Adjoint-based optimization of multi-phase flow through porous media – A review

The recovery of oil from subsurface reservoirs often requires the injection of water or gas to maintain reservoir pressure and to displace the oil from injection to production wells. The design of an economically optimal recovery strategy is usually based on ’reservoir simulation’, i.e. large-scale numerical simulation of the flow of multi-phase fluids through strongly heterogeneous porous media with uncertain coefficients. Control of the recovery process is through prescribing time-varying pressures or flow rates in the wells. Efficient methods to optimize the recovery strategy make use of gradients of an economic objective function with respect to the well controls at every time step. These can be obtained efficiently with the aid of adjoint-based techniques. Constraints, in particular those that involve states (reservoir pressures or saturations) or outputs (measured well pressures or rates) require special treatment. Uncertainty in the coefficients can be incorporated through robust optimization over an ensemble of models. The limited controllability of the reservoir states offers scope for reduced-order modeling using techniques like proper orthogonal decomposition. ‘Closed-loop’ optimization can be performed through frequent repetition of the optimization during the producing life of the field in combination with updating the of the model coefficients based on production measurements. Moreover, an emerging technology is the operational use of model-based optimization which requires a combination of long-term and short-term objectives through multi-level optimization strategies.     

Application of an enhanced decision tree learning approach for prediction of petroleum production

Economic evaluation of a new oil well is important for decision-making in the petroleum industry, and this evaluation is based on a good prediction on a well's production. However, it is difficult to accurately predict a well's production due to the complex subsurface conditions of reservoirs. The industrial standard approach is to use either curve-fitting methods or complex and time-consuming reservoir simulations. In this paper, an enhanced decision tree learning approach called neural-based decision tree (NDT) model is applied in an attempt to investigate its performance in predicting petroleum production. The primary strength of this model is that it can capture dependencies among attributes, and therefore, it is likely to provide an improved or more accurate prediction (Lee and Yen, 2002).This paper presents an application of the NDT model for petroleum prediction. Our models were developed based on the five most significant parameters that affect oil production: permeability, porosity, first shut-in pressure, residual oil and saturation of water. The five parameters were used as input variables, and oil production is the output variable for modeling. Four different models were generated in the modeling process, and each involves a different combination of parameters. First, an overall oil production model is developed using the three geoscience parameters of permeability, porosity and first shut-in pressure. Secondly, two different models, with different input parameters, were developed to predict production in the post-water flooding stage only. The results of the above models indicate that data-driven models may not be effective for classifying the data set. Hence, a trend model was developed in an attempt to improve the effectiveness and accuracy of the predictive model. The result shows that the trend model can provide an improved performance, and its performance is comparable to that of the artificial neural network.     

Upscaling relative phase permeability for superelement modeling of petroleum reservoir engineering

A technique for locally rescaling (upscaling) the functions of the relative phase permeability (RPP) has been developed, which minimizes the error in the approximating the phase filtration rates for the superelement modeling of waterflooding a layered heterogeneous oil reservoir. The RPP is locally upscaled for each superelement based on the solution of two-dimensional two-phase filtration problems on a refined computational grid. Modified RPP functions (MFRPPs) are represented in the parametric form; i.e., the values of the parameters are sought when solving the problem of minimizing the deviations of the averaged and approximated phase velocities at the sites corresponding to the faces of the superelement. The efficiency of applying MFRPP to superelement modeling is illustrated by an example of a model reservoir region where oil is extracted using injection and production wells and by an example of waterflooding at a real oilfield.     

On Generalized Reduced Gradient method with multi-start and self-optimizing control structure for gas lift allocation optimization

In most of the gas lifted oil fields, multiple oil wells share lift gas from a common gas distribution source. The lift gas should be distributed optimally among the wells to maximize total oil production. In this paper, a nonlinear dynamic model of the oil field is developed from first principles modeling. One of the objectives of this paper is to solve the optimal lift gas distribution problem using the Generalized Reduced Gradient (GRG) method. In addition, multi-start search routine is developed to ensure that the local optimal solution is closer to the global solution. Sensitivity of the optimal solution to changes in oil field parameters like reservoir pressure, Productivity Indices (PI), total lift gas supply (input disturbance) and separator pressure is studied. It is shown that the available lift gas is distributed among the wells according to the PI values of the wells and the optimal values are highly sensitive to the changes in PI values. A self-optimizing control structure using simple controllers is designed which is capable of keeping the oil field in optimal operating conditions without having to re-optimize the whole process when the input disturbance occur in the system. The simulation results show that the outcome of optimization is increased total oil production which leads to increased profit.     

