Accounting for Fluid Rheology in the Hydrophobization Model of Relative Permeability Hysteresis

A complex mathematical model of relative permeability hysteresis is developed based on percolation theory. The model takes into account the change in the surface properties of the pore space and the rheology of percolating fluids during the transition from drainage to imbibition, which gives rise to hysteresis. It is shown that accounting for the change in the rheology of percolation fluids, along with accounting for the hydrophobization of the surface of the pore space, provides a better agreement between the calculated and experimental curves of relative permeabilities.     

Numerical Simulation of Diagenetic Alteration and Its Effect on Residual Gas in Tight Gas Sandstones

In this study, we numerically cemented a segmented X-ray microtomography image of a sandstone to understand changes to pore space connectivity, capillary control on gas, and water distributions, and ultimately production behavior in tight gas sandstone reservoirs. Level set method-based progressive quasi-static algorithm (a state-of-the-art direct simulation of capillarity-dominated fluid displacement) was used to find the gas/water configurations during drainage and imbibition cycles. Further, we account for gas?Cwater interfacial tension changes using 1D burial history model based on available geologic data. We have found the displacement simulation method robust, and that diagenetic changes impart a significantly larger effect on gas trapping compared with interfacial tension changes.     

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 Archie's 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.     

Pore Space Microstructure Evolution of Regular Sphere Packings Undergoing Compaction and Cementation

We examine the pore space structure evolution of ordered uniform sphere packs: simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC), undergoing simple diagenetic processes that reduce their pore spaces. Focus is on the occurrence of pore space microstructure changes or transitions, which are followed through their characteristic or critical pore lengths (l _c). For almost all the cubic packings undergoing either compaction or cementation there are no singularities in l _c. This is a consequence of having a single pore shape controlling flow at all stages of the process. However, this is not so for the BCC packing under cementation, for which l _c is non-monotonic exhibiting a kink at ${\phi \approx 0.1452}$ , the porosity at which the pore shape controlling flow switches to a different form and position. These results for uniform compaction/cementation complement our previous works on pore networks under random shrinkage. Kinks in l _c as porosity decreases signal pore space microstructure transitions that anticipate sudden changes in the permeability?Cporosity relation as porosity decreases. The consequences are great; clearly l _c is not a constant unless the diagenetic process is mild. A l _c function of compaction/cementation advancement should be used above a transition and a different l _c function below. For the sphere packs here, once the diagenetic process has reduced the pore space substantially, a l _c function of compaction/cementation advancement is mandatory if we are to capture all significant flow features.     

An Ising-Based Simulator for Capillary Action in Porous Media

Multiphase flows in porous media are encountered in several contexts—e.g., hydrocarbon recovery operations, battery electrodes, microfluidic devices, etc. Capillary-dominated flows are interesting due to the complex interplay of interfacial properties and pore geometries. Conventional hydrodynamic flow solvers are computationally inefficient in the capillary-dominated regime, particularly in complex pore structures. The algorithm developed here specifically targets this regime to reduce simulation times. We minimise the fluid–fluid and fluid–solid interaction energies through an approach inspired by the ferromagnetic Ising model. We validate the algorithm on (1) model pore geometries with analytical solutions for capillary action, and (2) rocks with available mercury porosimetry data. We validate its predictions for model geometries and sandstones using (1) curvatures calculated from theories developed by Mayer–Stowe–Princen, Ma and Morrow, and Mason and Morrow; (2) predictions from GeoDict, a commercial software package, which also includes a state-of-the-art drainage simulator; (3) mercury porosimetry data. Drainage capillary pressure curves predicted for Bentheimer and Fontainebleau rocks reasonably match porosimetry data.     

Implications of Grain-Scale Mineralogical Heterogeneity for Radionuclide Transport in Fractured Media

The geological disposal of nuclear waste is based on the multi-barrier concept, comprising various engineered and natural barriers, to confine the radioactive waste and isolate it from the biosphere. Some of the planned repositories for high-level nuclear waste will be hosted in fractured crystalline rock formations. The potential of these formations to act as natural transport barriers is related to two coupled processes: diffusion into the rock matrix and sorption onto the mineral surfaces available in the rock matrix. Different in situ and laboratory experiments have pointed out the ubiquitous heterogeneous nature of the rock matrix: mineral surfaces and pore space are distributed in complex microstructures and their distribution is far from being homogeneous (as typically assumed by Darcy-scale coarse reactive transport models). In this work, we use a synthetically generated fracture–matrix system to assess the implications of grain-scale physical and mineralogical heterogeneity on cesium transport and retention. The resulting grain-scale reactive transport model is solved using high-performance computing technologies, and the results are compared with those derived from two alternative models, denoted as upscaled models, where mineral abundance is averaged over the matrix volume. In the grain-scale model, the penetration of cesium into the matrix is faster and the penetration front is uneven and finger-shaped. The analysis of the cesium breakthrough curves computed at two different points in the fracture shows that the upscaled models provide later first-arrival time estimates compared to the grain-scale model. The breakthrough curves computed with the three models converge at late times. These results suggest that spatially averaged upscaled parameters of sorption site distribution can be used to predict the late-time behavior of breakthrough curves but could be inadequate to simulate the early behavior.     

