Closed-loop reservoir management on the Brugge test case

This paper proposes an augmented Lagrangian method for production optimization in which the cost function to be maximized is defined as an augmented Lagrangian function consisting of the net present value (NPV) and all the equality and inequality constraints except the bound constraints. The bound constraints are dealt with using a trust-region gradient projection method. The paper also presents a way to eliminate the need to convert the inequality constraints to equality constraints with slack variables in the augmented Lagrangian function, which greatly reduces the size of the optimization problem when the number of inequality constraints is large. The proposed method is tested in the context of closed-loop reservoir management benchmark problem based on the Brugge reservoir setup by TNO. In the test, we used the ensemble Kalman filter (EnKF) with covariance localization for data assimilation. Production optimization is done on the updated ensemble mean model from EnKF. The production optimization resulted in a substantial increase in the NPV for the expected reservoir life compared to the base case with reactive control.     

Gaussian Process Emulators for Computer Experiments with Inequality Constraints

Physical phenomena are observed in many fields (science and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all input variables. The aim is to build a model capable of incorporating both data interpolation and inequality constraints into a Gaussian process emulator. By using a functional decomposition, a finite-dimensional approximation of Gaussian processes such that all conditional simulations satisfy the inequality constraints in the entire domain is proposed. To show the performance of the proposed model, some conditional simulations with inequality constraints such as boundedness, monotonicity or convexity conditions in one and two dimensions are given. A simulation study to investigate the efficiency of the method in terms of prediction is included.     

Optimization with the Gradual Deformation Method

Building reservoir models consistent with production data and prior geological knowledge is usually carried out through the minimization of an objective function. Such optimization problems are nonlinear and may be difficult to solve because they tend to be ill-posed and to involve many parameters. The gradual deformation technique was introduced recently to simplify these problems. Its main feature is the preservation of the spatial structure: perturbed realizations exhibit the same spatial variability as the starting ones. It is shown that optimizations based on gradual deformation converge exponentially to the global minimum, at least for linear problems. In addition, it appears that combining the gradual deformation parameterization with optimizations may remove step by step the structure preservation capability of the gradual deformation method. This bias is negligible when deformation is restricted to a few realization chains, but grows increasingly when the chain number tends to infinity. As in practice, optimization of reservoir models is limited to a small number of iterations with respect to the number of gridblocks, the spatial variability is preserved. Last, the optimization processes are implemented on the basis of the Levenberg–Marquardt method. Although the objective functions, written in terms of Gaussian white noises, are reduced to the data mismatch term, the conditional realization space can be properly sampled.     

带有控制结构约束的次优状态反馈律的研究

研究了带有约束机制的次优状态反馈律，主要对终端时间tf=∞系统建立次优状态反馈的数学模型。通过简单控制结构约束的引入，消除状态变量不完全可测所造成的障碍，从而得到了带控制结构约束的次优必要条件及改进后的迭代算法。     

Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

An adjoint formulation for the gradient-based optimization of oil–gas compositional reservoir simulation problems is presented. The method is implemented within an automatic differentiation-based compositional flow simulator (Stanford’s Automatic Differentiation-based General Purpose Research Simulator, AD-GPRS). The development of adjoint procedures for general compositional problems is much more challenging than for oil–water problems due to the increased complexity of the code and the underlying physics. The treatment of nonlinear constraints, an example of which is a maximum gas rate specification in injection or production wells, when the control variables are well bottom-hole pressures, poses a particular challenge. Two approaches for handling these constraints are presented—a formal treatment within the optimizer and a simpler heuristic treatment in the forward model. The relationship between discrete and continuous adjoint formulations is also elucidated. Results for four example cases of increasing complexity are presented. Improvements in the objective function (cumulative oil produced) relative to reference solutions range from 4.2 to 11.6 %. The heuristic treatment of nonlinear constraints is shown to offer a cost-effective means for obtaining feasible solutions, which are, in some cases, better than those obtained using the formal constraint handling procedure.     

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.     

