Rapid S-Curve Update Using Ensemble Variance Analysis With Model Validation
Authors: Carpenter Chris 
Published: April 2018

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 185630, “Rapid S-Curve Update Using Ensemble Variance Analysis With Model Validation,” by Jincong He, Shusei Tanaka, Xian-Huan Wen, and Jairam Kamath, Chevron, prepared for the 2017 SPE Western Regional Meeting, Bakersfield, California, USA, 23–27 April. The paper has not been peer reviewed.
In the complete paper, the authors propose a novel method to rapidly update the prediction S-curves given early production data without performing additional simulations or model updates after the data come in. The approach has been successfully applied in a Brugge waterflood benchmark study, in which the first 2 years of production data [rate and bottomhole pressure (BHP)] were used to update the S-curve of the estimated ultimate recovery. To the authors’ knowledge, the proposed work flow, including the model validation and the denoising techniques, is novel. The proposed work flow is also general enough to be used in other model-based data-interpretation applications.
Introduction
As surveillance data are obtained from the field, the S-curves of the key metrics need to be updated accordingly. This is normally accomplished by a two-step approach. First, the data are assimilated through history matching to calibrate the model parameter uncertainties to obtain their posterior distributions. Then, a probabilistic forecast is performed on the basis of the posterior distributions of the parameters to update the S-curve of the key metrics. However, obtaining an S-curve update with the traditional approach can take weeks or months after the data come in. There is a need for rapid interpretation of the incoming data and update of the S-curve without going through a full-blown history-matching and probabilistic-forecast process.
Recently, the approach called direct forecast (also called data-space inversion) has been a focus of attention. In direct forecast, the statistical relationship between the measurement data and the business objective is established on the basis of simulation-model responses before the data acquisition. This direct relationship can then be used to rapidly update the prediction of the objective once the data become available.
A process called canonical functional component analysis is proposed to map the data and forecast variables into a low-dimensional space; multilinear regression was implemented in the reduced space to establish the data/objective relationship. The authors explore the use of a simpler and more-intuitive method called ensemble variance analysis (EVA) for rapid update of the S-curve. The idea of EVA is to explore covariance between data and objectives, then use an analytical formula to calculate the posterior S-curve. In the complete paper, the authors adapt the formulation for rapid S-curve update after data come in.
While the direct forecast has attracted attention, less attention has been paid to validating the consistency between observed data and the simulation model after data come in. Blindly applying the direct-forecasting formula without identifying unmodeled features can lead to an incorrect posterior S-curve and misinformed decisions. The authors propose a procedure that detects and removes features in the measurement data that are inconsistent with the simulation responses. The complete paper describes formulation of the problem of updating S-curves with measurement data.