Model-based control of multiphase flow in subsurface oil reservoirs

An emerging method to increase the recovery of oil from subsurface reservoirs is the application of measurement and control techniques to better control the multiphase flow in the reservoir over the entire production period. In particular the use of sensors and remotely controllable valves in wells and at surface, in combination with large-scale reservoir flow models is promising. Various elements from process control may play a role in such ‘closed-loop’ reservoir management, in particular optimization, parameter estimation and model reduction techniques.     

An object-oriented approach to the solid modeling of empirical data

An object-oriented approach to the construction, manipulation, and display of complex geometric models of oil reservoirs is described. The authors have extended the traditional constructive solid geometry modeling techniques to accommodate the requirements for reservoir models. Both the user interface and the model building are implemented in Strobe, an object-oriented extension to Interlisp. The geometric model is specified through a CSG-graph editor built using an object-oriented toolkit for graphical interfaces. This editor proves to be an invaluable tool with which to build, maintain and manipulate large, complicated geometric models     

基于决策树的注采连通关系判别研究

判别注采连通关系的传统方法是由人工通过对比测井曲线, 逐个层位地进行连通关系的识别和分类, 这种方式工作量大、耗费劳动力多、判别效率较低。针对大庆油田注采连通关系判别的这种现状, 从油藏开发数据中提取并构建出注采井间的相对特征, 使用CART（分类回归树）算法建立了注采连通关系自动判别的决策树模型。实验结果表明, 该方法具有操作简单、判别速度快等优点, 在提高连通关系判别效率的同时保证了有较高的精度。     

智能完井技术测试与控制系统设计

智能完井技术是数字化智能化油藏开采的一项新技术,测控系统是其核心.对智能完井测控系统的硬件系统和软件系统进行了设计,通过井下温度和压力传感器采集温度和压力数据,利用温度、压力与流量的关系对井下每个层位的流量进行计算,开发了一套智能优化开采系统,对井下生产数据进行实时监测和分析,利用油藏优化开采理论,确定优化开采方案,自动控制井下各油层流量控制阀套,实现油井的优化开采.现场试验表明,该套智能完井测控系统可以实现油井的智能优化开采.     

Numerical simulation of non-conventional wells using adaptive finite element analysis

In recent years, non-conventional wells (NCWs), such as horizontal wells and drainhole drilling, have gained popularity as a means for enhancing the production and overall life of existing reservoirs. The present work investigates the benefits of using adaptive meshing in the modeling of NCWs. In particular, we employ special hp-adaptive finite element techniques (i.e. simultaneous manipulation of mesh size and polynomial order) to model the reservoir, as well as the wellbore, without relying on approximate well models and/or productivity/ injectivity index calculations. Reservoir and wellbore flows are solved in a consistent, coupled manner using unstructured meshes so as to provide the greatest flexibility in the geometric representation. Several examples are presented which highlight the flexibility and accuracy of the approach.     

油田注水井工况实时分析及管理系统开发与应用

注水是油田保持地层能量,维持高效经济开发最有效的手段.随着国内油田相继进入高含水开发期,稳产难度日益增大,油田数字化管理模式下如何加强精细注水管理,确保油藏“注好水,注够水”,是各大油田持续稳产面临的关键问题.研发的油田注水井工况分析及管理系统,利用多信息融合、数据集成及计算机技术,通过特定的融合模型及算法,实现注水井工况分析诊断、故障预警、指标统计、远程调配、注水曲线及报表自动生成等功能.系统采用B/S＋C/S架构,模块化设计,自动化数据与信息化融为一体.该系统在长庆油田l万余口注水井上应用,为油藏精细注水开发管理提供了有力的工具.     

Three-dimensional finite element simulation of three-phase flow in a deforming fissured reservoir

The development of a capacity to predict the exploitation of structurally complicated and fractured oil reservoirs is essential for the rational use of investment capital. A poor understanding of how the reservoir behaves during production may lead to inept, costly and inefficient development schemes. The mathematical formulation of a three-phase, three-dimensional fluid flow and rock deformation in fractured reservoirs is hence presented. The present formulation, consisting of both the equilibrium and multiphase mass conservation equations, accounts for the significant influence of coupling between the fluid flow and solid deformation, an aspect usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretise the governing equations in space and a finite difference scheme is used to march the solution in time. The final set of equations, which contain the additional cross coupling terms as compared to similar existing models, are highly non-linear and the elements of the coefficient matrices are updated implicitly during each iteration in terms of the independent variables. A field scale example is employed as an alpha case to test the validity and robustness of the currently formulation and numerical scheme. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered.     

