进化趋势,寻优效率好于GA、SA和PSO,可以有效求解地下水管理模型问题。     

Optimization of well placement by combination of a modified particle swarm optimization algorithm and quality map method

Determining the optimum placement of new wells in an oil field is a crucial work for reservoir engineers. The optimization problem is complex due to the highly nonlinearly correlated and uncertain reservoir performances which are affected by engineering and geologic variables. In this paper, the combination of a modified particle swarm optimization algorithm and quality map method (QM + MPSO), modified particle swarm optimization algorithm (MPSO), standard particle swarm optimization algorithm (SPSO), and centered-progressive particle swarm optimization (CP-PSO) are applied for optimization of well placement. The SPSO, CP-PSO, and MPSO algorithms are first discussed, and then the modified quality map method is discussed, and finally the implementation of these four methods for well placement optimization is described. Four example cases which involve depletion drive model, water injection model, and a real field reservoir model, with the maximization of net present value (NPV) as the objective function are considered. The physical model used in the optimization analyses is a 3-dimensional implicit black-oil model. Multiple runs of all methods are performed, and the results are averaged in order to achieve meaningful comparisons. In the case of optimizing placement of a single producer well, it is shown that it is not necessary to use the quality map to initialize the position of well placement. In other cases considered, it is shown that the QM + MPSO method outperforms MPSO method, and MPSO method outperforms SPSO and CP-PSO method. Taken in total, the modification of SPSO method is effective and the applicability of QM + MPSO for this challenging problem is promising     

水文地质参数反演的Hooke-Jeeves粒子群混合算法

水文地质参数寻优结果的好坏会直接影响到地下水数值模拟的精度,而参数寻优结果很大程度上取决于寻优方法的选择。粒子群算法是一种基于群智能的随机全局寻优方法,算法的缺陷是后期搜索效率低劣。基于随机寻优算法的混合策略,引入有效的约束处理手段和粒子群算法惯性因子的动态非线性调整技术,有机融合粒子群算法与Hooke-Jeeves方法,提出一种适用于水文地质参数反演的HJPSO混合算法。应用研究表明,HJPSO混合算法在参数反演计算中求解精度高、收敛速度快、寻优性能强,是一种值得推广的水文地质参数识别方法。     

板状体磁异常数据反演的PSO算法

粒子群优化(PSO)算法是根据鸟群觅食过程中的迁徙和群集模型而提出的用于解决优化问题的算法,是一类随机全局优化技术,它通过粒子间的相互作用搜索复杂空间中的最优区域,其优势在于效率高,且又简单易实现。本文讨论了PSO算法用于板状体磁异常数据反演的方法,并与遗传算法(GA)进行了比较。理论和实测磁异常数据反演的结果表明,PSO算法具有更高的找寻最优解效率,是一种很有潜力的位场反演工具。     

A unified formulation for generalized oilfield development optimization

Oilfield development involves several key decisions, including the number, type (injection/production), location, drilling schedule, and operating control trajectories of the wells. Without considering the coupling between these decision variables, any optimization problem formulation is bound to find suboptimal solutions. This paper presents a unified formulation for oilfield development optimization that seeks to simultaneously optimize these decision variables. We show that the source/sink term of the governing multiphase flow equations includes all the above decision variables. This insight leads to a novel and unified formulation of the field development optimization problem that considers the source/sink term in reservoir simulation equations as optimization decision variables. Therefore, a single optimization problem is formulated to simultaneously search for optimal decision variables by determining the complete dynamic form of the source/sink terms. The optimization objective function is the project net present value (NPV), which involves discounted revenue from oil production, operating costs (e.g. water injection and recycling), and capital costs (e.g., cost of drilling wells). A major difficulty after formulating the generalized field development optimization problem is finding an efficient solution approach. Since the total number of cells in a reservoir model far exceeds the number of cells that are intersected by wells, the source/sink terms tend to be sparse. In fact, the drilling cost in the NPV objective function serves as a sparsity-promoting penalty to minimize the number of wells while maximizing the NPV. Inspired by this insight, we solve the optimization problem using an efficient gradient-based method based on recent algorithmic developments in sparse reconstruction literature. The gradients of the NPV function with respect to the source/sink terms is readily computed using well-established adjoint methods. Numerical experiments are presented to evaluate the feasibility and performance of the generalized field development formulation for simultaneous optimization of the number, location, type, controls, and drilling schedule of the wells.     