Pore Network Analysis of Resistivity Index for Water-Wet Porous Media

Pore network analysis is used to investigate the effects of microscopic parameters of the pore structure such as pore geometry, pore-size distribution, pore space topology and fractal roughness porosity on resistivity index curves of strongly water-wet porous media. The pore structure is represented by a three-dimensional network of lamellar capillary tubes with fractal roughness features along their pore-walls. Oil-water drainage (conventional porous plate method) is simulated with a bond percolation-and-fractal roughness model without trapping of wetting fluid. The resistivity index, saturation exponent and capillary pressure are expressed as approximate functions of the pore network parameters by adopting some simplifying assumptions and using effective medium approximation, universal scaling laws of percolation theory and fractal geometry. Some new phenomenological models of resistivity index curves of porous media are derived. Finally, the eventual changes of resistivity index caused by the permanent entrapment of wetting fluid in the pore network are also studied.Resistivity index and saturation exponent are decreasing functions of the degree of correlation between pore volume and pore size as well as the width of the pore size distribution, whereas they are independent on the mean pore size. At low water saturations, the saturation exponent decreases or increases for pore systems of low or high fractal roughness porosity respectively, and obtains finite values only when the wetting fluid is not trapped in the pore network. The dependence of saturation exponent on water saturation weakens for strong correlation between pore volume and pore size, high network connectivity, medium pore-wall roughness porosity and medium width of the pore size distribution. The resistivity index can be described succesfully by generalized 3-parameter power functions of water saturation where the parameter values are related closely with the geometrical, topological and fractal properties of the pore structure.     

Mechanical study of the effect of fractional-wettability on multiphase fluid flow

Fractional wettability has been widely recognized in most of the oil reservoirs and it is a crucial factor that controls the fluid flow behavior in porous medium. The overall effect of the proportion of oil-wet grains on the fluid flow properties has been well discussed. However, recent studies found that the random distribution and coordination of oil-wet and water-wet grains could make multi-phase flow behaviors extremely complicated in such media. The multiphase flow mechanisms in fractional wettability media remains unclear. In this study, oil imbibition experiments were systematically conducted using glass cylinders packed with fractional-wet glass beads. To study the effect of fractional wettability on multiple-phase flow properties, samples with different oil-wet grain proportions were prepared, and fifteen repeated experiments were conducted for each oil-wet proportion. The experimental results showed that oil imbibition was largely dependent on but not strictly a function of the proportion of oil-wet grains in the medium. The imbibition behaviors of samples with the same fractional proportion could vary significantly, as some samples exhibited complete oil migration, while others did not. This probabilistic phenomenon is likely due to the random distribution of oil-wet and water-wet grains. A pore throat may behave as oil-wet or water-wet depending on the relative proportion of oil-wet grains the pore throat contains. When the grains that comprise the pore throat are dominated by oil-wet grains, the throat behaves as oil-wet, and vice versa. Only when these oil-wet pore throats are connected to form a complete oil-wet pathway throughout the medium can the oil continuously imbibe into the medium. Therefore, the extent of oil imbibition depends on the completeness of the oil-wet pathway, which is controlled by the proportion of oil-wet grains in the medium. The higher the proportion of oil-wet grains in the medium, the larger the number of oil-wet pore throats that can form; thus, the higher the possibility that those oil-wet pore throats can connect to form continuous oil-wet pathways.     

Percolation theory approach to transport phenomena in porous media

The percolation theory approach to static and dynamic properties of the single- and two-phase fluid flow in porous media is described. Using percolation cluster scaling laws, one can obtain functional relations between the saturation fraction of a given phase and the capillary pressure, the relative permeability, and the dispersion coefficient, in drainage and imbibition processes. In addition, the scale dependency of the transport coefficient is shown to be an outcome of the fractal nature of pore space and of the random flow pattern of the fluids or contaminant.     

