Local Porosity Variations Research Articles

Integrated internal-external thermal modeling for packed pebble beds

In this study, an integrated external-internal thermal DEM model is introduced in a GPU environment. The external model considers contact conduction and radiation, exhibiting accuracy validated against effective thermal conductivity (ETC) under packed bed conditions. The effective radiation range for a mono-sized packed bed is determined to be 3.5rp, providing accurate predictions of ETC. The internal model integrates FDM-based discretization to solve heat generation, heat conduction and thermal expansion. The model well predicts the temperature gradient of a sphere with partial heat generation. Additionally, preliminary analysis is conducted on the postulated heat generation of packed beds under a complete coolant-loss condition. The results reveal that fission-induced expansion may impact local porosity variations exceeding 2.5%. It is also observed that internally homogeneous models may overestimate heat transfer in packed beds, critical for safety. The model's accuracy and feasibility are demonstrated, providing insights for future research.

Groundwater Exploration in Carbonate Reservoirs Using Borehole Investigations: A Case Study from South Dobrogea, Romania

The Late Jurassic–Early Cretaceous (J3–K1) transboundary aquifer is the most important groundwater body in southern–southeastern Romania, shared with Bulgaria and hosted in karstic–fractured carbonates. We conducted an integrated evaluation of this aquifer by analyzing three 700 m deep groundwater exploration–exploitation boreholes, which intercepted it in the Cernavodă area (South Dobrogea region). The evaluation was based on geophysical wireline logging, drilling information, and borehole production tests. A K-means clustering of the logging data was performed for lithology typing, formation boundaries identification, and the delineation of probable producing intervals associated with secondary porosity development. Petrophysical interpretation was carried out via depth-constrained (zonal) inversion, using multimineral models, the estimated formation boundaries, and variable uncertainties for the main input logs. The optimal interpretation models were correlated with borehole testing results to gain insight into the hydrogeological properties of the aquifer complex. The fractured–vuggy interval with the highest water-producing potential was identified in the lower section of the J3-age Rasova Formation (639–700 m depth), comprising mainly undolomitized limestones. A southeast-to-northwest trend of increasing productivity of the boreholes, correlated with an increasing lateral dolomitization intensity within the Rasova Formation, suggests a highly heterogeneous character of the aquifer. The differences in productivity are due not only to local porosity variations but also to various degrees of pore space connectivity that are related to the amount of fracturing or karstification. The novel findings of this study have important practical implications for the optimal placement, design, and drilling program of future groundwater exploitation boreholes in the Cernavodă area and neighboring sectors.

Numerical investigation on the effect of porosity distribution on the flame characteristics

The low velocity filtration combustion of a lean methane/air mixture in the fixed bed reactors is numerically investigated using the system scale method. The effect of porosity on the flame characteristics, such as temperature profile, flame displacement speed and flame shape is examined in this study. For comparison, porosity is considered in two forms, i.e., volumetric average porosity (VAP) and porosity spatial distribution function (PSDF). The simulation results show that, local distribution of porosity primarily affects the flame shape, while having minimal impact on the peak flame temperature and mean flame displacement velocity. Quantitative analysis indicates that the flame displacement velocity obtained using VAP is closer to the experimental data compared to the PSDF. However, the simulation with PSDF explicitly captures the flame front bending caused by local porosity variation. Velocity and temperature fields suggests that flame front bending predominantly depends on the local flame displacement speed (LFDS), which is the vector sum of local interstitial airflow speed and the laminar flame speed of the combustible gas. The radial difference in LFDS, which is associated with uniformity in velocity and temperature fields, serves as the main driving force for flame front instability. The inclusion of PSDF enables a more accurate prediction of flame front development by capturing the preferential flow near the wall.

