Abstract
The In-situ Upgrading Process (IUP) is a thermal recovery technique that relies on pattern-based development process, a complicated physical process that involves thermal and mass transfer in porous media, which renders full-field-scale reservoir simulations impractical. Although it is feasible to quantify the impact of subsurface uncertainties on recovery for small-scale sector models via experimental design (ED), it is still a very challenging problem to quantify their impact on field-scale quantities. Straightforward upscaling to field scale does not work, because such conventional superposition-based methods do not capture the effects of spatial variability in rock and fluid properties and the time delay in sequential pattern development.
In this paper, we show that, under certain mild assumptions, an analytical superposition formulation can be developed that propagates the uncertainties of production forecasts and economic evaluations generated from a sector model to full field-scale quantities. This formulation can be further simplified such that the variance of a field-scale quantity is analytically expressed as the variance of the same single-pattern quantity multiplied by a (computable) scale-up factor. This makes it possible to implement a practical uncertainty quantification workflow, in which single-pattern results are upscaled to accurate full field results with reliable uncertainty ranges, without the need for full field-scale simulations.
We apply the proposed novel superposition and uncertainty propagation method to a multi-pattern IUP development, and demonstrate that this workflow produces reliable results for field-scale production and economics as well as realistic uncertainty ranges. Moreover, these results indicate that the scale-up factor for single-pattern results can accurately capture the impact of spatial correlations of subsurface uncertainties, the size of the field-scale model, the time-delay in pattern development and the discount rate.
Uncertainty quantification of field-scale production and economics is a key factor for the successful development of unconventional resources such as extra-heavy oil and oil shale with significant rewards in terms of risk management and project profitability. With minor modifications, the proposed method can also be applied to other pattern-driven processes such as the In-situ Conversion Process (ICP) and Steam Assisted Gravity Drainage (SAGD).
