Direct forecasting of reservoir performance using production data without history matching

The conventional paradigm for predicting future reservoir performance from existing production data involves the construction of reservoir models that match the historical data through iterative history matching. This is generally an expensive and difficult task and often results in models that do not accurately assess the uncertainty of the forecast. We propose an alternative re-formulation of the problem, in which the role of the reservoir model is reconsidered. Instead of using the model to match the historical production, and then forecasting, the model is used in combination with Monte Carlo sampling to establish a statistical relationship between the historical and forecast variables. The estimated relationship is then used in conjunction with the actual production data to produce a statistical forecast. This allows quantifying posterior uncertainty on the forecast variable without explicit inversion or history matching. The main rationale behind this is that the reservoir model is highly complex and even so, still remains a simplified representation of the actual subsurface. As statistical relationships can generally only be constructed in low dimensions, compression and dimension reduction of the reservoir models themselves would result in further oversimplification. Conversely, production data and forecast variables are time series data, which are simpler and much more applicable for dimension reduction techniques. We present a dimension reduction approach based on functional data analysis (FDA), and mixed principal component analysis (mixed PCA), followed by canonical correlation analysis (CCA) to maximize the linear correlation between the forecast and production variables. Using these transformed variables, it is then possible to apply linear Gaussian regression and estimate the statistical relationship between the forecast and historical variables. This relationship is used in combination with the actual observed historical data to estimate the posterior distribution of the forecast variable. Sampling from this posterior and reconstructing the corresponding forecast time series, allows assessing uncertainty on the forecast. This workflow will be demonstrated on a case based on a Libyan reservoir and compared with traditional history matching.     

Model-reduced gradient-based history matching

Gradient-based history matching algorithms can be used to adapt the uncertain parameters in a reservoir model using production data. They require, however, the implementation of an adjoint model to compute the gradients, which is usually an enormous programming effort. We propose a new approach to gradient-based history matching which is based on model reduction, where the original (nonlinear and high-order) forward model is replaced by a linear reduced-order forward model and, consequently, the adjoint of the tangent linear approximation of the original forward model is replaced by the adjoint of a linear reduced-order forward model. The reduced-order model is constructed with the aid of the proper orthogonal decomposition method. Due to the linear character of the reduced model, the corresponding adjoint model is easily obtained. The gradient of the objective function is approximated, and the minimization problem is solved in the reduced space; the procedure is iterated with the updated estimate of the parameters if necessary. The proposed approach is adjoint-free and can be used with any reservoir simulator. The method was evaluated for a waterflood reservoir with channelized permeability field. A comparison with an adjoint-based history matching procedure shows that the model-reduced approach gives a comparable quality of history matches and predictions. The computational efficiency of the model-reduced approach is lower than of an adjoint-based approach, but higher than of an approach where the gradients are obtained with simple finite differences.     

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.     

Determination of lower and upper bounds of predicted production from history-matched models

We present a method to determine lower and upper bounds to the predicted production or any other economic objective from history-matched reservoir models. The method consists of two steps: 1) performing a traditional computer-assisted history match of a reservoir model with the objective to minimize the mismatch between predicted and observed production data through adjusting the grid block permeability values of the model. 2) performing two optimization exercises to minimize and maximize an economic objective over the remaining field life, for a fixed production strategy, by manipulating the same grid block permeabilities, however without significantly changing the mismatch obtained under step 1. This is accomplished through a hierarchical optimization procedure that limits the solution space of a secondary optimization problem to the (approximate) null space of the primary optimization problem. We applied this procedure to two different reservoir models. We performed a history match based on synthetic data, starting from a uniform prior and using a gradient-based minimization procedure. After history matching, minimization and maximization of the net present value (NPV), using a fixed control strategy, were executed as secondary optimization problems by changing the model parameters while staying close to the null space of the primary optimization problem. In other words, we optimized the secondary objective functions, while requiring that optimality of the primary objective (a good history match) was preserved. This method therefore provides a way to quantify the economic consequences of the well-known problem that history matching is a strongly ill-posed problem. We also investigated how this method can be used as a means to assess the cost-effectiveness of acquiring different data types to reduce the uncertainty in the expected NPV.     

