Marios A. Ioannidis

Network modelling of pore structure and transport properties of porous media

Abstract A methodology is presented for the simultaneous prediction of absolute permeabilities, formation resistivity factors and drainage capillary pressure curves of sandstones by employing a network model of pore structure based on bond-correlated site percolation concepts. The model is a regular cubic lattice consisting of pore throats and pore bodies, having respective pore size distributions. Information about the pore structure, obtained from mercury porosimetry and photomicrographic analysis, is utilized to select the pore throat and pore body size distributions in a manner such that the resulting model (i) matches the porosity of the medium and (ii) satisfactorily simulates the drainage capillary pressure curve of the porous medium under consideration. Assumptions made about the cross-sectional shape of the pore throats and their effect on the network model predictions are discussed. Details of the methodology used in the simulation of transport properties with microscopic pore structure parameters are also presented and discussed. The problem of fluid and electric current flow through the simulated porous medium is reduced to an electric analogue-linear network problem and is numerically solved using a conjugate gradients method for computing the absolute permeability and the formation resistivity factor. Good agreement between the predicted and the measured values is observed for a number of sandstone samples having widely different transport properties.

Permeability and electrical conductivity of porous media from 3D stochastic replicas of the microstructure

In this paper we report on the application of low-order statistical information (porosity, two-point correlation function), obtained from 2D micrographs of real porous media, to derive stochastic replicas of their 3D pore networks. The main focus is on assessing the usefulness of stochastic reconstruction as a means of relating macroscopic transport coefficients (intrinsic permeability and effective electrical conductivity) to the geometry and topology of the pore space. To this end we employ newly developed algorithms, based on morphological skeletonization, to obtain a comprehensive geometric and topological description of each simulated pore network. Using the skeleton or graph of the pore space as a basis, detailed geometrical measurements are performed to estimate the effective hydraulic and electrical conductance of individual flow paths, identified with skeleton links. In combination with exact knowledge of the network topology, these measurements enable the specification of equivalent resistor-type network models for the calculation of intrinsic permeability and formation factor. Consistently successful predictions of permeability over a wide range of values are obtained for five reservoir rock samples of diverse origin and lithology. Predictions of formation factor are within a factor of three of the experimental values. These predictions are, however, inconsistent, a fact attributed to the inability of the reconstruction method to accurately reflect the contributions of smaller pores and throats to electrical conductivity. Additionally, it is shown that the hydraulic conductance of pore space channels in stochastically simulated pore networks is spatially correlated over distances equal to the characteristic length scale of the two-point correlation function. The effect of spatial resolution and sample size on the prediction of macroscopic properties is also investigated. Finally, the physical meaning of various length scales relating flow permeability to effective electrical conductivity is elucidated.

Dissolution of residual non-aqueous phase liquids in porous media : Pore-scale mechanisms and mass transfer rates

Abstract Experiments designed to elucidate the pore-scale mechanisms of the dissolution of a residual non-aqueous phase liquid (NAPL), trapped in the form of ganglia within a porous medium, are discussed. These experiments were conducted using transparent glass micromodels with controlled pore geometry, so that the evolution of the size and shape of individual NAPL ganglia and, hence, the pore-scale mass transfer rates and mass transfer coefficients could be determined by image analysis. The micromodel design permitted reasonably accurate control of the pore water velocity, so that the mass transfer coefficients could be correlated in terms of a local (pore-scale) Peclet number. A simple mathematical model, incorporating convection and diffusion in a slit geometry was developed and used successfully to predict the observed mass transfer rates. For the case of non-wetting NAPL ganglia, water flow through the corners in the pore walls was seen to control the rate of NAPL dissolution, as recently postulated by Dillard and Blunt [Water Resour. Res. 36 (2000) 439–454]. Break-up of doublet non-wetting phase ganglia into singlet ganglia by snap-off in pore throats was also observed, confirming the interplay between capillarity and mass transfer. Additionally, the effect of wettability on dissolution mass transfer was demonstrated. Under conditions of preferential NAPL wettability, mass transfer from NAPL films covering the solid surfaces was seen to control the dissolution process. Supply of NAPL from the trapped ganglia to these films by capillary flow along pore corners was observed to result in a sequence of pore drainage events that increase the interfacial area for mass transfer. These observations provide new experimental evidence for the role of capillarity, wettability and corner flow on NAPL ganglia dissolution.