Dynamics of Viscous Entrapped Saturated Zones in Partially Wetted Porous Media

As a typical multiphase fluid flow process, drainage in porous media is of fundamental interest both in nature and in industrial applications. During drainage processes in unsaturated soils and porous media in general, saturated regions, or clusters, in which a liquid phase fully occupies the pore space between solid grains, affect the relative permeability and effective stress of the system. Here, we experimentally study drainage processes in unsaturated granular media as a model porous system. The distribution of saturated clusters is analysed by optical imaging under different drainage conditions, with pore-scale information from Voronoi and Delaunay tessellation used to characterise the topology of saturated cluster distributions. By employing statistical analyses, we describe the observed spatial and temporal evolution of multiphase flow and fluid entrapment in granular media. Results indicate that the distributions of both the crystallised cell size and pore size are positively correlated to the spatial and temporal distribution of saturated cluster sizes. The saturated cluster size is found to follow a lognormal distribution, in which the generalised Bond number (\( Bo^{*} \)) correlates negatively to the scale parameter (μ) and positively to the shape parameter (σ). With further consideration of the total surface energy obtained based on liquid–air interfaces, we were able to include additional grain-scale information in the constitutive modelling of unsaturated soils using both the degree of saturation and generalised Bond number. These findings can be used to connect pore-scale behaviour with overall hydro-mechanical characteristics in granular systems.     

Decomposing <Emphasis Type="Italic">J</Emphasis>-function to Account for the Pore Structure Effect in Tight Gas Sandstones

The J-function predicts the capillary pressure of a formation by accounting for its transport properties such as permeability and porosity. The dependency of this dimensionless function on the pore structure is usually neglected because it is difficult to implement such dependency, and also because most clastic formations contain mainly one type of pore structure. In this paper, we decompose the J-function to account for the presence of two pore structures in tight gas sandstones that are interpreted from capillary pressure measurements. We determine the effective porosity, permeability, and wetting phase saturation of each pore structure for this purpose. The throats, and not the pores, are the most important parameter for this determination. We have tested our approach for three tight gas sandstones formations. Our study reveals that decomposing the J-function allows us to capture drainage data more accurately, so that there is a minimum scatter in the scaled results, unlike the traditional approach. This study can have major implications for understanding the transport properties of a formation in which different pore structures are interconnected.     

Pore-throat size correlation from capillary pressure curves

Void spaces in porous media can be considered as three-dimensional networks consisting of bulges (pores) connected by constrictions (throats). Computer simulations of drainage-imbibition processes show that the critical end points of wetting-phase and nonwetting-phase saturation, in drainage and imbibition respectively, and the form of simulated relative permeability curves all were significantly different for uncorrelated and correlated pore-throat models. Since these models were identical except for the arrangement of throats in relation to pores, the degree of pore-throat size correlation appears to be an important property influencing flow and fluid displacement. Examples of uncorrelated and correlated pore-throat structures in rocks are presented and it is shown that this property, although difficult to quantify by direct observation, can be evaluated from capillary pressure curves.     

On the Potential of Tomographic Methods when Applied to Compacted Crushed Rock Salt

Compacted crushed rock salt is considered as potential backfill material in repositories for nuclear waste. To evaluate the sealing properties of this material knowledge concerning the nature of the pore space is of eminent interest. Here, the pore microstructures of crushed rock salt samples with different compaction states were investigated by X-ray (XCT) computed tomography and Focused Ion Beam nanotomography (FIB-nt). Based on these methods the pore microstructures were reconstructed and quantitatively analyzed with respect to porosity, connectivity and percolation properties. Regarding pores with radii \(> 4\,\upmu \hbox {m}\) , porosity differs substantially in the two analyzed samples ( \(\phi = 0.01\) and 0.10). The pore microstructures are considered isotropic in connectivity and percolation threshold. Using two finite-scaling schemes we found percolation thresholds with critical porosities \(\phi _{c} > 0.05\) . Based on statistical considerations, the millimeter size samples that can be analyzed by XCT are large enough to provide a meaningful picture of the pore geometry related to macroporosity. The samples contain also a small fraction (i.e. \(< 0.01\) ) of pores with radii \(< 1\,\upmu \hbox {m}\) , which were resolved by FIB-nt. Often these pores can be found along grain boundaries. These pores are granular shaped and are not connected to each other. Typical samples size that can be analyzed by FIB-nt is on the order of tens of microns, which turned out to be too small to provide representative geometric information unless an effort is made that involves several FIB-nt realizations per sample.     

Characterization of Single-Phase Flow Through Carbonate Rocks: Quantitative Comparison of NMR Flow Propagator Measurements with a Realistic Pore Network Model

We report here the quantitative comparisons between the measured NMR flow propagator of a carbonate rock and the flow propagator calculated with a porous network extracted from the micro-CT image of the twin plug. We developed a numerical model based on a particle tracking algorithm in pore space. The particle tracking in throats is described using the first arrival time distribution. As pores have an important volume fraction in the sample considered, we implemented a time-delay mechanism for particle transport in the pores. We consider that the nodes have volume and there is a transport of the tracking particles inside the nodes, which leads to an “apparent” time-delay. Simulations of flow propagator show good agreement with low field NMR experiments performed on the twin plug of the sample used for pore network extraction with a single adjustable parameter (that describes the dynamics in the pores). These results lead us to a better understanding of the connection between pore structure and the behavior of NMR flow propagator in fluid-saturated rocks and are essential in interpreting the experimental data and correlating NMR parameters to petrophysical properties.     

