Production forecasts for petroleum reservoirs are essentially uncertain due to the lack of data. The unknown parameters are calibrated so that the simulated profile can match the observed data. This process is an inverse problem called history-matching which is ill-posed and may have non-unique solutions. This paper addresses two issues: 1) How can we calibrate physical properties in history-matching? 2) How can we predict uncertain reservoir performance based on history-matching?
The aim of our study is to quantify uncertainty of reservoir connectivity in a Turbidite sandstone reservoir. The target reservoir is in the on-shore oil field of which the depositional environment is a submarine fan of turbidite deposits. For the calibration we parameterise the reservoir properties and adopt a stochastic sampling method called Particle Swarm Optimisation (PSO) which is one of the swarm intelligence algorithms. Then a Bayesian framework along with Markov Chain Monte Carlo (MCMC) and Neighbourhood Approximation in parameter space is used to calculate the posterior probability. The MCMC is used to overcome the numerical difficulties calculating the normalisation constant in Bayesian inference.
A Bayesian framework and PSO have been applied to the evaluation of CO2 injection test in the tight oil reservoir where the wells have been stimulated by hydraulic fracturing. 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. The in-place volumes and connectivity between the wells have been calibrated in a simple model using the effective algorithm of PSO. The calibrated parameters include permeabilities and porosities in the fracture cells, the length of the injector hydraulic fracture, the net-to-gross ratios and the horizontal and vertical permeabilities around one 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. The probability given production history is calculated from the prior belief and the misfit between the observed data and the simulated profiles, because the likelihood function can be calculated from the misfit. Our results contribute to the evaluation of the pilot test for a continuous CO2 injection in the tight oil reservoir.
The simplification in parameterising the very heterogeneous reservoir was the key to generating multiple history-matched models, because the amount of computation is prohibitive. It is much quicker to adjust large-scale heterogeneity in a simple model than in a detailed model. The simple model calibration with PSO and the forecast of Bayesian inference have been successfully applied to a real field data.