Reservoir Model History-Matching and Uncertainty Quantification in Reservoir Performance Forecast Using Bayesian Framework

Abstract

Reservoir performance forecasts are essentially uncertain due to the lack of data. The unknown parameters are calibrated so that the simulated profile can match the observed data. However the history-matching is ill-posed and may have non-unique solutions. The aim of our study is to quantify uncertainty of reservoir connectivity in a Turbidite sandstone reservoir where the wells have been stimulated by hydraulic fracturing. The reservoir properties were calibrated using a stochastic sampling algorithm called Differential Evolution (DE). Then a Bayesian framework along with Markov Chain Monte Carlo and Neighbourhood Approximation in parameter space is used to calculate the posterior probability.A Bayesian framework and DE have been applied to the evaluation of CO 2 injection test in the tight oil reservoir. The in-place volumes and connectivity between the wells have been calibrated in a simple model. The calibrated parameters include the length of a hydraulic fracture around the injector well and net-to-gross ratios. The observed data used for history-matching include the bottom-hole flowing pressure at the injector well and the gas composition at the wellhead of the producer wells.We showed the best fit model for the gas breakthrough and the P10-90 envelopes in the reservoir performance forecast. Assuming an on-going injection after the actual pilot test, the uncertainty envelopes in the CO 2 mole fraction in the produced gas were estimated to see a gas breakthrough at each of the producer wells. Our results contribute to the evaluation of the pilot test for a continuous CO 2 injection in the tight oil reservoir.The key is starting with a simple model, because it is much quicker to adjust large-scale heterogeneity in a simple model than in a detailed model. The simple model calibration with DE and the forecast of Bayesian inference have been successfully applied to the field test evaluation.

Assisted history matching using pattern recognition technology

“…Finally, decide if the misfit value is satisfying; the stoppage criteria here can be design by the engineer. shown great performance for petroleum engineering case studies (Wang and Buckley 2006) (Decker and Mauldon 2006, Jahangiri 2007, Wang and Gao 2010, Wang, Gao and Yang, et al 2011, Mirzabozorg, et al 2013) (Okano 2013). In this section we talk about the necessity of having an optimization method and then introduce DE as a novel optimization algorithm.…”

“…Recently, a new optimization method known as Differential Evolution (DE) which belongs to the class of evolutionary algorithms has been used in numerous case studies of history matching , Wang and Gao 2010, Wang, Gao and Yang, et al 2011, Mirzabozorg, et al 2013, Okano 2013). This optimization method has been tried in many other problems outside of the oil industry and showed multiple strengths over the other global optimization methods.…”

Assisted History Matching Using Pattern Recognition Technology

“…DE recently has been applied to a variat of petroleum engineering case studies (Wang, et al, 2006) (Decker, et al, 2006;Jahangiri, 2007;2010;Wang, et al, 2010;Wang, et al, 2011;Mirzabozorg, et al, 2013) (Okano, 2013).…”