Quantifying Uncertainty in Production Forecast for Fields With Significant History
Authors: Denney Dennis 
Published: February 2015

This article, written by Technology Editor Dennis Denney, contains highlights of paper IPTC 10987, "Quantifying Uncertainty in Production Forecast for Fields With Significant History: A West African Case Study," by A. Castellini, SPE, I. Gullapalli, SPE, V. Hoang, and P. Condon, SPE, Chevron, prepared for the 2005 International Petroleum Technology Conference, Doha, Qatar, 21–23 November.
Understanding the effects of subsurface uncertainties on production responses is an integral part of the decision-making process. A more accurate quantification of the uncertainty of production forecasts contributes to better business decisions. When a field has produced for several years, models must be conditioned to available production data to obtain meaningful predictions. Data integration and uncertainty assessment of future performance of the reservoir are indivisible processes that cannot be addressed generally by simple techniques. A method is presented to solve complex inverse problems that involve highly nonlinear responses.

Introduction
Quantifying uncertainty in production forecasts for a field with complex history is difficult. Monte Carlo simulations coupled with probabilistic inverse theory generally are not practical because of the large number of simulations required. Efficient alternatives involving proxies and various optimization algorithms have been investigated. The fitness of the model to the observed data (history-match error function) is modeled with response surfaces. Sampling the proxy for the error function and retaining the best acceptable combinations identify multiple solutions to the history match. A similar proxy for the forecast might be constructed and sampled at the "good" locations identified with the error function. In practical fieldwide applications, it often is very costly to build a high-quality response surface for the forecast variables. A more practical alternative consists of obtaining prediction responses directly from the acceptable models. This solution is retained for this study.
The goal of any history-matching procedure is to find the minimum value of an objective function that measures the misfit between actual and simulated data. In general, the objective function has an erratic form, and the number of parameters is large. Space-filling designs, such as uniform designs or Hammersley sequences, sample the search space efficiently, but the number of simulations required for an acceptable sampling usually is large in high-dimensional problems. In this study, such designs are used to screen the parameter space.
Optimization algorithms can reduce the need for exhaustive sampling. Such techniques often require calculating the sensitivity of flow responses with respect to reservoir properties. The performance of such gradient-based algorithms degrades as the problem gets larger and strongly depends on the initial guess of the solution vector. Genetic algorithms (GAs) have a better global-convergence property and were selected as the main optimization tool in this study. To reduce the number of actual simulations and to accelerate the overall procedure, nonlinear-response surfaces, built with kriging interpolants at each iteration of the optimization routine, filter out unnecessary combinations of parameters. The strategy ensures multiple and significantly different history-matched models that provide equiprobable estimation of the performance of the reservoir. The coupling of space-filling sampling strategies, optimization algorithms, and nonlinear response surfaces proved efficient in addressing the issue.