Quantification of Uncertainty Due to Subgrid 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 historymatching 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. Introduction Production forecasts for petroleum reservoirs are essentially uncertain due to the lack of data. Firstly, direct measurements of rock and fluid properties are available at only a small number of sparse well locations. Secondly, oil production and pressure data reflect roughly integrated responses over a limited number of time intervals. As a result, a reservoir engineer needs to calibrate the unknown petrophysical parameters based on insufficient observations which cannot constrain the subsurface properties all over a field. Reservoir simulation is routinely employed in the prediction of reservoir performance under different depletion and operating scenarios. This practical use of reservoir simulation requires two steps: one is history-matching, and the other is quantification of uncertainty in forecasting. In the traditional approach, a single history-matched model, conditioned to production data, is obtained, and is used to forecast future production profiles, [e.g., 1]. As stated above, the history-matching is non-unique and the forecast production profiles are uncertain. Recently, a new methodology for uncertainty quantification has been introduced to the petroleum industry [2, 3]. This method adopts the Markov Chain Monte Carlo method along with the Neighbourhood Approximation [4, 5]. The petrophysical properties to be adjusted in this paper were coarse-scale relative permeabilities. In general, rock relative permeability curves are often altered in a coarse-scale model during the process of history-matching, [6]. Traditionally, this has been based on rough justifications. Firstly, in practice, it is difficult to evaluate rock curves in an ideal way so that the background theory is satisfied. Secondly, the spatial distribution of the properties cannot be obtained apart from at well locations. Finally, an upscaling procedure including the grouping of the curves is problematic and leads to the uncertainty in relative permeabilities at the coarse scale, [7, 8]. Unfortunately, because guidelines for changing the shape of the curves have not been clearly established, there is no guarantee that the resulting history-matched model is reliable for production performance forecasting. SPE 100223 Quantification of Uncertainty Due to Subgrid Heterogeneity in Reservoir Models H. Okano, SPE, Heriot-Watt U. and Japan Oil, Gas and Metals Natl. Corp.; G.E. Pickup, SPE, and M.A. Christie, SPE, Heriot-Watt U.; S. Subbey, Inst. of Marine Research; and M. Sambridge, Australian Natl. U.