Forecasting of cyclone Viyaru and Phailin by NWP-based cyclone prediction system (CPS) of IMD – an evaluation

An objective NWP-based cyclone prediction system (CPS) was implemented for the operational cyclone forecasting work over the Indian seas. The method comprises of five forecast components, namely (a) Cyclone Genesis Potential Parameter (GPP), (b) Multi-Model Ensemble (MME) technique for cyclone track prediction, (c) cyclone intensity prediction, (d) rapid intensification, and (e) predicting decaying intensity after the landfall. GPP is derived based on dynamical and thermodynamical parameters from the model output of IMD operational Global Forecast System. The MME technique for the cyclone track prediction is based on multiple linear regression technique. The predictor selected for the MME are forecast latitude and longitude positions of cyclone at 12-hr intervals up to 120 hours forecasts from five NWP models namely, IMD-GFS, IMD-WRF, NCEP-GFS, UKMO, and JMA. A statistical cyclone intensity prediction (SCIP) model for predicting 12 hourly cyclone intensity (up to 72 hours) is developed applying multiple linear regression technique. Various dynamical and thermodynamical parameters as predictors are derived from the model outputs of IMD operational Global Forecast System and these parameters are also used for the prediction of rapid intensification. For forecast of inland wind after the landfall of a cyclone, an empirical technique is developed. This paper briefly describes the forecast system CPS and evaluates the performance skill for two recent cyclones Viyaru (non-intensifying) and Phailin (rapid intensifying), converse in nature in terms of track and intensity formed over Bay of Bengal in 2013. The evaluation of performance shows that the GPP analysis at early stages of development of a low pressure system indicated the potential of the system for further intensification. The 12-hourly track forecast by MME, intensity forecast by SCIP model and rapid intensification forecasts are found to be consistent and very useful to the operational forecasters. The error statistics of the decay model shows that the model was able to predict the decaying intensity after landfall with reasonable accuracy. The performance statistics demonstrates the potential of the system for improving operational cyclone forecast service over the Indian seas.     

模糊均生函数残差模型在地下水数值模拟降水量预报中的应用

地下水主要补给来源为大气降水的入渗和地表水体的渗漏.在地下水模拟预报模型中需要预先知道降水量.迄今为止,年降水量的预测仍然是一个不易解决的难题.在模糊均生函数模型(FAFM)基础上,利用其残差数据序列对FAFM进行校正,提出了模糊均生函数残差模型(REMFAF),给出了模型预报精度的检验方法.实例研究表明,REMFAF模型应用于吉林省西部地区地下水数值模拟中的降水量预报,比FAFM的预报精度更高,取得了较为理想的结果.     

A method for automatic history matching of a compositional reservoir simulator with multipoint flux approximation

A method for history matching of an in-house petroleum reservoir compositional simulator with multipoint flux approximation is presented. This method is used for the estimation of unknown reservoir parameters, such as permeability and porosity, based on production data and inverted seismic data. The limited-memory Broyden–Fletcher–Goldfarb–Shanno method is employed for minimization of the objective function, which represents the difference between simulated and observed data. In this work, we present the key features of the algorithm for calculations of the gradients of the objective function based on adjoint variables. The test example shows that the method is applicable to cases with anisotropic permeability fields, multipoint flux approximation, and arbitrary fluid compositions.     

Real-time flood forecasting of the Tiber river in Rome

An adaptive, conceptual model for real-time flood forecasting of the Tiber river in Rome is proposed. This model simulates both rainfall-runoff transformations, to reproduce the contributions of 37 ungauged sub-basins that covered about 30% of the catchment area, and flood routing processes in the hydrographic network. The adaptive component of the model concerns the rainfall-runoff analysis: at any time step the whole set of the model parameters is recalibrated by minimizing the objective function constituted by the sum of the squares of the differences between observed and computed water surface elevations (or discharges). The proposed model was tested through application under real-time forecasting conditions for three historical flood events. To assess the forecasting accuracy, to support the decision maker and to reduce the possibility of false or missed warnings, confidence intervals of the forecasted water surface elevations (or discharges), computed according to a Monte Carlo procedure, are provided. The evaluation of errors in the prediction of peak values, of coefficients of persistence and of the amplitude of confidence intervals of prediction shows the possibility to develop a flood forecast model with a lead time of 12 h, which is useful for civil protection actions.     