Effect of pressure pulse stimulation on imbibition displacement within a tight sandstone reservoir with local variations in porosity

The pressure pulse technique has been suggested as a potential method to enhance oil recovery from tight oil reservoirs. To investigate the variations in the pore structure of tight sandstone samples from the Triassic Yanchang Formation in the Ordos Basin (China), a combination of casting thin sections, high-pressure mercury intrusion, and nuclear magnetic resonance was employed. Imbibition experiments combined with the imposed pressure pulse were performed to quantitively examine the effects of the primary parameter relevant to pressure pulse on displacement efficiency and oil recovery contribution of the various pore systems. By testing the effect of different pulse pressures, it was investigated which mechanisms controlled the oil recovery. It was thus found that a series of four pulses could enhance the oil recovery significantly, and that the pressure should be 2 MPa，4 MPa and 6 MPa for the three investigated types of reservoirs, respectively. In these cases, their corresponding pulse times are 48 h, 96 h, and 144 h, respectively. The oil displacement efficiency increases with the increasing pressure and pulse cycles; however, the amplitude in oil recovery gradually diminishes. It was also found that an increasing pulse pressure is favorable for mobilizing oil that is trapped in pore spaces, especially for the low-permeability samples, despite the longer pulse time. Employing the pressure pulse method could markedly improve the imbibition oil recovery, and the simultaneous pulse pressure with imbibition leads to a higher oil recovery than the approach that adopts the pulse pressure after imbibition experiments. The main cause is that the former method facilitates oil recovery, particularly from intermediate-sized pores in relatively porous media. Furthermore, there is a significant difference in oil displacement within the various pore systems for the various types of reservoirs. The developed microfractures greatly contribute to oil recovery during the early imbibition stage, and the pressure pulse method appears most suitable to tight reservoirs with a relatively uniform pore size distribution and a higher proportion of medium-large pores.

Spatially distributed damage in sandstone under stress-freeze-thaw coupling conditions

In the present study, we tried to understand the spatially distributed damage in sandstone samples under the coupled stress-freeze-thaw (SFT) conditions. Firstly, uniaxial compressive stresses (i.e. 0 MPa, 10 MPa, 20 MPa, and 25 MPa) were applied to the samples, and then freeze-thaw (FT) cycles (0, 8, 16, and 24) were performed on the uniaxially stressed samples to realize the SFT coupling. Next, real-time CT scanning was conducted to observe the induced damage. The total porosity was introduced to quantitatively evaluate the damage degree. The local porosity variation, with the distance from the center of the sandstone sample, was analyzed to understand the spatial distribution of damage. Finally, the coupling effects of SFT on the damage gradient were discussed. The results indicate that the porosity rises with FT cycles, and the applied stresses can accelerate the increase in porosity. The damage increases exponentially with the distance from the center of the sample. The damage presents a spatial gradient distribution, not the commonly used uniform distribution in various studies. The damage gradient increases with FT cycles, and the increasing rate in damage gradient decreases at uniaxial stress of 0 MPa and 10 MPa first, but the increasing rate in damage gradient increases with FT cycles then at stress increasing to 20 MPa.

Pore and permeability properties of reservoir sandstone under a uniaxial compression CT test

For underground gas storage projects that use depleted gas reservoirs, cyclic gas injection will change the stress fields and cause rock deformation. In-depth knowledge of the stress-induced deformation of reservoir rocks is important for secure gas storage. In this study, we performed a uniaxial compression computed tomography (CT) test with a reservoir sandstone sample to investigate the influence of rock deformation on the pore and permeability properties. Based on scanned 3D images, we analyzed the axial strain evolution by using the digital volume correlation (DVC) technique and the variations in pore properties with the microstructures and permeability properties that were extracted by the pore network modeling method. The DVC analysis shows that strain localization develops gradually with increasing axial stress. The initial porosity distribution with sample height is inhomogeneous. The local porosity variations are not completely consistent with the global porosity variations under increasing axial stress. The level of inconsistency will decrease with increasing axial stress in both the volumetric compression and dilation stages. Increases in axial stress mainly induce the variations in pore numbers and pore volumes. The variations in pore connectivity are not significant. For the permeability evolution, X-ray CT scanning combined with pore network modeling can simulate the permeability decreases during volumetric compression. For high porosity sandstones (>15%), the permeability still decreases in the volumetric dilation stage due to grain size reductions and tortuosity increases. However, this technique has limitations in analyzing the permeability reductions in the volumetric dilation stage. The microcracks that are induced inside the grain particles are too small to be recognized. The variations in the relative gas and water permeabilities at different axial stresses are not significant.

How does porosity heterogeneity affect the transport properties of multibore filtration membranes?

