The paper presents a stochastic analysis of the growth rate of viscous fingers in miscible displacement in a heterogeneous porous medium. The statistical parameters characterizing the permeability distribution of a reservoir vary over a wide range. The formation of fingers is provided by the mixing of different-viscosity fluids — water and polymer solution. The distribution functions of the growth rate of viscous fingers are numerically determined and visualized. Careful data processing reveals the non-monotonic nature of the dependence of the front end of the mixing zone on the correlation length of the permeability of the reservoir formation. It is demonstrated that an increase in correlation length up to a certain value causes an expansion of the distribution shape and a shift of the distribution maximum to the region of higher velocities. In addition, an increase in the standard deviation of permeability leads to a slight change in the shape and characteristics of the density distribution of the growth rates of viscous fingers. The theoretical predictions within the framework of the transverse flow equilibrium approximation and the Koval model are contrasted with the numerically computed velocity distributions.
Monitoring is an important component of geological carbon storage operations because it provides data that can be used to estimate key quantities such as CO(_{2}) plume location. The design of the monitoring strategy is complicated, however, because the monitoring plan must be established prior to the availability of extensive flow data. In this work, we present and apply a framework that integrates monitoring well optimization and (subsequent) history matching. The monitoring well optimization entails finding the locations of monitoring wells such that, with the data acquired at those locations, the expected uncertainty reduction in a particular flow quantity is maximized. This optimization requires the simulation of a large set of prior models, though these simulations need only be performed once for a given injection scenario. Once the monitoring wells are in place and CO(_{2}) injection begins, history matching is performed using the monitoring data. This is accomplished here using an ensemble smoother with multiple data assimilation. The overall framework is applied to variogram-based geomodels that are representative of an actual storage project under development in the USA. Two injection scenarios are considered with two different (synthetic) ‘true’ models, which provide the observed data. History matched models are constructed using data from both optimally located and heuristically placed monitoring wells. Posterior uncertainty, evaluated in terms of the cumulative distribution function for a metric related to plume extent over the ensemble of history matched models, is shown to be minimized through use of optimized monitoring wells. These results demonstrate the importance of optimizing the monitoring plan, and the degree of uncertainty reduction that can be realistically achieved.
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：