History matching of statistically anisotropic fields using the Karhunen-Loeve expansion-based global parameterization technique

Traditional ensemble-based history matching method, such as the ensemble Kalman filter and iterative ensemble filters, usually update reservoir parameter fields using numerical grid-based parameterization. Although a parameter constraint term in the objective function for deriving these methods exists, it is difficult to preserve the geological continuity of the parameter field in the updating process of these methods; this is especially the case in the estimation of statistically anisotropic fields (such as a statistically anisotropic Gaussian field and facies field with elongated facies) with uncertainties about the anisotropy direction. In this work, we propose a Karhunen-Loeve expansion-based global parameterization technique that is combined with the ensemble-based history matching method for inverse modeling of statistically anisotropic fields. By using the Karhunen-Loeve expansion, a Gaussian random field can be parameterized by a group of independent Gaussian random variables. For a facies field, we combine the Karhunen-Loeve expansion and the level set technique to perform the parameterization; that is, for each facies, we use a Gaussian random field and a level set algorithm to parameterize it, and the Gaussian random field is further parameterized by the Karhunen-Loeve expansion. We treat the independent Gaussian random variables in the Karhunen-Loeve expansion as the model parameters. When the anisotropy direction of the statistically anisotropic field is uncertain, we also treat it as a model parameter for updating. After model parameterization, we use the ensemble randomized maximum likelihood filter to perform history matching. Because of the nature of the Karhunen-Loeve expansion, the geostatistical characteristics of the parameter field can be preserved in the updating process. Synthetic cases are set up to test the performance of the proposed method. Numerical results show that the proposed method is suitable for estimating statistically anisotropic fields.     

指数趋势模型在斜坡变形位移预测中的应用

应用斜坡变形破坏预测的一种新方法--指数趋势模型,预测了链子崖危岩体GA监测点的位移量。首先,把非线性的指数趋势模型经线性化处理后,用线性最小二乘法对待定参数作出估计, 然后,得出指数趋势模型,并对危岩体位移量进行了预测,其预测结果与实际位移值误差很小,说明该方法可用于斜坡变形破坏的预测预报。最后,还对预测值的区间和区间长度作出了预测。     

Calculating derivatives for automatic history matching

Automatic history matching is based on minimizing an objective function that quantifies the mismatch between observed and simulated data. When using gradient-based methods for solving this optimization problem, a key point for the overall procedure is how the simulator delivers the necessary derivative information. In this paper, forward and adjoint methods for derivative calculation are discussed. Procedures for sensitivity matrix building, sensitivity matrix and transpose sensitivity matrix vector products are fully described. To show the usefulness of the derivative calculation algorithms, a new variant of the gradzone analysis, which tries to address the problem of selecting the most relevant parameters for a history matching, is proposed using the singular value decomposition of the sensitivity matrix. Application to a simple synthetic case shows that this procedure can reveal important information about the nature of the history-matching problem.     

小湾水电站坝址区三维初始地应力场反演回归分析

基于小湾水电站坝址区工程地质地形条件,研究分析了影响工程考察域初始地应力场的基本因素及其空间分布,建立了坝址区三维有限元计算模型和初始地应力场参数空间分布模型;利用大型通用有限元软件MSC.Marc和地应力实测资料,借助最小二乘法原理,以回归精度为目标函数,优化了构造挤压荷载的模拟和作用组合,实现了初始应力场空间分布模型的参数估计。计算结果表明,改进后的方法较传统方法回归精度有了较大提高,能较为合理地模拟小湾坝址区三维初始地应力场。     

Calibration of an elasto-plastic constitutive model by a constrained optimisation procedure

The presented paper deals with a constrained optimisation technique for the calibration of elasto-plastic model parameters in a rational and objective manner. The procedure consists in finding a set of model parameters which minimise the difference between the experimental data and the numerical simulations defined by an objective function. For this purpose, an optimisation routine, termed ParaID, has been developed which combines the quasi-Newton and stochastic methods. The optimisation technique was employed to calibrate a multi-mechanism elasto-plastic constitutive model. Using the results of three isotropically consolidated drained triaxial compression tests, a comparison between numerical and experimental results clearly shows the capability of the optimisation procedure to determine the model parameters correctly.     