Stabilization of gas-lift oil wells by a nonlinear model predictive control scheme based on adaptive neural network models

Producing oil from gas-lift wells are often faced with severe producing oscillatory flow regimes. A major source of the oscillations is recognized as casing–heading instability which is caused by dynamic interaction between injection gas and multiphase fluid. This phenomenon poses strict production-related challenges in terms of lower average production and strain on downstream equipment. In this paper, an effective solution is proposed based on integration of an online interpretation dynamic model and a nonlinear model predictive control (NMPC) scheme. The paper uses adaptive growing and pruning radial basis function (GAP-RBF) neural networks (NNs) to recursively capture the essential dynamics of casing–heading instability in a nonlinear model structure. Extended Kalman filter (EKF) and unscented Kalman filter (UKF) are comparatively investigated to adaptively train modified GAP-RBF NNs. NMPC methodology is developed on the basis of the identified nonlinear NN model for real-time stabilization of casing–heading instability in an oil reservoir equipped with a gas-lift production well. A set of test studies has been conducted to explore the superior performance of the proposed adaptive NMPC controller under different scenarios for an oil reservoir simulated in ECLIPSE and linked to a complementary gas-lifted oil well simulated in programming environment.     

基于MLP和Sobol的注采连通情况判别

在油田实际生产中,注采连通情况是一个很难确定却又十分重要的问题,它对油田开发方案的制定、剩余油分布的描述具有重要意义。本文采用大港油田某油藏的生产动态资料,建立基于贝叶斯优化的MLP神经网络模型,使用Sobol敏感性分析方法计算敏感性系数,通过敏感性系数的大小定量评判注采连通情况的好坏,通过与示踪剂解释结果的对比进而验证该方法的有效性和可靠性。研究表明,建立的基于贝叶斯优化的MLP神经网络模型取得了较好的拟合效果,Sobol敏感性系数能有效评价注采连通情况,结果符合油藏的实际情况。     

新一代并行可扩展裂缝性油藏聚合物驱模拟器的开发

石油作为一种主要能源,在交通、工业生产以及日常生活中发挥着重要作用。大量的新技术已经被开发并用于最大化石油生产,比如聚合物驱等技术在我国得到了广泛的应用。天然裂缝油藏聚合物驱模拟对油田的可持续生产和延长油田寿命至关重要。开发了一种可扩展的并行油藏模拟器,用于使用聚合物驱技术模拟天然裂缝性油藏的石油开采,使油藏工程人员能够利用强大的并行计算机研究生产技术,优化采油过程。通过与现有的商用软件对比,数值结果验证了该模拟器的正确性和有效性。此外,数值实验也证明了该模拟器拥有良好的扩展性,它可以使用成千上万的CPU核来计算具有数亿个网格块的大规模油藏模型。     

Designing cyclic pressure pulsing in naturally fractured reservoirs using an inverse looking recurrent neural network

In this paper, an inverse looking approach is presented to efficiently design cyclic pressure pulsing (huff ‘n’ puff) with N₂ and CO₂, which is an effective improved oil recovery method in naturally fractured reservoirs. A numerical flow simulation model with compositional, dual-porosity formulation is constructed. The model characteristics are from the Big Andy Field, which is a depleted, naturally fractured oil reservoir in Kentucky. A set of cyclic pulsing design scenarios is created and run using this model. These scenarios and corresponding performance indicators are fed into the recurrent neural network for training. In order to capture the cyclic, time-dependent behavior of the process, recurrent neural networks are used to develop proxy models that can mimic the reservoir simulation model in an inverse looking manner. Two separate inverse looking proxy models for N₂ and CO₂ injections are constructed to predict the corresponding design scenarios, given a set of desired performance characteristics. Predictive capabilities of developed proxy models are evaluated by comparing simulation outputs with neural-network outputs. It is observed that networks are able to accurately predict the design parameters, such as the injection rate and the duration of injection, soaking and production periods.     