Pore Network Modelling of Electrical Resistivity and Capillary Pressure Characteristics

In order to model petrophysical properties of hydrocarbon reservoir rocks, the underlying physics occurring in realistic rock pore structures must be captured. Experimental evidence showing variations of wetting occurring within a pore, and existence of the so-called 'non-Archie' behaviour, has led to numerical models using pore shapes with crevices (for example, square, elliptic, star-like shapes, etc.). This paper presents theoretical derivations and simulation results of a new pore space network model for the prediction of petrophysical properties of reservoir rocks. The effects of key pore geometrical factors such as pore shape, pore size distribution and pore co-ordination number (pore connectivity) have been incorporated into the theoretical model. In particular, the model is used to investigate the effects of wettability and saturation history on electrical resistivity and capillary pressure characteristics. The petrophysical characteristics were simulated for reservoir rock samples. The use of the more realistic grain boundary pore (GBP) shape allows simulation of the generic behaviour of sandstone rocks, with various wetting scenarios. The predictions are in close agreement with electrical resistivity and capillary pressure characteristics observed in experiments.     

Estimation of Shale Intrinsic Permeability with Process-Based Pore Network Modeling Approach

A multi-scale pore network model is developed for shale with the process-based method (PBM). The pore network comprises three types of sub-networks: the \(\upmu \)m-scale sub-network, the nm-scale pore sub-network in organic matter (OM) particles and the nm-scale pore sub-network in clay aggregates. Process-based simulations mimic shale-forming geological processes and generate a \(\upmu \)m-scale sub-network which connects interparticle pores, OM particles and clay aggregates. The nm-scale pore sub-networks in OM and clay are extracted from monodisperse sphere packing. Nm-scale throats in OM and clay are simplified to be cylindrical and cuboid-shaped, respectively. The nm-scale pore sub-networks are inserted into selected OM particles and clay aggregates in the \(\upmu \)m-scale sub-network to form an integrated multi-scale pore network. No-slip permeability is evaluated on multi-scale pore networks. Permeability calculations verify that shales permeability keeps decreasing when nm-scale pores and throats replace \(\upmu \)m-scale pores. Soft shales may have higher porosity but similar range of permeability with hard shales. Small compaction leads to higher permeability when nm-scale pores dominate a pore network. Nm-scale pore networks with higher interconnectivity contribute to higher permeability. Under constant shale porosity, the shale matrix with cuboid-shaped nm-scale throats has lower no-slip permeability than that with cylindrical throats. Different from previous reconstruction processes, the new reconstruction process first considers the porous OM and clay distribution with PBM. The influence of geological processes on the multi-scale pore networks is also first analyzed for shale. Moreover, this study considers the effect of OM porosities and different pore morphologies in OM and clay on shale permeability.     

Effect of Organosilicon-Acrylic Emulsion Treatment on Wettability of Porous Media

To investigate the influence of the organosilicon-acrylic on wetting properties of porous media, contact angle tests were performed on two different sandstones. In addition, the effectiveness of the emulsion on wettability alteration of porous media was validated by capillary rise and spontaneous imbibition tests. The results of wettability tests showed that the wettability of two sandstones was altered from water-wet to gas-wet after treatment with the emulsion. The principle that the critical radius of pore throats and wettability of porous media affect liquids flow was derived analytically and verified experimentally. Coreflood results demonstrated that the latex resulted in increasing the water permeability through altering the rock wettability to gas-wetting, then decreasing the friction drag between liquids and rocks surface. Thereby, the emulsion treatment could increase the flowback rate of trapped liquids. Experimental results were in good agreement with the theoretical analysis. In conclusion, all results indicated that the emulsion could alter the wettability from water-wet to intermediate gas-wet and enhance water permeability in porous media. It was extrapolated that the emulsion had the tremendous potential to be applied in field conditions, enhancing gas productivity through the cleanup of trapped water in the vicinity of the wellbore.     

Micromechanical model for cohesive materials based upon pseudo-granular structure

A micromechanical model for cohesive materials is derived by considering their underlying microstructure conceptualized as a collection of grains interacting through pseudo-bonds. The pseudo-bond or the inter-granular force–displacement relations are formulated taking inspiration from the atomistic-level particle interactions. These force–displacement relationships are then used to derive the incremental stiffnesses at the grain-scale, and consequently, obtain the sample-scale stress–strain relationship of a representative volume of the material. The derived relationship is utilized to study the stress–strain and failure behavior including the volume change and “brittle” to “ductile” transition behavior of cohesive materials under multi-axial loading condition. The model calculations are compared with available measured data for model validation. Model predictions exhibit both quantitative and qualitative consistency with the observed behavior of cohesive material.