Approximate Derivative Computations for the Gradient-Based Optimization Methods in the Local Gradual Deformation for History Matching

Reservoir characterization needs the integration of various data through history matching, especially dynamic information such as production or four-dimensional seismic data. To update geostatistical realizations, the local gradual deformation method can be used. However, history matching is a complex inverse problem, and the computational effort in terms of the number of reservoir simulations required in the optimization procedure increases with the number of matching parameters. History matching large fields with a large number of parameters has been an ongoing challenge in reservoir simulation. This paper presents a new technique to improve history matching with the local gradual deformation method using the gradient-based optimizations. The new approach is based on the approximate derivative calculations using the partial separability of the objective function. The objective function is first split into local components, and only the most influential parameters in each component are used for the derivative computation. A perturbation design is then proposed to simultaneously compute all the derivatives with only a few simulations. This new technique makes history matching using the local gradual deformation method with large numbers of parameters tractable.     

Rural organizational impacts,mitigation strategies,and resilience to the 2010 Darfield earthquake,New Zealand

A methodology for evaluating real-time optimal reservoir releases under flooding conditions that minimizes flood damages for a river-reservoir system is described in this paper. The problem is formulated as a discrete-time optimal control problem in which reservoir releases are the control variables, and water surface elevations and discharges are the state variables. Constraints imposed on the reservoir’s water surface elevations and reservoir releases to the downstream reaches are incorporated into an objective function using a penalty function method. The optimal control model consists of the two primary interfaced components: (1) the U.S. Geological Survey Full EQuation routing model to simulate the unsteady flow dynamics of the river-reservoir system and (2) an optimization technique, simulated annealing that optimizes reservoir releases (flood control gate operations) subject to system constraints. The model solves an augmented control problem. The model was applied to the river-reservoir system of Lake Travis on the Lower Colorado River in Texas. The model application to Lake Travis revealed the usefulness of the model in improving a given operation policy, regardless of the type objective function (linear or nonlinear). The methodology and the operation model developed here are unique since they can be applied to any river-reservoir system, do not require simplification of nonlinearities, and guarantee the determination of an optimal or near-global optima.     

随钻测斜仪误差补偿实验研究

为消除测斜仪传感器因温度变化引起的温度漂移和降低安装误差,在随钻测斜仪的姿态数学模型及其产生误差原因分析的基础上,建立了基于最小二乘法的多项式拟合以及约束条件下多变量函数寻最优解的测斜仪温度漂移误差和安装误差补偿数学模型。通过ADXL345加速度传感器的温度误差补偿及安装误差校正的实验研究,结果表明,补偿后的测斜仪井斜角输出达到了较高的精度,满足了测斜仪的精度要求,表明建立的误差补偿数学模型正确,可应用于随钻测斜仪的误差补偿。      

基于遗传算法的分级预泄调度方案优化研究

采用分级预泄进行汛限水位动态控制,综合考虑洪水、预报系统、调度决策系统等不确定性因素影响,留有余地地选择浮动库容、预泄级数、相应泄流及流量控制点。此种调度方案能在保证防洪安全的前提下获得较大的兴利效益。实例表明,借助于遗传算法良好的全局优化搜索能力,合理设置参数约束范围和适应度函数,可以得出比较满意的调度方案。     

基于线性互补的非连续变形分析

非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题,合理设定罚参数很困难,此外,因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代,用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上,综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势,提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序,算例计算结果证明了方法的精度及可行性。     

Optimal lower bound of passive earth pressure using finite elements and non-linear programming

The present study pertains to the finding of the lower bound solution, formulating it as a non-linear programming problem using the generalized method developed by Lysmer with certain variations to incorporate the non-linear no-yield condition constraints directly in the analysis. The method considers the family of plane stress fields having the property that all stresses vary linearly within each triangular element of some mesh which covers the soil mass under study. For this type of stress field it is possible to express all equilibrium conditions as a set of linear constraints and the no-yield as a set of non-linear constraints. The boundary condition constraints may be of linear equality or inequality type. By expressing some of the design variables in terms of the remaining variables the linear equality constraints are implicity satisfied. Such a technique minimizes the complexity of the problem by eliminating the equality constraints and reduces the dimensionality of the problem, saving much, computational effort. The optimal lower bound is isolated by formulating it as a non-linear programming (NLP) problem subjected to both linear and non-linear inequality constraints. The sequential unconstrained minimization technique using the extended penalty function method as suggested by Kavlie has been used to isolate the optimal lower bound. The method has successfully been applied to the passive earth pressure and bearing capacity problem. Numerical results are obtained and compared with Lysmer's solution to show the effectiveness of the present approach.     