地下水污染源反演的Hooke Jeeves吸引扩散粒子群混合算法

根据污染物质量浓度监测数据进行地下水污染源反演是一类典型的地下水逆问题,该问题可转化为决策变量为污染源位置和强度的最优化问题进行求解。基于Hooke-Jeeves粒子群混合算法,引入吸引扩散粒子群(ARPSO)算法的粒子群发散算子,保证混合算法的种群多样性,并提出HJ-ARPSO混合算法,再结合地下水污染物迁移模型MT3DMS反演地下水污染源的位置和强度信息。在已知污染源位置和未知污染源位置两种情形下,分别利用HJ-ARPSO算法、HJ-PSO算法和GA算法进行地下水污染源反演。在两种情形下,HJ-ARPSO算法均具有较高的寻优成功率(分别对应为100%和90%);与之相比,未引入粒子群发散算子的HJ-PSO算法在未知污染源位置情形下其寻优成功率迅速降为60%;GA算法寻优效率则最低。算例结果表明,HJ-ARPSO算法是一种有效的地下水污染源反演优化算法。     

基于引力搜索法的隧道围岩微震定位研究

针对目前深埋隧道围岩微震源定位难且精度不高等问题,采用启发式算法——引力搜索法（GSA）对隧道围岩微震源位置进行搜索,并将该算法与粒子群算法和单纯形法的搜索结果进行对比。发现在双速度模型和三速度模型下,引力搜索法相较于粒子群算法和单纯形法,都具有快速收敛、精度较高的优点,且与震源位置的距离能够控制在10 m以内。对双速度模型,引力搜索法的精度相对于单纯形法提高了83.71%,相对于粒子群算法提高了7.77%。对三速度模型,引力搜索法的精度相对于单纯形法提高了70.67%,相对于粒子群算法提高了39.36%。可见,该方法为深埋隧道微围岩震源定位提供了一种新思路。     

Computation of Periodic Orbits around L1 and L2 using PSO Technique

Astronomy Reports - In this work, an optimization problem related to a non-linear function is tackled mathematically by the use of particle swarm optimization (PSO) method in the case of circular...     

基于粒子群优化的岩土工程反分析研究

岩土工程优化反分析本质上看是一个典型的复杂非线性函数优化问题,采用全局优化算法是解决这个问题的理想途径,但由于优化反分析中多次调用正分析的特点使得整个算法的计算效率很低。为了提高优化反分析的计算效率,把一种计算效率更高的新型仿生算法--粒子群优化引入岩土工程反分析领域,提高反分析的计算效率。在此基础上,结合有限元数值分析技术,提出了一种新的岩土工程优化反分析算法--粒子群优化反分析。并通过一个简单算例验证了该法的有效性。     

Bat algorithm for dam–reservoir operation

Optimizing reservoir operation rule is considered as a complex engineering problem which requires an efficient algorithm to solve. During the past decade, several optimization algorithms have been applied to solve complex engineering problems, which water resource decision-makers can employ to optimize reservoir operation. This study investigates one of the new optimization algorithms, namely, Bat Algorithm (BA). The BA is incorporated with different rule curves, including first-, second-, and third-order rule curves. Two case studies, Aydoughmoush dam and Karoun 4 dam in Iran, are considered to evaluate the performance of the algorithm. The main purpose of the Aydoughmoush dam is to supply water for irrigation. Hence, the objective function for the optimization model is to minimize irrigation deficit. On the other hand, Karoun 4 dam is designed for hydropower generation. Three different evaluation indices, namely, reliability, resilience, and vulnerability were considered to examine the performance of the algorithm. Results showed that the bat algorithm with third-order rule curve converged to the minimum objective function for both case studies and achieved the highest values of reliability index and resiliency index and the lowest value of the vulnerability index. Hence, the bat algorithm with third-order rule curve can be considered as an appropriate optimization model for reservoir operation.     

A simultaneous perturbation stochastic approximation algorithm for coupled well placement and control optimization under geologic uncertainty

Development of subsurface energy and environmental resources can be improved by tuning important decision variables such as well locations and operating rates to optimize a desired performance metric. Optimal well locations in a discretized reservoir model are typically identified by solving an integer programming problem while identification of optimal well settings (controls) is formulated as a continuous optimization problem. In general, however, the decision variables in field development optimization can include many design parameters such as the number, type, location, short-term and long-term operational settings (controls), and drilling schedule of the wells. In addition to the large number of decision variables, field optimization problems are further complicated by the existing technical and physical constraints as well as the uncertainty in describing heterogeneous properties of geologic formations. In this paper, we consider simultaneous optimization of well locations and dynamic rate allocations under geologic uncertainty using a variant of the simultaneous perturbation and stochastic approximation (SPSA). In addition, by taking advantage of the robustness of SPSA against errors in calculating the cost function, we develop an efficient field development optimization under geologic uncertainty, where an ensemble of models are used to describe important flow and transport reservoir properties (e.g., permeability and porosity). We use several numerical experiments, including a channel layer of the SPE10 model and the three-dimensional PUNQ-S3 reservoir, to illustrate the performance improvement that can be achieved by solving a combined well placement and control optimization using the SPSA algorithm under known and uncertain reservoir model assumptions.     