The prediction of pressure and flow distributions inside porous membranes is important if the geometry deviates from single-bore tubular geometries. This task remains challenging, especially when considering local porosity variations caused by lumen- and shell-side membrane skins and macro- and micro-void structures, all of them present in multibore membranes.This study analyzes pure water forward and reverse permeation and backwashing phenomena for a polymeric multibore membrane with spatially-varying porosity and permeability properties using computational fluid dynamics simulations. The heterogeneity of porosity distribution is experimentally characterized by scanning electron microscopy scans and reconstructed cuboids of X-ray micro-computed tomography scans. The reconstructed cuboids are used to determine porosity, pore size distribution, and intrinsic permeability in the membrane’s porous structure in all spatial directions. These position-dependent properties are then applied to porous media flow simulations of the whole membrane domain with different properties for separation layer, support structure, and outside skin layer. Various cases mimicking the pure water permeation, fouling, and backwashing behavior of the membrane are simulated and compared to previously obtained MRI measurements.This work reveals (a) anisotropic permeability values and isoporosity in all directions and (b) differing contributions of each lumen channel to the total membrane performance, depending on the membrane-skin’s properties. This study encourages to pertain the quest of understanding the interaction of spatially distributed membrane properties and the overall membrane module performance of multibore membranes.

Numerical investigation of mixed layer effect on permeability in a dynamic blast furnace

AbstractGas flow distribution in a blast furnace (BF) plays a significant role in BF smooth operation, productivity, and thermal efficiency. It is affected by the distribution of burden materials composed of alternating coke and ferrous ore layers. While moving downward coke and ferrous layers of different sizes can mix and form the so‐called mixed layers. Generally, the porosity is lower and hence the pressure drop is higher in the mixed layers. These variations can change the gas flow distribution and BF performance. Previous work tried to quantify the effect of material properties and process conditions on the formation of mixed layers and the resulting local porosity variation. However, these studies were often conducted under simplified conditions. Few were dedicated to the formation of mixed layers in a BF and its effect on BF performance. This work studies the formation of mixed layers in an experimental BF by using a combined computational fluid dynamics and discrete element method approach. The effect on BF performance was evaluated under different operational conditions including different size ratios of coke to iron ore particles, burden distribution, batch weight, and discharge rate. The results obtained were helpful to optimize burden charge for improving BF performance.

Fluid Permeability of Graded Porosity Scaffolds Architectured with Minimal Surfaces.

The natural local porosity variation in the native tissue can be replicated by graded porosity scaffolds. Scaffolds with radial porosity distribution can be a solution to improve both mechanical and biological functions of the biomimetic scaffolds. In the present study, fluid permeability as a quantitative indicator of biological performance is studied numerically and experimentally for different pore shapes and porosity distribution patterns in the scaffolds designed on the basis of triply periodic minimal surfaces (TPMSs). Among the uniform porosity scaffolds, those designed on the basis of P* (P surface) and Y** (G surface) showed the highest permeability. In the radially graded porosity scaffolds with linear porosity distribution, permeability was found to be about twice more sensitive to the peripheral porosity than the porosity at the center. The results suggest that the permeability-gradient parameter relationships can follow different trends depending on the pore shape as opposed to the conventional uniform porosity scaffolds. This implies the need for the design maps that were developed to choose appropriate scaffold pore design parameters. Finally, experimental permeability measurement was performed via a constant head permeability test, and the effect of test parameters (i.e., fluid height) was discussed.

Investigating the influence of local porosity variations and anisotropy effects on the permeability of fibrous media for air filtration

The permeability prediction of real fibrous media remains a major challenge due to their complex porous structure. The existing models generally take two parameters into account that depict the average structural properties of fibrous media: porosity (or solid volume fraction) and fibre diameter (or radius). Due to the local variations that those parameters can exhibit the models often fail to accurately predict the permeability. In this study experimental data of three fibrous media of different porous structures employed in air filtration are used to assess numerous empirical and analytical models from the literature. It is found that all the models considered significantly under-predict the experimental permeability values. Special attention is given to the analytical Representative Unit Cell (RUC) model which is physically adaptable and can therefore be used to investigate the aforementioned discrepancies between model and experiment. Local porosity variations are investigated through a sensitivity analysis on the minimum and maximum solid volume fraction values. Incorporation of the porosity variations into the RUC model significantly reduces its under-prediction and may also serve as explanation for the discrepancies observed. An adaptation to the RUC model is proposed that takes into account the anisotropy effects as a result of the stacking of fibrous medium sheets into several layers and the increase in porosity as a result thereof. The adapted analytical model gives an indication on the factor to apply on the mean porosity in order to incorporate the anisotropy effect into the model prediction, and so reduce the observed under-predictions.

