Gaussian Processes for history-matching: application to an unconventional gas reservoir

Abstract

The process of reservoir history-matching is a costly task. Many available history-matching algorithms either fail to perform such a task or they require a large number of simulation runs. To overcome such struggles, we apply the Gaussian Process (GP) modeling technique to approximate the costly objective functions and to expedite finding the global optima. A GP model is a proxy, which is employed to model the input-output relationships by assuming a multi-Gaussian distribution on the output values. An infill criterion is used in conjunction with a GP model to help sequentially add the samples with potentially lower outputs. The IC fault model is used to compare the efficiency of GP-based optimization method with other typical optimization methods for minimizing the objective function. In this paper, we present the applicability of using a GP modeling approach for reservoir history-matching problems, which is exemplified by numerical analysis of production data from a horizontal multi-stage fractured tight gas condensate well. The results for the case that is studied here show a quick convergence to the lowest objective values in less than 100 simulations for this 20-dimensional problem. This amounts to an almost 10 times faster performance compared to the Differential Evolution (DE) algorithm that is also known to be a powerful optimization technique. The sensitivities are conducted to explain the performance of the GP-based optimization technique with various correlation functions

Experimental and computational evaluation of cyclic solvent injection in fractured tight hydrocarbon reservoirs

“…History matching was conducted manually to achieve the ‘best-match’ because there were numerical challenges to complete the history matching using other assisted approaches (e.g. Adaptive Differential Evolution 35 and Bayesian Optimization methods 36 ). The latter observation is attributed to (1) the small grid block thickness (as small as 0.003 cm), (2) the complexity of the compositional simulation for near-miscible conditions, (3) large pore volumes and transmissibility differences between the simulation cells (due to the presence of fracture), and (4) most importantly, including effective dispersion/diffusion coefficient as an input parameter for simulations.…”

Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

“…Compared to GP-based AHM [7], GP-VARS [29] introduced the extra GPIS to model the probability distribution of non-unique solutions. Furthermore, in the proposed GPLVM-VARS, GPLVMIS instead of GPIS is developed to further improve the performance of GP-VARS.…”

“…To address the issue, Assisted History Matching (AHM) techniques have been proposed to replace labor-intensive and costly manual history matching [1,[4][5][6]. Roughly, these methods for assisted history matching can be divided into two categories [7]: the data assimilation approaches (such as Ensemble Kalman Filter and Ensemble Smoother) and the optimization approaches (such as gradient, evolutionary or data-driven-based algorithms). Ensemble Kalman Filter (EnKF) and Ensemble Smoother (ES) are representative methods for data assimilation [8].…”

“…The past decade has witnessed various proxy models for AHM based on machine learning algorithms. For example, Principal Component Analysis (PCA) [21,22], Artificial Neural Network (ANN) [23][24][25], Deep Learning (DL) [12,26,27], Support Vector Machine (SVM) [28] and Gaussian Process (GP) [7,29] have been introduced to replace computationally intensive numerical simulators. Optimization-based PCA and two-dimensional PCA were applied to characterize the channelized geological models [21,22], but they could fail when dealing with the complex and nonlinear channelized structures in some geological models although kernel tricks can be adopted.…”

“…Thus, applying GP is easy for AHM without manually parameters tuning. Hamdi et al [7] first introduced GP for history matching with single GP as the proxy model plus Expected Improvement based Bayesian optimization, and they concluded that the covariance function Matern class 3 provided the best results for some history matching problems according to the sensitivity analysis regarding various covariance functions. Sachin Rana et al [29] further proposed the GP proxy models and Variogram Analysis of Response Surface (GP-VARS) by making use of two GPs to obtain forward (GPFS) and inverse (GPIS) solutions to improve the performance of a single GP-based proxy models for AHM where Empirical Bayes approach [30] was employed to choose and optimize the covariance function for any given data automatically.…”