Effects of reservoir heterogeneity on scaling of effective mass transfer coefficient for solute transport.

Modeling transport process at large scale requires proper scale-up of subsurface heterogeneity and an understanding of its interaction with the underlying transport mechanisms. A technique based on volume averaging is applied to quantitatively assess the scaling characteristics of effective mass transfer coefficient in heterogeneous reservoir models. The effective mass transfer coefficient represents the combined contribution from diffusion and dispersion to the transport of non-reactive solute particles within a fluid phase. Although treatment of transport problems with the volume averaging technique has been published in the past, application to geological systems exhibiting realistic spatial variability remains a challenge. Previously, the authors developed a new procedure where results from a fine-scale numerical flow simulation reflecting the full physics of the transport process albeit over a sub-volume of the reservoir are integrated with the volume averaging technique to provide effective description of transport properties. The procedure is extended such that spatial averaging is performed at the local-heterogeneity scale. In this paper, the transport of a passive (non-reactive) solute is simulated on multiple reservoir models exhibiting different patterns of heterogeneities, and the scaling behavior of effective mass transfer coefficient (Keff) is examined and compared. One such set of models exhibit power-law (fractal) characteristics, and the variability of dispersion and Keff with scale is in good agreement with analytical expressions described in the literature. This work offers an insight into the impacts of heterogeneity on the scaling of effective transport parameters. A key finding is that spatial heterogeneity models with similar univariate and bivariate statistics may exhibit different scaling characteristics because of the influence of higher order statistics. More mixing is observed in the channelized models with higher-order continuity. It reinforces the notion that the flow response is influenced by the higher-order statistical description of heterogeneity. An important implication is that when scaling-up transport response from lab-scale results to the field scale, it is necessary to account for the scale-up of heterogeneity. Since the characteristics of higher-order multivariate distributions and large-scale heterogeneity are typically not captured in small-scale experiments, a reservoir modeling framework that captures the uncertainty in heterogeneity description should be adopted.

Modeling impacts of subscale heterogeneities on dispersive solute transport in subsurface systems.

Previous works in the literature demonstrated that dispersion increases with heterogeneities and travel distance in heterogeneous reservoirs. However, it remains challenging to quantify the effects of subscale heterogeneities on dispersion. Scale-up of input dispersivity and other reservoir attributes to the transport modeling scale should account for subscale heterogeneity and its variability. A method is proposed to quantify the uncertainties in reservoir attributes and dispersivity introduced by scale-up. A random walk particle tracking (RWPT) method, which is not prone to numerical dispersion, is used for transport modeling. First, to scale-up rock properties including porosity and permeability, volume variance at the transport modeling scale is computed corresponding to a given spatial correlation model; numerous sets of "conditioning data" are sampled from probability distributions whose mean is the block average of the actual measure values and the variance is the variance of block mean. Stochastic simulations are subsequently performed to generate multiple realizations at the transport modeling scale. Next, multiple sub-grid geostatistical realizations depicting detailed fine-scale heterogeneities and of the same physical sizes as the transport modeling grid block are subjected to RWPT simulation. Effective longitudinal and transverse (horizontal) dispersivities in two-dimensional models are determined simultaneously by matching the corresponding breakthrough concentration history for each realization with an equivalent medium consisting of averaged homogeneous rock properties. Aggregating results derived with all realizations, we generate probability distributions of scaled-up dispersivities conditional to particular averaged rock properties, from which values representative of the transport modeling scale are randomly drawn. The method is applied to model a tracer injection process. Results obtained from coarse-scale models, where reservoir properties and dispersivities are populated with the proposed approach, are compared to those obtained from fine-scale models. Our results verify that dispersivity increases with scale and demonstrate that (1) uncertainty distributions in recovery obtained by accounting for variability owing to scale-up capture the actual fine-scale behavior; and (2) ignoring sub-scale uncertainties would underestimate the ensuing uncertainty in recovery performance. An important contribution of this work is that it presents a quantitative and systematic procedure to scale-up both rock and flow-related properties. It reinforces the notion that deterministic conditioning data does not exist in reservoir modeling.