2D conditional simulation of channels on wells using a random walk approach

Channel modeling is one of the popular topics in the application of geostatistics to fluvial reservoir modeling. This paper presents an approach to designing channels which have a general flow direction through sand well locations and which avoid shale well locations. This approach is named the random walk on graphs of well locations, and is applied to model channel reservoirs.This modeling process consists of two parts: one direction walk modeling and two direction walk modeling. The first model aims to determine each channel location by the use of a transition probability with a random walk essentially in the main flow direction, say the north–south direction, while the second model simulates different channels that can be oriented in both directions, either from north to south or from south to north. In both parts of the model, the transition probability is estimated based on two coefficients: one is the correlation coefficient of channel observations; the other is the obstacle coefficient of non-channel observations. A case study with a dense array of 332 wells is presented using the proposed random walk model. For the purpose of model verification, channel maps created by the random walk are compared to the hand-drawn channel maps made by geologists. The results show a good agreement in both types of maps, but in contrast to the single map supplied by geologists, the random walk model is capable of generating many realizations of channel configuration, hence allowing for uncertainty evaluation.A limitation of this approach, related to the influence of the number of wells, is discussed.     

A semi-Markov model with Bayesian belief network based human error probability for availability assessment of downhole optical monitoring systems

Compelled by increasing oil prices, a research effort is underway for designing and implementing intelligent oil fields in Brazil, with a first pilot directed towards mature wells in the Northeast. One of the major benefits of this technology is the anticipation of oil production volumes and an improved reservoir management and control. Given the considerable steep investment on the new technology, availability is a key attribute: higher availability means higher production volumes. An important part of this effort is the development of pressure–temperature optical monitoring systems (OMS) and their availability assessment. Availability analysis of an OMS impose some complexities, where the most relevant aspects are: (i) the system is under a deteriorating process; (ii) the available time to complete the maintenance; and (iii) human error probability (HEP) during maintenance that is influenced by the available time and other factors (e.g., experience, fatigue) in returning an OMS to its normal operational condition. In this paper we present a first attempt to solve this problem. It is developed an availability assessment model in which the system dynamics is described via a continuous-time semi-Markovian process specified in terms of probabilities. This model is integrated with a Bayesian belief network characterizing the cause-effect relationships among factors influencing the repairman error probability during maintenance. The model is applied to a real case concerning mature oil wells.     

Optimal feedback control of oil reservoir waterflooding processes

Waterflooding is a process where water is injected into an oil reservoir to supplement its natural pressure for increment in productivity. The reservoir properties are highly heterogeneous, its states change as production progresses which require varying injection and production settings for economic recovery. As water is injected into the reservoir, more oil is expected to be produced. There is also likelihood that water is produced in association with the oil. The worst case is when the injected water meanders through the reservoir, it bypasses pools of oil and gets produced. Therefore, any effort geared toward finding the optimal settings to maximize the value of this venture can never be over emphasized. Waterflooding can be formulated as an optimal control problem. However, traditional optimal control is an open-loop solution, hence cannot cope with various uncertainties inevitably existing in any practical systems. Reservoir models are highly uncertain. Its properties are known with some degrees of certainty near the well-bore region only. In this work, a novel data-driven approach for control variable (CV) selection was proposed and applied to reservoir waterflooding process for a feedback strategy resulting in optimal or near optimal operation. The results indicated that the feedback control method was close to optimal in the absence of uncertainty. The loss recorded in the value of performance index, net present value (NPV) was only 0.26%. Furthermore, the new strategy performs better than the open-loop optimal control solution when system/model mismatch was considered. The performance depends on the scale of the uncertainty introduced. A gain in NPV as high as 30.04% was obtained.     

System performances analysis of reservoir optimization–simulation model in application of artificial bee colony algorithm

In reservoir system operation, optimization is very much essential and the compatibility of different optimization techniques is essential to be checked by some performance checking indices. In this study, various types of performance-measuring index are used and compared to provide a complete knowledge on adopting different approaches. Here, the considered performance-measuring indicators will check the operation policy in terms of three different scenarios—how the method is efficient in achieving best results (reliability); how vulnerable the method is for different critical situation (vulnerability); and how capable it is to handle a failure of the model (resiliency). Therefore, the study proposed the artificial bee colony (ABC) optimization technique to develop an optimal water release policy for the well-known Aswan High Dam, Egypt. Particle swarm optimization, genetic algorithm and neural network-based stochastic dynamic programming are also used in a view of comparing model performances. A release curve is developed for every month as a guidance to the decision maker. Simulation has been done for each method using historical actual inflow data, and reliability, resiliency and vulnerability are measured. All model indicators proved that the release policy provided by ABC optimization outperforms in terms of achieving minimum water deficit, less waste of water and handling critical situations.