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 CO2 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 CO2 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 CO2 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.