Wolf Val Pinczewski

Fluid Distribution and Pore-Scale Displacement Mechanisms in Drainage Dominated Three-Phase Flow

This paper presents a precise description of the fluid distribution and pore-scale displacement mechanisms for three-phase flow under strongly wetting conditions when the displacing fluid is a nonwetting phase. It is shown that on the pore-scale the fluids may adopt one of three basic configurations depending on the values of the three interfacial tensions and the wetting preference of the solid. The nature of the three-phase displacement mechanisms is determined by the pore-scale fluid distribution. The displacing phase may advance by two basic mechanisms; a double drainage mechanism involving all three phases — a three-phase displacement — or, a direct drainage mechanism — a two-phase displacement. The three-phase displacement mechanism is described by a simple generalisation of two-phase flow mechanisms. The basic displacement mechanisms are incorporated into a numerical percolation-type network model which is used to compute phase recoveries for three-phase displacements. Computed recoveries are shown to be in good agreement with those determined experimentally. The model may therefore provide a basis for modelling three-phase flows in actual porous media.

Direct and Stochastic Generation of Network Models from Tomographic Images: Effect of Topology on Residual Saturations

We generate the network model equivalents of four samples of Fontainebleau sandstone obtained from the analysis of microtomographic images. We present the measured distributions of flow-relevant geometric and topological properties of the pore space. We generate via bond dilution from a regular lattice, stochastic network models with identical geometric (pore-size, throat-size) and topological (coordination number distribution) properties. We then simulate the two-phase flow properties directly on the network model and the stochastic equivalent for each sample. The simulations on the stochastic networks are found to provide a poor representation of the results on the direct network equivalents. We find that the description of the network topology is particularly crucial in accurately predicting the residual phase saturations. We also find it necessary to introduce into the stochastic network geometry both extended pore-pore correlations and local pore-throat correlations to obtain good agreement with flow properties on the rock-equivalent network.

Pore-scale network model for drainage-dominated three-phase flow in porous media.

Drainage displacements in three-phase flow under strongly wetting conditions are completely described by a simple generalisation of well understood two-phase drainage mechanisms. As in two-phase flow, the sequence of throat invasions in three-phase flow is determined by fluid connectivity and threshold capillary pressure for the invading interface. Flow through wetting and intermediate spreading films is important in determining fluid recoveries and the progress of the displacement in three-phase flow. Viscous pressure drops associated with flow through films give rise to multiple filling and emptying of pores. A three-phase, two-dimensional network model based on the pore-scale fluid distributions and displacement mechanisms reported by Øren et al. and which accounts for flow through both wetting and intermediate fluid films is shown to correctly predict all the important characteristics of three-phase flow observed in glass micromodel experiments.

Effect of Network Topology on Relative Permeability

We consider the role of topology on drainage relative permeabilities derived from network models. We describe the topological properties of rock networks derived from a suite of tomographic images of Fontainbleau sandstone (Lindquist et al., 2000, J. Geophys. Res.105B, 21508). All rock networks display a broad distribution of coordination number and the presence of long-range topological bonds. We show the importance of accurately reproducing sample topology when deriving relative permeability curves from the model networks. Comparisons between the relative permeability curves for the rock networks and those computed on a regular cubic lattice with identical geometric characteristics (pore and throat size distributions) show poor agreement. Relative permeabilities computed on regular lattices and on diluted lattices with a similar average coordination number to the rock networks also display poor agreement. We find that relative permeability curves computed on stochastic networks which honour the full coordination number distribution of the rock networks produce reasonable agreement with the rock networks. We show that random and regular lattices with the same coordination number distribution produce similar relative permeabilities and that the introduction of longer-range topological bonds has only a small effect. We show that relative permeabilities for networks exhibiting pore–throat size correlations and sizes up to the core-scale still exhibit a significant dependence on network topology. The results show the importance of incorporating realistic 3D topologies in network models for predicting multiphase flow properties.

Invasion Percolation: New Algorithms and Universality Classes

Employing highly efficient algorithms for simulating invasion percolation (IP), whose execution time scales as O[Mlog(M)] or better for a cluster of M sites, and for determining the backbone of the cluster, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in order to identify the universality classes of four different IP processes (site and bond IP, with and without trapping). In two dimensions IP is characterized by two universality classes, one each for IP without trapping, and site and bond IP with trapping. In a three-dimensional site IP with and without trapping is in the universality class of random percolation, while bond IP with trapping is in a distinct universality class, which may be the same as that of optimal paths in strongly disordered media.

