Pål-Eric Øren

3-D Pore-Scale Modelling of Sandstones and Flow Simulations in the Pore Networks

A new method for generating realistic homogenous and heterogeneous 3-D pore-scale sandstone models is presented. The essence of our method is to build sandstone models which are analogs of actual sandstones by numerically modelling the results of the main sandstone-forming geological processes - sandgrain sedimentation, compaction, and diagenesis. The input data for the modelling are obtained from image analyses of thin section images of the actual sandstone. The spatial continuity of the sandstone model in the X, Y, and Z directions is determined using a scale-independent invasion percolation based algorithm. The resulting spatial continuity function, which is an ellipsoid, may be used as a heterogeneity descriptor for the sandstone model. Heterogeneity analyses show that compaction reduces the spatial continuity in the horizontal direction more rapidly than in the vertical one. The architecture and geometry of the network representation of the pore space are determined by applying various 3-D image analysis algorithms directly on the fully characterised sandstone model. A 3-D pore network which was generated from thin section data from a strongly water wet Bentheimer sandstone is used as input to a two-phase network flow simulator. Simulated transport properties for the sandstone model are in good agreement with those determined experimentally.

Process Based Reconstruction of Sandstones and Prediction of Transport Properties

We present a process based method for reconstructing the full three-dimensional microstructure of sandstones. The method utilizes petrographical information obtained from two-dimensional thin sections to stochastically model the results of the main sandstone forming processes – sedimentation, compaction, and diagenesis. We apply the method to generate Fontainebleau sandstone and compare quantitatively the reconstructed microstructure with microtomographic images of the actual sandstone. The comparison shows that the process based reconstruction reproduces adequately important intrinsic properties of the actual sandstone, such as the degree of connectivity, the specific internal surface, and the two-point correlation function. A statistical reconstruction of Fontainebleau sandstone that matches the porosity and two-point correlation function of the microtomography data differs strongly from the actual sandstone in its connectivity properties. Transport properties of the samples are determined by solving numerically the local equations governing the transport. Computed permeabilities and formation factors of process based reconstructions of Fontainebleau sandstone compare well with experimental measurements over a wide range of porosity.

Reconstruction of Berea sandstone and pore-scale modelling of wettability effects

Abstract We present an integrated procedure for estimating permeability, conductivity, capillary pressure, and relative permeability of porous media. Although the method is general, we demonstrate its power and versatility on samples of Berea sandstone. The method utilizes petrographical information obtained from 2D thin sections to reconstruct 3D porous media. The permeability and conductivity are determined by solving numerically the local equations governing the transport. The reconstructed microstructure is transformed into a topologically equivalent network that is used directly as input to a network model. Computed two-phase and three-phase relative permeabilities for water wet conditions are in good agreement with experimental data. We present a method for characterizing wettability on the pore-scale from measured Amott wettability indices. Simulated effects of wettability on waterflood relative permeabilities and oil recovery compare favourably with experimental results.

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.

Dimensional analysis of pore scale and field scale immiscible displacement

AbstractA basic re-examination of the traditional dimensional analysis of microscopic and macroscopic multiphase flow equations in porous media is presented. We introduce a ‘macroscopic capillary number’

Quantitative analysis of experimental and synthetic microstructures for sedimentary rock

\overline {Ca}

A Dynamic Network Model for Two-Phase Flow in Porous Media

which differs from the usual microscopic capillary number Ca in that it depends on length scale, type of porous medium and saturation history. The macroscopic capillary number