Designing infill directional drilling in mineral exploration by using particle swarm optimization algorithm

Geostatistical optimization in designing infill boreholes is an important cost-effective approach in increasing the accuracy of the tonnage and grade of an ore deposit. In this research, a new approach is proposed to design the optimum infill directional boreholes. In the proposed approach, the Kriging estimation variance is considered as the objective function and the number and properties of the optimum boreholes are estimated to minimize the objective function. The optimization procedure is implemented by Particle Swarm Optimization (PSO) algorithm. Range of the spatial and directional properties of new boreholes is determined by considering the primary information of the mineralization and administrative constraint of drilling. Then, the PSO algorithm is iteratively applied, and in each iteration, the variation of the estimated Kriging variance after drilling the new boreholes is determined and properties of the new boreholes are updated. The iterative procedure of the algorithm is continued until minimum Kriging variance is satisfied. The approach was applied to the Dalli Cu-Au porphyry deposit in Iran and three new infill directional boreholes were designed by considering six earlier boreholes from the preliminary exploration stage. New optimum boreholes were located where less information from the preliminary exploration stage exists and the highest variance is considered. Two new boreholes are near to vertical (78°) and the third is an inclined with 55° dip. By drilling these three new boreholes, the estimated grade model could be upgraded by 20%. For simplicity, quickness and the ability to search for the required numbers and specifications of a group of directional boreholes in a 3D environment are the most advantages aspects of the proposed approach.     

An Improved Gradual Deformation Method for Reconciling Random and Gradient Searches in Stochastic Optimizations

Constraining stochastic models of reservoir properties such as porosity and permeability can be formulated as an optimization problem. While an optimization based on random search methods preserves the spatial variability of the stochastic model, it is prohibitively computer intensive. In contrast, gradient search methods may be very efficient but it does not preserve the spatial variability of the stochastic model. The gradual deformation method allows for modifying a reservoir model (i.e., realization of the stochastic model) from a small number of parameters while preserving its spatial variability. It can be considered as a first step towards the merger of random and gradient search methods. The gradual deformation method yields chains of reservoir models that can be investigated successively to identify an optimal reservoir model. The investigation of each chain is based on gradient computations, but the building of chains of reservoir models is random. In this paper, we propose an algorithm that further improves the efficiency of the gradual deformation method. Contrary to the previous gradual deformation method, we also use gradient information to build chains of reservoir models. The idea is to combine the initial reservoir model or the previously optimized reservoir model with a compound reservoir model. This compound model is a linear combination of a set of independent reservoir models. The combination coefficients are calculated so that the search direction from the initial model is as close as possible to the gradient search direction. This new gradual deformation scheme allows us for reducing the number of optimization parameters while selecting an optimal search direction. The numerical example compares the performance of the new gradual deformation scheme with that of the traditional one.     

Streeter-Phelps模型参数估计的遗传算法

提出Streeter-Phelps模型参数估计的新方法--遗传算法(Genetic Algorithm),它不同于常规参数估计方法,其优点在于,从多个初始点开始寻优,并采用交迭和变异运算避免过早地收敛到局部最优解,可获得全局最优解,且不受初始值影响.该方法不必求导计算,编程简单快捷.给出了实例计算及与其他方法相比较的结果.     

Optimization of nonconventional wells under uncertainty using statistical proxies

The determination of the optimal type and placement of a nonconventional well in a heterogeneous reservoir represents a challenging optimization problem. This determination is significantly more complicated if uncertainty in the reservoir geology is included in the optimization. In this study, a genetic algorithm is applied to optimize the deployment of nonconventional wells. Geological uncertainty is accounted for by optimizing over multiple reservoir models (realizations) subject to a prescribed risk attitude. To reduce the excessive computational requirements of the base method, a new statistical proxy (which provides fast estimates of the objective function) based on cluster analysis is introduced into the optimization process. This proxy provides an estimate of the cumulative distribution function (CDF) of the scenario performance, which enables the quantification of proxy uncertainty. Knowledge of the proxy-based performance estimate in conjunction with the proxy CDF enables the systematic selection of the most appropriate scenarios for full simulation. Application of the overall method for the optimization of monobore and dual-lateral well placement demonstrates the performance of the hybrid optimization procedure. Specifically, it is shown that by simulating only 10% or 20% of the scenarios (as determined by application of the proxy), optimization results very close to those achieved by simulating all cases are obtained.