Digital Core Laboratory: Properties of reservoir core derived from 3D images

A facility for digital imaging, visualizing and calculation of reservoir rock properties in three dimensions (3D) is described. The facility includes a high resolution X-ray micro-computed tomography system capable of acquiring 3D images made up of 2000 voxels on core plugs up to 5 cm diameter with resolutions down to 2 μm. Subsets of four sandstone reservoir core plugs (5 mm in diameter) from a single well of a producing gas field are imaged in this study. The four cores exhibit a broad range of pore and grain sizes, porosity, permeability and mineralogy. Computational results made directly on the digitized tomographic images are presented for the pore size distribution, permeability, formation factor, NMR response and drainage capillary pressure. We show that data across a range of porosity can be computed from the suite of 5 mm plugs. Computations of permeability, formation factor and drainage capillary pressure are compared to data from a comprehensive SCAL laboratory study on 70 cores from the same well. The results are in good agreement. Empirical correlations between permeability and other petrophysical parameters are made and compared to common correlations. The results demonstrate the potential to predict petrophysical properties from core material not suited for laboratory testing (e.g., drill cuttings, sidewall core or damaged core) and the feasibility of combining digitized images with numerical calculations to predict properties and derive correlations for individual reservoir rock lithologies.

Permeability Upscaling for Carbonates from the Pore-Scale Using Multi-Scale Xray-CT Images

bility due to large permeability contrasts. The most accurate upscaling technique is employing Darcy’s law. A key part of the study is the establishment of porosity transforms between highresolution and low-resolution images to arrive at a calibrated porosity map to constraint permeability estimates for the whole core.

Invasion Percolation on Correlated and Elongated Lattices: Implications for the Interpretation of Residual Saturations in Rock Cores

The invasion percolation model is used to investigate the effect of correlated heterogeneity on capillary dominated displacements in porous media. The breakthrough and residual saturations are shown to be strongly influenced by the correlations. Correlated heterogeneity leads to lower residual saturations than those observed in random systems and the scatter commonly observed in laboratory core measurements of the residual saturations can be attributed to the presence of such heterogeneity at the pore scale. Invasion percolation computations on elongated lattices, those with a geometry of Ld−1 × nL where n denotes the aspect ratio, show that residual saturations for systems with correlated heterogeneity exhibit a strong dependence on aspect ratio. This effect is not considered by experimentalists who advocate the use of long (high aspect ratio) cores in order to overcome “end-effects” in experiments on shorter cores. A new scaling law is proposed for the residual saturations in elongated systems with correlated heterogeneity, and is confirmed by numerical simulations.

Computation of Relative Permeability from Imaged Fluid Distributions at the Pore Scale

Image-based computations of relative permeability for capillary-dominated quasi-static displacements require a realistic description of the distribution of the fluids in the pore space. The fluid distributions are usually computed directly on the imaged pore space or on simplified representations of the pore space extracted from the images using a wide variety of models which capture the physics of pore-scale displacements. Currently this is only possible for uniform strongly wetting conditions where fluid–fluid and rock–fluid interactions at the pore-scale can be modelled with a degree of certainty. Recent advances in imaging technologies which make it possible to visualize the actual fluid distributions in the pore space have the potential to overcome this limitation by allowing relative permeabilities to be computed directly from the imaged fluid distributions. The present study explores the feasibility of doing this by comparing laboratory measured capillary-dominated drainage relative permeabilities with relative permeabilities computed from micro-CT images of the actual fluid distributions in the same rock. The agreement between the measurements and the fluid image-based computations is encouraging. The paper highlights a number of experimental difficulties encountered in the study which should serve as a useful guide for the design of future studies.

The Effects of Displacement Rate and Wettability on Imbibition Relative Permeabilities

A new dynamic network model is used to investigate the effects of displacement rate and wettability on imbibition relative permeability. The network geometry and topology is representative of Berea sandstone. In contrast to existing quasi-static network models where snap-off, the major pore-scale trapping mechanism in imbibition, is suppressed by contact angle alone, the dynamic model introduces displacement rate as an additional snap-off inhibiting mechanism. The network model is used to analyse the complex rate dependence of relative permeability and residual saturation displayed by laboratory measured data reported in the literature.