Rules for Flight Paths and Time of Flight for Flows in Porous Media with Heterogeneous Permeability and Porosity

Porous media like hydrocarbon reservoirs may be composed of a wide variety of rocks with different porosity and permeability. Our study shows in algorithms and in synthetic numerical simulations that the flow pattern of any particular porous medium, assuming constant fluid properties and standardized boundary and initial conditions, is not affected by any spatial porosity changes but will vary only according to spatial permeability changes. In contrast, the time of flight along the streamline will be affected by both the permeability and porosity, albeit in opposite directions. A theoretical framework is presented with evidence from flow visualizations. A series of strategically chosen streamline simulations, including systematic spatial variations of porosity and permeability, visualizes the respective effects on the flight path and time of flight. Two practical rules are formulated. Rule 1 states that an increase in permeability decreases the time of flight, whereas an increase in porosity increases the time of flight. Rule 2 states that the permeability uniquely controls the flight path of fluid flow in porous media; local porosity variations do not affect the streamline path. The two rules are essential for understanding fluid transport mechanisms, and their rigorous validation therefore is merited.

Water loss and crust formation during bread baking, Part I: Interpretation aided by mathematical models with highlights on the role of local porosity

ABSTRACTThis study aimed to achieve greater understanding of the contributions of different mechanisms of water transport to the overall amount of water lost by bread loaves during baking. The analysis was based on simulations from a previously published baking model which takes into account heat and mass transport as well as the expansion of the gaseous phase leading to oven rise. Liquid and gaseous diffusion, convective transport through the gaseous phase (Darcy’s law), and the diffusive transport of vapor (evaporation–condensation–diffusion) were considered. When only permeation (Darcy’s law) prevailed, the greater the porosity of the top dough surface, the lower and slower the water loss (WL): in fact, the greater the porosity, the thicker the top area. This in turn limited the rate at which heat penetrated the top layers down to the vaporization front and slowed WL. At earlier baking times, when the ebullition temperature was not reached uniformly through the crumb, the evaporation–condensation–diffusion was involved at the same time as permeation. The water flux by evaporation–condensation–diffusion was orientated toward the dough core; it accelerated the crust thickening and slowed WL. It appeared that the higher the porosity in the crumb beneath the crust, the higher the flux by evaporation–condensation–diffusion, and the lower the WL. Local porosity variations in the crust (top surface) and the crumb beneath the crust could be reproduced experimentally by constraining the total expansion of the loaf with a permeable fabric cover. Experimental and simulated trends in WL were consistent, supporting the understanding of WL proposed.

Rules for Flight Paths and Time of Flight for Flows in Porous Media with Heterogeneous Permeability and Porosity

Porous media like hydrocarbon reservoirs may be composed of a wide variety of rocks with different porosity and permeability. Our study shows in algorithms and in synthetic numerical simulations that the flow pattern of any particular porous medium, assuming constant fluid properties and standardized boundary and initial conditions, is not affected by any spatial porosity changes but will vary only according to spatial permeability changes. In contrast, the time of flight along the streamline will be affected by both the permeability and porosity, albeit in opposite directions. A theoretical framework is presented with evidence from flow visualizations. A series of strategically chosen streamline simulations, including systematic spatial variations of porosity and permeability, visualizes the respective effects on the flight path and time of flight. Two practical rules are formulated. Rule 1 states that an increase in permeability decreases the time of flight, whereas an increase in porosity increases the time of flight. Rule 2 states that the permeability uniquely controls the flight path of fluid flow in porous media; local porosity variations do not affect the streamline path. The two rules are essential for understanding fluid transport mechanisms, and their rigorous validation therefore is merited.

Halfdan 4D workflow and results leading to increased recovery

In 2012, a repeat time-lapse seismic survey was acquired over the Halfdan oil field located in the Danish North Sea. The main oil reservoir is the Cretaceous chalk Tor Formation, and the field is developed with a line-drive water flood. The reservoir saturation changes due to water injection and gas breakout lead to large changes in acoustic impedance, which can be imaged with 4D seismic. The 4D acoustic-impedance changes, in conjunction with production and geologic data, were analyzed on a well-by-well basis and resulted in several interesting correlations between the geology and the 4D response. The 4D was used to update the seismic interpretation of some important layers within the static and dynamic model. In some areas, the impact of local porosity variations on the lateral sweep could be seen. The 4D also provided evidence that some faults serve as potential pathways for formation-water entry into the oil-producing layers. In addition, numerous well-intervention opportunities were identified through integrating the 4D with the production, geologic, and dynamic data. Examples from the two-vintage and three-vintage 4D acoustic-impedance data illustrating these key 3D and 4D learnings and a successful well intervention are shown.