Electrical Conductivity and Percolation Aspects of Statistically Homogeneous Porous Media

A method of 3-D stochastic reconstruction of porous media based on statistical information extracted from 2-D sections is evaluated with reference to the steady transport of electric current. Model microstructures conforming to measured and simulated pore space autocorrelation functions are generated and the formation factor is systematically determined by random walk simulation as a function of porosity and correlation length. Computed formation factors are found to depend on correlation length only for small values of this parameter. This finding is explained by considering the general percolation behavior of a statistically homogeneous system. For porosities lower than about 0.2, the dependence of formation factor on porosity shows marked deviations from Archies law. This behavior results from the relatively high pore space percolation threshold (∼0.09) of the simulated media and suggests a limitation to the applicability of the method to low porosity media. It is additionally demonstrated that the distribution of secondary porosity at a larger scale can be simulated using stochastic methods. Computations of the formation factor are performed for model media with a matrix-vuggy structure as a function of the amount and spatial distribution of vuggy porosity and matrix conductivity. These results are shown to be consistent with limited available experimental data for carbonate rocks.

Stochastic Reconstruction of Chalk from 2D Images

We study the stochastic reconstruction of the microstructure of chalk, from limited morphological information that may be readily extracted from 2D images of the pore space. Backscatter Scanning Electron Microscope images of a North Sea chalk sample are analyzed to determine de-scriptors of pore space morphology, such as the void-phase autocorrelation function, and void- and solid-phase chord distribution functions. This information is used to constrain the stochastic reconstruction of the chalk sample in 2D and 3D by a simulated annealing method. Quantitative analysis of 2D reconstructions using different morphological constraints reveals that imposing chord distribution functions results only in minor improvement over what is achieved by using the void-phase autocorrelation function as the only constraint. This result is further verified by geometric and topological characterization of a 3D replica of the sample generated using only autocorrelation function constraints. Pore and throat size distributions determined by 3D pore space partitioning methods, are consistent with mercury porosimetry results. The predicted permeability and formation factor are shown to be in very good agreement with experimentally determined values.

Macroscopic Percolation Model of Immiscible Displacement: Effects of Buoyancy and Spatial Structure

Percolation theory, commonly used to study quasi-static immiscible displacement at the microscopic scale, is here extended to simulations of gravity-stable drainage and imbibition in three-dimensional porous media with spatially correlated macroscopic properties. The result of this extension is a macroscopic percolation on a regular lattice of sites, where lattice sites represent regions in a porous medium characterized by different macroscopic properties (e.g., absolute permeability, capillary pressure, and relative permeability curves). These properties are assigned to lattice sites by virtue of parametrizations in terms of local permeability. We present a general formulation of macroscopic percolation that accounts for gravitational effects, which can be important in large-scale immiscible displacements with nonzero density difference. In such cases, we find that the local saturation distribution is markedly different from the distribution of saturation under conditions of negligible buoyancy. Displacements with nonzero density difference proceed with the formation of a transition zone of length inversely proportional to a macroscopic Bond number which characterizes the relative importance of capillary and buoyancy forces at the macroscopic scale. Several important features of percolation at the microscopic scale are also manifested at the macroscopic scale. These include the effects of lattice dimensionality and spatial correlation on the macroscopic percolation threshold and accessibility characteristics. In the absence of buoyancy forces, the large-scale capillary pressure and relative permeability behavior of a heterogeneous system is dictated mainly by the structure of the permeability field and can be explained in terms of macroscopic accessibility. Spatial correlation of permeability is found to have pronounced effects on the large-scale drainage relative permeability curves.