洪水预报模型输入与输出的误差分布及相关性分析

降雨预报信息作为洪水预报模型的输入,该信息的准确性直接影响洪水预报模型输出的准确性.为探究模型输入(降雨预报)误差与输出(洪水预报)误差之间的关系,以英那河流域为例,分析了不同雨量等级下,预报模型的输入误差与输出误差的分布规律,并定性分析了两种误差的相关关系.结果表明,降雨量等级若为无雨及小雨时,两种误差不相关;若为中...     

区域防洪治涝生产函数研究

分析了防洪治涝部门投入与产出的特殊性:年效益具有随机性;基建投入具有长效性,同时又具有逐年损耗性。为使基建投入、运行费和效益三者生产函数方程建立在各因素之间的内在因果联系上,提出采用效益累计值或移动平均值以消除逐年效益的随机性干扰;基建投入因素采用与效益同期的损耗值以考虑长效性和损耗性。在此基础上建立了累计效益与累计耗用基建投资、累计运行费的关系和平均年效益与平均年耗用基建投资、平均年运行费的关系。结合江苏省防洪治涝生产函数研究实例,用相关分析得出多项式和幂函数形式的生产函数,得出江苏省防洪治涝在1990年后的投入水平和投入结构下,边际效益很高,并且进一步加大投入水平或增加运行费的相对比例可得到更高的回报率。实例验证了方法的正确性与实用性。     

Hydro-thermal performance of multilayer capillary barriers in arid lands

In this study, a capillary barrier system was designed and tested for an arid land environment. To simulate arid land conditions of high temperature and sub-irrigation systems, the barrier was subjected to thermal and hydraulic gradients in opposite directions; to test the barrier system under these severe conditions, an experimental apparatus was designed and fabricated. The multilayer capillary barrier consisted of three layers made of silica sand, a mixture of sand and bentonite in equal portions, and a mixture of clay (25%) and aggregate (75%). Several one dimensional coupled heat and moisture tests were performed. Temperature variations along the thickness of the barrier were recorded as a function of time, and at the end of each test, the barrier was sliced into small sections, for the determination of volumetric water content as a function of distance from the heat source. The experimental results were discussed in view of the barrier's intended purpose of its ability to store moisture for long time durations. Coupled heat and moisture flow equations were developed and solved numerically via a finite difference method. Diffusivity parameters were calculated by using experimental results, a numerical model, and Powell's conjugate directions method of nonlinear optimization. The model was calibrated and the results were discussed. Good agreement between calculated and experimental results was obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于粒子群优化的BP神经网络模型参考自适应控制系统

将粒子群优化的BP神经网络作为模型，参考自适应控制系统的控制器，把参考模型输出与系统实际输出的均方误差作为PSO-BP神经网络的适应函数，通过PSO算法强大的搜索性能使自适应控制系统的均方误差最小化。仿真实例结果表明，基于粒子群优化算法的BP神经网络自适应控制系统收敛快、精度高，有较好的网络的泛化和适应能力，能够很好地控制系统的输出跟随参考模型的输出。     

二维地基中空沟−波阻板联合隔振屏障分析

针对地基隔振控制,提出了一类新型的空沟?波阻板联合隔振屏障,并对其隔振性能进行了数值分析。首先,利用复伸展坐标变换,在频域内建立了完全匹配层（perfect matched layer, PML）吸收边界的控制方程;其次,利用Galerkin近似技术,给出了以位移为基本未知量的二阶非分裂格式PML的频域有限元计算列式;最后,通过数值算例分析了空沟?波阻板联合隔振屏障的物性参数（地基与波阻板的模量比）、几何参数（空沟深度、波阻板深度）以及载荷参数（振动波频率）等对其隔振性能的影响规律。结果表明,空沟?波阻板联合隔振屏障结合了空沟和波阻板各自的优势,可以有效地控制不同频率振源引起的地基振动。     

Constraints and perspectives in aquaculture development

Aquaculture can be considered as a rapidly growing industry in many parts of the world. The impressive overall upward trend in production is likely to continue for the rest of the century. However, aquaculture will still be a minor contributor to the world's protein supply, even though the projected annual output of about 30 million tons can be realized by the year 2000. Nevertheless, aquaculture can play an important role in many developing countries not only within the context of rural development, but also as a commercial activity that focuses on export markets. Progress in aquaculture will always be accompanied by a number of constraints that occur with or through expansion of this industry. Some of the most important problem areas are briefly addressed, including those related to environmental degradation, disease control, human health and competition for resources. Finally, gaps in science and technology as well as research priorities are identified.