Statistical Analysis of Li-Oxygen Batteries

The reported values of the specific capacity and energy and power densities of Li-oxygen batteries vary from battery to battery even when the they are fabricated using the same technological processes and when much care is given to produce identical cells. In addition, the practical discharge curves of Li-air batteries are significantly different from one battery to another even when these curves are measured under the same discharge conditions. In this presentation, we introduce a mathematical model to analyze the statistical variability of the discharge characteristics in Li-air batteries with organic and aqueous electrolyte. In this model, the variability of the discharge curves is due to microscopic variations of the cathode structure that result in random local values of the porosity, specific area, and reaction rates. It is shown that microscopic variations of the cathode microstructure from one location to another inside the same battery as welll as from one battery to another result in large variations of the discharge characteristics. These variations can explain in part the large variability of the discharge curves reported in the literature for Li-air/oxygen batteries. The basic idea of our mathematical model is to write the transport model equations into the form of a system of stochastic partial differential equations, and to solve this system using Monte-Carlo techniques. In the case of Li-oxygen batteries, the transport model equations can be written as a system of five partial differential equations that include the migration and diffusion of the electrolyte, oxygen diffusion, local porosity variation, and electron conductivity equation (1, 2). These equations are discretized on a finite element grid and a solved self-consistently to compute the discharge voltage as a function of the specific capacity. Due to the stochastic nature of the transport system, the solution of the transport equations will also be stochastic and will vary from battery to battery. In order to perform a comprehensive statistical analysis of the discharge curves in Li-oxygen batteries, we generate a large number of the batteries with identical macroscopic characteristics (i.e. identical geometrical dimensions, average porosity, and specific area) but with different microscopic structures and simulate each battery independently. In this way we accumulate statistics for the parameters of interest – in our case for the discharge curves, the specific capacity, and the energy density – and compute the average values and standard deviations of these parameters. We observe that the standard deviation of the specific capacity decreases with increasing the d.c. discharge current, however, the relative variability, defined as the standard deviation of the specific capacity divided by the mean value of the specific capacity, increases dramatically. Finally, we investigate the sensitivity of the discharge characteristics to variations of the structural properties of the battery by performing a sensitivity analysis of the discharge voltage as a function of the local values of the porosity and reaction kinetic constant. We observe that initial local variations of the porosity at the air side increase the variability of the discharge voltage curves more than variations of the porosity at the separator side. Unlike variations of the porosity, variations of the reaction kinetic constant do not influence the discharge characteristics significantly. More details about the numerical implementation of our method as well as simulation results for the variability of the discharge characteristics, specific capacity, and energy density will be presented at the conference. 1. P. Andrei, J. P. Zheng, M. Hendrickson and E. J. Plichta, “Some Possible Approaches for Improving the Energy Density of Li-Air Batteries”, Journal of the Electrochemical Society, 157, A1287 (2010). 2. M. Mehta and P. Andrei, “Variability Analysis of Discharge Characteristics and Impedance Spectra in Li-Air Batteries”, 228 ECS Meeting, Phoenix, AZ, 2015.

Determination of porosity variations in powder beds.

A gamma-ray attenuation technique for detecting local porosity variations in packings of pharmaceutical powders has been developed and assessed. It proved necessary to employ an empirical expression describing the attenuation coefficient of the model material, lactose, as a function of porosity. The precision of measurement of local porosity can be pre-selected due to the statistical basis of the method, and local porosity measurements with 95% confidence intervals of +/- 0.005 can readily be carried out. A method of producing grey-scale images of porosity distributions has been employed to enable the degree of inhomogeneity of a powder bed to be seen.

