Modeling and Investigation of the Influence of Capillary Heterogeneity on Relative Permeability

A recently developed technique to accurately characterize sub-core scale heterogeneity by Krause et al. (2011, 2012) is applied to investigate the flow rate dependency of relative permeability on heterogeneity. Leverett (1939) first reported the dependency of laboratory measured relative permeability on flow rate, these results have since been both supported (Rapoport and Leas 1953) and challenged (Richardson 1957) by a number of investigators. Studies have shown that this apparent flow rate dependency is a result of both sub-core scale heterogeneity (Corey and Rathjens 1956) and outlet boundary effects (Richardson et al. 1952), however this has only been demonstrated numerically for highly simplified models of porous media. In this paper, flow rate dependency of effective relative permeability is demonstrated using two sandstone rock cores, one a Berea Sandstone having a low degree of heterogeneity, the other a heterogeneous sandstone from the Otway Basin Pilot Project in Australia. Steady-state coreflooding simulations are conducted at a number of injection rates using a single set of input characteristic relative permeability curves, and flow rate dependent effective relative permeability is calculated from the simulation data using Darcy's law. An optimization procedure is then used to derive the input characteristic relative permeability from the flow rate affected effective relative permeability. Results show that even in a Berea Sandstone, which has a relatively low degree of heterogeneity, the impact of fine-scale heterogeneities on measured relative permeability can be significant. Results also show that the apparent flow rate dependency of effective relative permeability is a stronger function of fine-scale heterogeneities than of capillary pressure gradients caused by the end effect. In addition to these observations, this work supports two important conclusions: the first is that using a one-dimensional homogeneous grid to simulate what is really a three-dimensional heterogeneous core can lead to significant errors in the derived relative permeability, even for cores of low heterogeneity. Second, the characteristic relative permeability curves can be accurately determined using flow rate affected effective relative permeability data using numerical simulation, provided the sub-core scale permeability distribution is accurately characterized.