Shear dispersion in a capillary tube with a porous wall

A new analytical model for flow in acidized fractured-vuggy porous media

Acidizing is one of the widely used technologies that makes the development of naturally fractured-vuggy reservoirs effective. During the process of acidizing, carbonate minerals are dissolved by hydrochloric acid, which can create high conductivity channels and wormholes to connect fractures and pores. In this work, a new analytical model, incorporating the heterogeneity of the pore networks into acidizing region, is proposed to study the flow characteristics in acidized fractured-vuggy reservoirs. The model is coupled by an acidized inner region and a conceptualized outer region of common triple medium. The porosity and permeability of inner region, which are rather heterogeneous and disordered when observed at different length scales, can be well addressed by fractal theory. The properties of the outer region can be described with three basic parameters: the matrix block size L_M, the space interval of fracture L_F and the radius of the vug L_v. Results show that the flow characteristic curves can be characterized by six flow stages (i.e. wellbore storage stage, radial flow stage in the interior region, fracture-vug inter-porosity flow stage, transition flow stage, fracture-matrix inter-porosity flow stage and external boundary response stage). It can be applied to estimate reservoir parameters for uncertainty reduction using inverse modeling.

Testing the limits of the spatial Markov model for upscaling transport: The role of nonmonotonic effective velocity autocorrelations

The spatial Markov model is a Lagrangian random walk model, widely and successfully used for upscaling transport in heterogeneous flows across a broad range of problems. It is particularly useful at early or pre-asymptotic times when many other conventional upscaling approaches may not be valid. However, as with all upscaled models, it must have its limits. In particular, the question of what the smallest scale at which it can be legitimately applied, without violating implicit assumptions, remains. Here we address this issue by considering one of the most classical transport upscaling problems: Taylor dispersion in a bounded shear flow. We demonstrate that the smallest scale for the spatial Markov model depends on the transverse width of the domain, the variability of the flow field as quantified by a coefficient of variation, and the competition of longitudinal and transverse diffusion coefficients. We show that this scale is a factor of the Peclet number smaller than the classical Taylor dispersion scale, meaning that for advection-dominated systems where Peclet numbers are large, this model can be applied at much smaller scales than classical Taylor-Aris dispersion theories.