Measurement of Porosity in Granular Particle Distributions Using Adaptive Thresholding

It has been shown that the flow and shear characteristics of granular particles such as soils are significantly dependent on the shape of the particles. This is important from a practical viewpoint because a fundamental understanding of granular behavior will lead to an improved understanding of soil stability and influence the design of structural foundations. Furthermore, the calculation of soil stability and, consequently, structural stability is particularly useful during earthquake events. In previous work, we have demonstrated the applicability of X-ray and optical tomography measurements for characterizing 3-D shapes of natural sands and manufactured granular particles. In this paper, we extend the work to measure the arrangement and the orientation of an assemblage of such particles. A combination of X-ray computed tomography (CT) for measuring the coordinates of the individual particles and an iterative adaptive thresholding technique for computing the local variations in porosity is employed to generate porosity maps. Such maps can be used to gain a more fundamental understanding of the shear characteristics of granular particles. In this paper, we demonstrate the success of our technique by exercising the method on several sets of granular particles-glass beads (used as a control), natural Michigan Dune and Daytona Beach sand, and processed Dry #1 sand.

Combined kinetic and X-ray electron probe microanalysis characterization of local porosity variation and pore shape across anodic alumina films

Porous anodic alumina films on Al were prepared by anodic oxidation of Al in H 2SO 4 electrolyte at a constant temperature and current density and different thicknesses, up to ≈ 41 μm. Their cross section was examined by EPMA for revealing the variation of local porosity across the films and shape of pores while a kinetic model for film growth was developed describing the variation of pore diameter. It was found that the pores open, and local porosity increases, towards the film surface, predicting a conical pore shape, while the results coincided with those obtained by kinetic study. The EPMA analysis combined with kinetic results emerges as a promising tool for studying structural features of these films.

Porosity and permeability of the Tiwi geothermal field, Philippines, based on continuous and spot core measurements

Petrologic analyses of corehole Mat-25 provide a detailed look at the influence of lithology, depth of burial, temperature and hydrothermal fluid chemistry on matrix porosity and permeability in a geothermal system. Average porosity values decline from about 10% at the top of the reservoir to 2.5% at the bottom. A similar trend of declining porosity with depth is observed in spot cores from other wells. The trend of declining porosity with depth is ascribed mainly to increasing overburden stresses and chemical reaction with hydrothermal fluids. Local variations in porosity are a complex function of sample-to-sample variations in the original texture, phenocryst abundance, and amount of glass in the primary rocks, and their exposure to tectonic and hydrothermal processes. Matrix permeability mimics porosity, but is very low within the reservoir section (<10 microdarcy), and even lower above and below the reservoir (<1 microdarcy) in Mat-25. Image analysis indicates that pores >1 μm form mainly by dissolution and partial replacement of plagioclase phenocrysts in the andesitic reservoir rocks, with calcic plagioclase being most susceptible. This relationship between hydrothermal alteration and pore formation may link these larger pores to fracture permeability. The size of the pores can be enhanced by further dissolution of the plagioclase and other minerals or sealed by illite, which is supersaturated in the present-day reservoir fluid.

Statistical characterization and stochastic modeling of pore networks in relation to fluid flow

Flow properties of reservoir rocks can be computed from an accurate depiction of the porosity network in three dimensions available from synchrotron Xray microtomography. In order to relate computed transport properties to the input dataset, the complex pore networks must be described statistically. A porous media description was deemed adequate if a synthetic medium, possessing similar transport properties, could be generated from acquired statistical information. Synthetic media, based upon Berea sandstone extended variogram statistics, were generated with an actual slice from a 3-D microtomographic image as conditioning data. Control of local porosity variation was observed to be important in the stochastic simulation of porous media by the simulated annealing method, as inclusion of this higher order constraint data reproduced natural variations observed in pore-size distributions. Realizations with the traditional variogram as the only target in the objective function did not honor poresize distribution information. Permeability estimates by the lattice Boltzmann method indicated that the proper level of interConnectivity was not achieved during geostatistical modeling with only two point spatial statistics. Connectedness information, readily available from primary drainage capillary pressure data, forced permeability estimates of synthetic media in the direction of the permeability computed for the parent microtomographic image of Berea sandstone. As a result of this study, it was concluded that global spatial correlation statistics, for example, the traditional variogram, must be supplemented with local variability and connectivity information to adequately characterize a three-dimensional property distribution for fluid transport. Extended porosity spatial correlation structure, extracted from standard imaging techniques, and a capillary pressure drainage curve are perhaps sufficient to characterize a system in terms of pore size, connectedness, and permeability. However, more rapid algorithms are needed to introduce porosimetry information as standard practice in stochastic modeling by the simulated annealing method.