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.     

Numerical Calculation of Equivalent Cell Permeability Tensors for General Quadrilateral Control Volumes

A new method for upscaling fine scale permeability fields to general quadrilateral-shaped coarse cells is presented. The procedure, referred to as the conforming scale up method, applies a triangle-based finite element technique, capable of accurately resolving both the coarse cell geometry and the subgrid heterogeneity, to the solution of the local fine scale problem. An appropriate averaging of this solution provides the equivalent permeability tensor for the coarse scale quadrilateral cell. The general level of accuracy of the technique is demonstrated through application to a number of flow problems. The real strength of the conforming scale up method is demonstrated when the method is applied in conjunction with a flow-based gridding technique. In this case, the approach is shown to provide results that are significantly more accurate than those obtained using standard techniques.     

新疆希勒库都克铜钼矿区岩浆混合作用: 来自锆石U-Pb年代学的证据

新疆北部富蕴县内希勒库都克铜钼矿区的花岗闪长岩及其包体岩相学、矿物化学和岩石地球化学特征及野外地质特征显示其为岩浆混合作用的结果。本文获得花岗闪长岩及其中暗色微粒包体玄武安山玢岩、细粒辉长闪长岩锆石U-Pb年龄为326.8±2.1Ma、327.6±2.4Ma、329.3±2.3Ma,年龄值基本一致,这一结果从年代学角度为花岗闪长岩及其中暗色微粒包体的岩浆混合作用成因提供证据。偏酸性的花岗闪长质与偏基性玄武安山质岩浆混合作用形成了331.9±2.1Ma的安山玢岩脉。     

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.     

A Deep-Learning-Based Geological Parameterization for History Matching Complex Models

A new low-dimensional parameterization based on principal component analysis (PCA) and convolutional neural networks (CNN) is developed to represent complex geological models. The CNN–PCA method is inspired by recent developments in computer vision using deep learning. CNN–PCA can be viewed as a generalization of an existing optimization-based PCA (O-PCA) method. Both CNN–PCA and O-PCA entail post-processing a PCA model to better honor complex geological features. In CNN–PCA, rather than use a histogram-based regularization as in O-PCA, a new regularization involving a set of metrics for multipoint statistics is introduced. The metrics are based on summary statistics of the nonlinear filter responses of geological models to a pre-trained deep CNN. In addition, in the CNN–PCA formulation presented here, a convolutional neural network is trained as an explicit transform function that can post-process PCA models quickly. CNN–PCA is shown to provide both unconditional and conditional realizations that honor the geological features present in reference SGeMS geostatistical realizations for a binary channelized system. Flow statistics obtained through simulation of random CNN–PCA models closely match results for random SGeMS models for a demanding case in which O-PCA models lead to significant discrepancies. Results for history matching are also presented. In this assessment CNN–PCA is applied with derivative-free optimization, and a subspace randomized maximum likelihood method is used to provide multiple posterior models. Data assimilation and significant uncertainty reduction are achieved for existing wells, and physically reasonable predictions are also obtained for new wells. Finally, the CNN–PCA method is extended to a more complex nonstationary bimodal deltaic fan system, and is shown to provide high-quality realizations for this challenging example.

     

Age verification,growth and life history of rubyfish Plagiogeneion rubiginosum

Age verification of rubyfish (Plagiogeneion rubiginosum) was sought using the bomb radiocarbon chronometer procedure. Stable isotopes were investigated for life history characteristics. Radiocarbon (¹⁴C) and stable isotope (δ¹⁸O and δ¹³C) levels were measured in micro-samples from five otoliths that had been aged using a zone count method. All the core ¹⁴C measurements were ‘pre-bomb’ indicating ages of at least 45 years, and the ¹⁴C measurements across the otolith sections suggested that the zone-count ageing method described herein is not biased. Maximum estimated age was 100 years. There was no significant between-sex difference in the von Bertalanffy growth curves. The δ¹⁸O values indicated that rubyfish are near-surface as juveniles, and move deeper with age. Adults appear to reside in 600–1000 m; this is deeper than most trawl-capture data suggest, but not implausible, and has stock assessment implications. The δ¹³C values reflect fish metabolic rates, trophic feeding levels and oceanographic conditions. The stable isotopes record the environmental life history of each fish, and have value in distinguishing stocks and/or indicating vertical and latitudinal migratory patterns.     

Kernel Principal Component Analysis for Efficient,Differentiable Parameterization of Multipoint Geostatistics

This paper describes a novel approach for creating an efficient, general, and differentiable parameterization of large-scale non-Gaussian, non-stationary random fields (represented by multipoint geostatistics) that is capable of reproducing complex geological structures such as channels. Such parameterizations are appropriate for use with gradient-based algorithms applied to, for example, history-matching or uncertainty propagation. It is known that the standard Karhunen–Loeve (K–L) expansion, also called linear principal component analysis or PCA, can be used as a differentiable parameterization of input random fields defining the geological model. The standard K–L model is, however, limited in two respects. It requires an eigen-decomposition of the covariance matrix of the random field, which is prohibitively expensive for large models. In addition, it preserves only the two-point statistics of a random field, which is insufficient for reproducing complex structures. In this work, kernel PCA is applied to address the limitations associated with the standard K–L expansion. Although widely used in machine learning applications, it does not appear to have found any application for geological model parameterization. With kernel PCA, an eigen-decomposition of a small matrix called the kernel matrix is performed instead of the full covariance matrix. The method is much more efficient than the standard K–L procedure. Through use of higher order polynomial kernels, which implicitly define a high-dimensionality feature space, kernel PCA further enables the preservation of high-order statistics of the random field, instead of just two-point statistics as in the K–L method. The kernel PCA eigen-decomposition proceeds using a set of realizations created by geostatistical simulation (honoring two-point or multipoint statistics) rather than the analytical covariance function. We demonstrate that kernel PCA is capable of generating differentiable parameterizations that reproduce the essential features of complex geological structures represented by multipoint geostatistics. The kernel PCA representation is then applied to history match a water flooding problem. This example demonstrates that kernel PCA can be used with gradient-based history matching to provide models that match production history while maintaining multipoint geostatistics consistent with the underlying training image.     

青海锡铁山铅锌矿床硫同位素地球化学研究——深源与海水硫的混合

锡铁山铅锌矿床发育较为完整的喷流沉积系统,包括管道相、近喷口相、远端沉积相及各种喷流沉积岩,并有后期改造作用形成的脉状铅锌矿体。本文通过喷流沉积系统各部位硫化物硫同位素的分析,不同部位硫化物硫同位素组成不同,且规律性变化。以黄铁矿分析结果为例,网脉状石英钠长岩δ34S=+0.8‰,代表供给系统的硫化物脉2.95‰,非层状矿体4.48‰,层状矿体3.25‰,炭质片岩为+6.26‰,后期改造型铅锌矿脉为+2.93‰。代表管道相的网脉状石英钠长岩黄铁矿具有深源(幔源)的硫同位素组成,而矿体或大理岩上盘炭质片岩具有海水硫来源的特点。矿体的硫介于二者之间,更靠近炭质片岩的硫化物同位素组成,其来源可能更多受海水硫酸盐的制约,即锡铁山矿床硫具有混合来源性质,主要是海水硫酸盐的还原,部分来源于深部卤水的供给。硫的还原方式以生物细菌还原为主。层状矿体中硫同位素组成由早至晚δ34S逐渐降低,表明层状矿体成矿作用过程中,发生了生物成因的H2S的大量加入。