Rapid Forecast Calibration Using Nonlinear Simulation Regression With Localization
Authors: Feder Judy 
Published: March 2020

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 193845, “Rapid Forecast Calibration Using Nonlinear Simulation Regression With Localization,” by Jincong He, SPE, Wenyue Sun, and Xian-Huan Wen, SPE, Chevron, prepared for the 2019 SPE Reservoir Simulation Conference, Galveston, Texas, 10–11 April. The paper has not been peer reviewed.
The industry increasingly relies on forecasts from reservoir models for reservoir management and decision making. However, because forecasts from reservoir models carry large uncertainties, calibrating them as soon as data come in is crucial. Traditional probabilistic history matching remains time-consuming because it needs to calibrate the models before using them to update probability distributions (S-curves) of quantities of interest (QOIs). This paper presents a direct forecast method called simulation regression with localization (SRL), which is able to calibrate the forecast with observed data without calibrating the model.
Introduction
Production forecasts from reservoir-simulation models can be affected by the various uncertainties present in the subsurface, such as those in the geological characterization and rock and fluid properties. Calibrating uncertain QOIs, such as production-forecast or key subsurface parameters, to observation data is a crucial element in the context of closed-loop reservoir management. Traditionally, this task is accomplished by a two-step approach, as depicted in Fig. 1a.
First, a probabilistic history-matching process needs to be carried out to condition the simulation models to the data. Probabilistic history matching generates an ensemble of reservoir models that characterize the posterior uncertainty given the measurement data (e.g., historical well-test and production data), as opposed to deterministic history matching, in which only one model that best matches the measurement data is generated.
In the second step, reservoir simulations, subject to a given reservoir operation plan, are performed on the generated posterior samples, or models, to estimate the posterior distribution of the QOIs. There is rich literature on various probabilistic history-matching methods, and the complete paper cites and assesses several examples. However, the authors state that, although much progress has been made in probabilistic history matching, the resulting procedures still are generally time-consuming for realistic systems, and may not provide accurate sampling of posterior distribution when strong nonlinearity and non-Gaussianity exist.
Proposed Work Flow
The complete paper explores an alternative forecasting framework, as shown in Fig. 1b. The authors propose using SRL for direct forecasting to derive the posterior distributions for QOIs given the measurement data. As with other direct forecasting methods, the ﬁrst step of SRL is to perform an ensemble of simulation runs according to the previous distributions of the uncertainties and construct a training data set for the QOIs and measurement data. Then, in SRL, a regression model is built on this training data set to estimate the mean value of the posterior distribution. Depending on the case at hand, this regression model can be as simple as a linear regression model, or as complex as a deep-learning model.
The authors found that the quadratic partial least square (QPLS) regression model offers flexibility to handle a wide range of problems. However, the posterior variances of the QOIs are estimated by a localization process wherein the mismatch of the regression model for samples closed to observed data is used to estimate the posterior variance. Finally, the entire posterior distribution (in terms of the cumulative distribution function; i.e., the S-curve) can be estimated by scaling the prior S-curve with the updated mean and variance.