Stochastic Reconstruction, 3D Characterization and Network Modeling of Chalk

Abstract Systematic studies involving stochastic reconstruction, geometric and topological characterization, and network modeling of chalk, aiming at computation of petrophysical properties, are reported. The numerical chalk models are constructed exclusively from limited morphological information obtained from 2D backscatter scanning electron microscope images of the microstructure. Two different stochastic reconstruction methods are considered: conditioning and truncation of Gaussian random fields (GRF), and simulated annealing (SA). The potential of initializing the simulated annealing reconstruction with input generated using the Gaussian random fields method is evaluated and found to accelerate significantly the rate of convergence of simulated annealing reconstruction. This finding is important because the main advantage of simulated annealing method, namely its ability to impose a variety of reconstruction constraints, is usually compromised by its very slow rate of convergence. A detailed description of the chalk microstructure in the form of 3D volume data is essential for the prediction of petrophysical properties from first principles. The prediction of absolute permeability and formation factor directly from such information are considered first. The prediction of absolute permeability, formation factor and mercury–air capillary pressure curves are then considered using approximate network models constrained by information (pore- and throat-size distributions, coordination number) obtained from geometric and topological analysis of the reconstructed pore networks. Such information is extracted from the 3D volume data using morphological skeletonization and pore space partitioning methods. Very good agreement between the predicted and measured data is found for samples of North Sea chalk. On the basis of this study, it is concluded that (a) stochastic reconstruction from limited morphological information reproduces the essential features of pore geometry and connectivity of chalk, and (b) network modeling techniques can be used to predict petrophysical properties of chalk based on geometric and topological information of the stochastically reconstructed media.

The effect of spatial correlations on the accessibility characteristics of three-dimensional cubic networks as related to drainage displacements in porous media

Percolation theory is used in this paper to study the general accessibility characteristics of bond site correlated networks in the presence or absence of spatial correlations among the sites. Spectral methods are employed to generate networks in which the sites are spatially correlated according to exponential or Gaussian autocovariance functions. Monte Carlo simulations are performed for bond-correlated site percolation with and without trapping, as related to drainage-type displacements of water by oil (or air) and air by mercury, respectively. For the correlation modes studied, it is found that spatial correlations result in significant reduction of the site percolation threshold with a concomitant modification of the site accessibility. However, the bond accessibility characteristics and the bond percolation threshold are not significantly affected. The simulated drainage capillary pressure curves become more gradual and the residual wetting phase saturation associated with oil (or air)-water displacements is significantly decreased when spatial correlations among the pore bodies exist.

Impact of Liquid Water on Reactant Mass Transfer in PEM Fuel Cell Electrodes

The breakthrough conditions (capillary pressure and liquid water saturation) in a fibrous gas diffusion medium (GDM) used in polymer electrolyte membrane (PEM) fuel cell electrodes have been studied experimentally by two independent techniques and numerically by pore network modeling. Experiments show that treatment of the GDMs with a hydrophobic polymer coating reduces the water saturation at a breakthrough by 50%. Invasion percolation modeling is employed to simulate the breakthrough process and to determine mass-transfer rates through the partially saturated network. This model shows that the water saturation at breakthrough is drastically reduced when a microporous layer (MPL) is incorporated into the GDM, agreeing with experiments. However, the simulations yield limiting currents significantly higher than those observed in practice whether or not an MPL is present. Further calculations to include the contribution of condensation to water saturation within the GDM also result in unrealistically high limiting currents and suggest that mass-transfer resistance in the catalyst layer that is not included in the model plays an important role. If condensation is the principal mode for water accumulation within the GDM, simulations show that the MPL has only a small impact on liquid water distribution and does not improve performance, contrary to expectation.

Irreversible adsorption-driven assembly of nanoparticles at fluid interfaces revealed by a dynamic surface tension probe.

Adsorption-driven self-assembly of nanoparticles at fluid interfaces is a promising bottom-up approach for the preparation of advanced functional materials and devices. Full realization of its potential requires quantitative understanding of the parameters controlling the self-assembly, the structure of nanoparticles at the interface, the barrier properties of the assembly, and the rate of particle attachment. We argue that models of dynamic surface or interfacial tension (DST) appropriate for molecular species break down when the adsorption energy greatly exceeds the mean energy of thermal fluctuations and validate alternative models extending the application of generalized random sequential adsorption theory to nanoparticle adsorption at fluid interfaces. Using a model colloidal system of hydrophobic, charge-stabilized ethyl cellulose nanoparticles at neutral pH, we demonstrate the potential of DST measurements to reveal information on the energy of adsorption, the adsorption rate constant, and the energy of particle-interface interaction at different degrees of nanoparticle coverage of the interface. These findings have significant implications for the quantitative description of nanoparticle adsorption at fluid interfaces.