Effects of Heterogeneity and Wetting on Relative Permeability Using Pore Level Modeling
- Martin J. Blunt
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 1997
- Document Type
- Journal Paper
- 70 - 87
- 1997. Society of Petroleum Engineers
- 5.1 Reservoir Characterisation
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We present a three-dimensional, capillary equilibrium based, pore level network model that computes relative permeability and capillary pressure for drainage and imbibition cycles. The model accounts for wetting layers in crevices of the pore space, cooperative pore filling and different contact angles. Arbitrary distributions of pore size with different spatial correlations are studied. We show that relative permeabilities for unconsolidated media can be represented in the model using spatially uncorrelated distributions of pore size, but that curves typical of consolidated rock can only be explained by allowing spatial correlation in the pore structure. We also study the effects of flow in wetting layers and different types of cooperative pore filling. This represents changes in contact angle from a completely water-wet system to a neutrally-wet rock. Relative permeability can be extremely sensitive to small changes in contact angle. In general, the residual non-wetting phase saturation decreases as the system becomes less strongly water-wet.
Since the work, of Fatt,1-3 numerical networks of interconnected pores have been used to study multiphase flow in porous media.4-70 Sahimi71,72 and Berkowitz73 have presented reviews of the literature. In recent years, the models have become more sophisticated and have been used to provide insight into a variety of different phenomena, such as relative permeability and capillary pressure hysteresis,23,65 the perturbative effects of viscous and buoyancy forces,14,15,74 the behavior of mixed-wet media.,30,40,41,75 and three phase flow.42-44,68,76-78 Using reasonable approximations, parameters that control the geometry of the pore space can be varied to obtain excellent agreement with measured relative permeability and capillary pressure data (see, for instance.18,23,28,29,31) If the pore structure is known, network modeling can predict relative permeabilities from first principles.16,66,69,79
In this paper we extend previous work by introducing a model with the following three features. (1) We study short and long-range spatial correlations in the pore size. Jerauld and Salter23 investigated a variety of different spatial correlations that had a short range of approximately one pore length. Ferrand and Celia47 studied drainage capillary pressures for networks with a variety of correlated structures, but did not compute relative permeabilities or study imbibition. Chaouche et al.63 studied displacement patterns for networks correlated at the pore scale in two dimensions, but did not discuss the effects on relative permeability. Paterson et al.80,81 have studied the effect of long range correlations for drainage-type displacements. Here we will show that long range correlations (greater than a pore length) greatly increase the non-wetting phase relative permeability and may be necessary to explain experimental measurements on consolidated rock. (2) We include explicitly the effects of the wetting phase in crevices of the pore space by using expressions for the conductance of wetting layers as a function of local interfacial curvature computed by Ransohoff and Radke.82 In another study we also accounted explicitly for pressure gradients in wetting layers to explain the decrease in residual oil saturation with flow rate.15 Here we will always assume that the network is in capillary equilibrium, appropriate for flow at low capillary numbers. The role of wetting layers has also been studied by Billiote et al.,83 who studied gas/water cycling in two-dimensional systems and by Øren et al.,43,68 and Fenwick and Blunt76,78 for three phase flow. (3) We introduce a parametric model of pore and throat filling in imbibition, consistent with the results of extensive micromodel experiments by Lenormand et al.25,84-86 This enables us to study the effect of changing contact angle on the displacement patterns and the relative permeabilities. We demonstrate that changing the model from strongly to weakly water-wet improves the waterflood recovery efficiency.
We first review pore level displacements and then we describe the network model. The approximations of the model and its sensitivities to various parameters are investigated. We use to model to compute relative permeabilities and capillary pressures that are representative of real systems. Lastly we discuss the different types of invasion pattern that may be obtained as the contact angle is increased.
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