阶跃型位移特征滑坡时间预测预报研究

滑坡时间预测预报目前主要以滑坡最终破坏的时间为目标函数,但对于变形特征为阶跃型的滑坡却难以准确地预测其破坏时间。为此,提出以位移作为此类滑坡时间预报的目标函数。将滑坡位移分解为蠕变位移和波动位移,采用二次移动平均法分别提取,然后采用多项式拟合和灰色GM(1,1)模型分别对蠕变位移和波动位移进行预测,最后将两部分预测位移相加得到滑坡预测的总位移。以典型阶跃型位移特征滑坡——三峡库区八字门滑坡为例,运用其位移监测数据进行验证,并对多模型预测结果进行对比分析,结果表明,该位移预测模型预测精度良好,能较好地预测阶跃型位移特征滑坡位移。     

新安江模型参数多目标优化研究

水文模型的参数优化率定一直以来是水文预报领域的重要研究内容,当水文模型的结构确定后,水文模型参数的选择对水文模型整体性能和水文预报结果的好坏有着至关重要的影响.针对传统水文模型参数优选采用单一目标不能充分全面挖掘水文观测资料中蕴含的水文特征信息的缺陷,本文以新安江三水源模型为例,尝试采用多目标优化算法优化率定水文模型,算例应用分析表明,通过合理的选择目标函数的种类和数目,采用多目标进化算法优化率定模型参数,可以获得相对于单目标率定模型参数更优的结果.进一步,研究工作针对模型参数优化的结果进行分析,可以明显看出模型参数优化中存在“异参同效”现象,为后续模型参数不确定性分析等相关研究工作的开展做好了铺垫.     

Forecasting seismicity rates in western Turkey as inferred from earthquake catalog and stressing history

The spatio-temporal variation in seismicity in western Turkey since the late 1970s is investigated through a rate/state model, which considers the stressing history to forecast the reference seismicity rate evolution. The basic catalog was divided according to specific criteria into four subsets, which correspond to areas exhibiting almost identical seismotectonic features. Completeness magnitude and reference seismicity rates are individually calculated for each subset. The forecasting periods are selected to be the inter-seismic time intervals between successive strong (M ≥ 5.8) earthquakes. The Coulomb stress changes associated with their coseismic slip are considered, along with the constant stressing rate to alter the rates of earthquake production. These rates are expressed by a probability density function and smoothed over the study area with different degrees of smoothing. The influence of the rate/state parameters in the model efficiency is explored by evaluating the Pearson linear correlation coefficient between simulated and observed earthquake occurrence rates along with its 95 % confidence limits. Application of different parameter values is attempted for the sensitivity of the calculated seismicity rates and their fit to the real data to be tested. Despite the ambiguities and the difficulties involved in the experimental parameter value determination, the results demonstrate that the present formulation and the available datasets are sufficient enough to contribute to seismic hazard assessment starting from a point such far back in time.     

贝叶斯概率水文预报系统在中长期径流预报中的应用

采用贝叶斯概率水文预报理论制订水电站水库中长期径流预报模型,以概率分布的形式定量地描述水文预报的不确定度,探索概率水文预报理论及其应用价值。采用气象因子灰关联预报模型处理输入因子的不确定度,将实时气象信息和历史水文资料有效结合,突破传统确定性预报方法在信息利用和样本学习方面的局限性,以提高水文预报的精确度。以丰满水电厂水库为例对所建模型进行检验,模拟计算结果表明,该模型与确定性径流预报方法相比,不仅有利于决策人员定量考虑不确定性,而且在期望意义上提高了径流预报精度,具有较高的应用价值。     

Integrating production data under uncertainty by parallel interacting Markov chains on a reduced dimensional space

In oil industry and subsurface hydrology, geostatistical models are often used to represent the porosity or the permeability field. In history matching of a geostatistical reservoir model, we attempt to find multiple realizations that are conditional to dynamic data and representative of the model uncertainty space. A relevant way to simulate the conditioned realizations is by generating Monte Carlo Markov chains (MCMC). The huge dimensions (number of parameters) of the model and the computational cost of each iteration are two important pitfalls for the use of MCMC. In practice, we have to stop the chain far before it has browsed the whole support of the posterior probability density function. Furthermore, as the relationship between the production data and the random field is highly nonlinear, the posterior can be strongly multimodal and the chain may stay stuck in one of the modes. In this work, we propose a methodology to enhance the sampling properties of classical single MCMC in history matching. We first show how to reduce the dimension of the problem by using a truncated Karhunen–Loève expansion of the random field of interest and assess the number of components to be kept. Then, we show how we can improve the mixing properties of MCMC, without increasing the global computational cost, by using parallel interacting Markov Chains. Finally, we show the encouraging results obtained when applying the method to a synthetic history matching case.