Quantification of uncertainty due to sub-grid heterogeneity in reservoir models

Due to the lack of data, a reservoir engineer needs to calibrate unknown petrophysical parameters based on production history. However, because the observations cannot constrain all the subsurface properties over a field, production forecasts for reservoirs are essentially uncertain. In general, many parameters of the model must be adjusted in the history-matching process, and the amount of computation required to solve the inverse problem may be prohibitive. To address this issue, we proposed a new methodology which restricts the parameter ranges of the calibration by using physically based prior information, extracted from geological and petrophysical input. The aim of the work is to have a sound basis for forecasting uncertainty in reservoir production. We demonstrate the applicability of the methodology using quarter five-spot pattern waterflooding models. The petrophysical properties to be adjusted in this paper are coarse-scale relative permeabilities. Coarse-scale models have the disadvantage of omitting the effects of fine-scale heterogeneity and suffering from solution errors, although in practice they are often employed in field-scale simulation because of the computational cost. Here, we history-match relative permeabilities at the coarse scale in order to encapsulate physical dispersion and compensate for numerical dispersion. The prior information was estimated from a range of possible geostatistical parameters. It allowed us not only to determine the parameterisation of the grouped relative permeabilities but also to set up the bounds of each type of curve. We used a synthetic data set for which the true solution is known. The resulting posterior expectations and P10/P90 cut-offs of the production data and the relative permeabilities were examined in comparison with the reference results. We conclude that this new approach enabled us to quantify the uncertainty of sub-grid heterogeneity through the use of coarse-scale relative permeabilities without refining the model.