A pore-scale network modelling study to explain the observed differences between steady-state and unsteady-state relative permeabilities

Abstract

It is widely recognized that multiphase flow through porous media – in particular, hydrocarbon displacement – is controlled by the physics, rock network topology and geometry at the pore scale. Indeed, as early as 1937, one of the pioneers of subsurface flow modelling, Maurice Muskat, suggested that “It is necessary to know the pore geometry of a rock before fluid movement through it can be analyzed” (Muskat, (1937)). Since the 1950s, pore scale network modelling (PNM) has been used to investigate a number of issues in the analysis and modelling of multiphase flow through porous media. Relative permeability is one of the most important macroscopic properties in reservoir simulations that characterise multiphase flow and this is also determined by the microstructure of porous medium (Oren et al. (1998)). The motivation for the work in this thesis is to utilise PNM to resolve or shed light on the differences between steadystate (SS) and unsteady-state (USS) oil/water relative permeabilities. To do this, two models have been developed in this work: (1) an improved quasi-static model based on the MixWet model of McDougall and Sorbie in 1990s (McDougall and Sorbie (1994, 1995)) and (2) a novel dynamic model of water imbibition which has been developed entirely in this thesis. Both of these PNM models simulate 2-phase flow in porous media including a more detailed treatment of film flow in the system. The modified quasi-static model implements angular pores to accommodate the formation and flow of wetting films. A detailed sensitivity study of wettability and some other parameters is conducted using this model. However, such quasi-static models can only examine the capillary dominated flow regimes. The new dynamic pore-scale network model has been developed to study the effect of flow rate and the balance of viscous to capillary forces, in order to understand all of the parameters that affect two phase imbibition processes and hence relative permeability. The dynamic model concentrates on simulating 2-phase displacement during water imbibition by explicitly modelling intra-pore dynamic bulk and film flows. A new dynamic switching parameter, λ, is proposed within this model which is able to simulate the competition between capillary forces and viscous forces under any flow conditions. This quantity (λ) determines the primary pore filling mechanism in imbibition; i.e. whether the dominant force is (i) piston-like displacement under viscous forces, (ii) film swelling/collapse and snap-off because of capillary forces, or (iii) some intermediate combination of both mechanisms. Indeed, this λ parameter may vary in different pores in different regions of the network in the same displacement. Using this model, the origin of the observed rate-dependency in unsteady-state displacements has been correctly reproduced and explained. Furthermore, this new dynamic network model quantifies the complex relationships between displacement mechanisms and several process controlling parameters of interest. For example, using this dynamic model, the sensitivities to flow rate (Q), viscosity ratio ( Uo/ Uw), pore-size distribution (PSD), wettability state (contact angle θ), pore geometry (pore half angles β), interfacial tension (σ) and initial water saturation (Swi) have all been examined in both 2D and 3D network models. Our new dynamic model also provides a set of fractional flows and global pressure data, which can subsequently be used to generate unsteady-state relative permeability (USSRP) curves for any given conditions specified in terms of the above controlling parameters based on Buckley-Leverett theory. Furthermore, similar to the actual experiments, our model can also select a middle section of the dynamic model, record the fluid configurations at some particular instants, and then apply the quasi-static model on this “lifted-out” section to derive the current relative permeabilities. The comparison between these unsteady-state relative permeability curves with the corresponding steady-state RP can help us to understand the observed differences between SS and USS approaches, and study the ways in which these relate to the underlying pore-scale physics of the various processes.