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  • Journal article
    Debbabi Y, Jackson MD, Hampson GJ, Salinas Pet al., 2017,

    Capillary Heterogeneity Trapping and Crossflow in Layered Porous Media

    , Transport in Porous Media, Vol: 120, Pages: 183-206, ISSN: 0169-3913

    We examine the effect of capillary and viscous forces on the displacement of one fluid by a second, immiscible fluid across and along parallel layers of contrasting porosity, and relative permeability, as well as previously explored contrasts in absolute permeability and capillary pressure. We consider displacements with wetting, intermediate-wetting and non-wetting injected phases. Flow is characterized using six independent dimensionless numbers and a dimensionless storage efficiency, which is numerically equivalent to the recovery efficiency. Results are directly applicable to geologic carbon storage and hydrocarbon production. We predict how the capillary–viscous force balance influences storage efficiency as a function of a small number of key dimensionless parameters, and provide a framework to support mechanistic interpretations of complex field or experimental data, and numerical model predictions, through the use of simple dimensionless models. When flow is directed across layers, we find that capillary heterogeneity traps the non-wetting phase, regardless of whether it is the injected or displaced phase. However, minimal trapping occurs when the injected phase is intermediate-wetting or when high-permeability layers contain a smaller moveable volume of fluid than low-permeability layers. A dimensionless capillary-to-viscous number defined using the layer thickness rather than the more commonly used system length is most relevant to predict capillary heterogeneity trapping. When flow is directed along layers, we show that, regardless of wettability, increasing capillary crossflow reduces the distance between the leading edges of the injected phase in each layer and increases storage efficiency. This may be counter-intuitive when the injected phase is non-wetting. Crossflow has a significant impact on storage efficiency only when high-permeability layers contain a smaller moveable volume of fluid than low-permeability layers. In that case, capillary he

  • Journal article
    Zhang J, Vinogradov J, Leinov E, Jackson MDet al., 2017,

    Streaming potential during drainage and imbibition

    , JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH, Vol: 122, Pages: 4413-4435, ISSN: 2169-9313
  • Journal article
    Salinas P, Pavlidis D, Xie Z, Jacquemyn C, Melnikova Y, Jackson MD, Pain CCet al., 2017,

    Improving the robustness of the control volume finite element method with application to multiphase porous media flow

    , International Journal for Numerical Methods in Fluids, Vol: 85, Pages: 235-246, ISSN: 1097-0363

    Control volume finite element methods (CVFEMs) have been proposed to simulate flow in heterogeneous porous media because they are better able to capture complex geometries using unstructured meshes. However, producing good quality meshes in such models is nontrivial and may sometimes be impossible, especially when all or parts of the domains have very large aspect ratio. A novel CVFEM is proposed here that uses a control volume representation for pressure and yields significant improvements in the quality of the pressure matrix. The method is initially evaluated and then applied to a series of test cases using unstructured (triangular/tetrahedral) meshes, and numerical results are in good agreement with semianalytically obtained solutions. The convergence of the pressure matrix is then studied using complex, heterogeneous example problems. The results demonstrate that the new formulation yields a pressure matrix than can be solved efficiently even on highly distorted, tetrahedral meshes in models of heterogeneous porous media with large permeability contrasts. The new approach allows effective application of CVFEM in such models.

  • Journal article
    Debbabi Y, Jackson MD, Hampson GJ, Fitch PJR, Salinas Pet al., 2017,

    Viscous crossflow in layered porous media

    , Transport in Porous Media, Vol: 117, Pages: 281-309, ISSN: 1573-1634

    We examine the effect of viscous forces on the displacement of one fluid by a second, immiscible fluid along parallel layers of contrasting porosity, absolute permeability and relative permeability. Flow is characterized using five dimensionless numbers and the dimensionless storage efficiency, so results are directly applicable, regardless of scale, to geologic carbon storage. The storage efficiency is numerically equivalent to the recovery efficiency, applicable to hydrocarbon production. We quantify the shock-front velocities at the leading edge of the displacing phase using asymptotic flow solutions obtained in the limits of no crossflow and equilibrium crossflow. The shock-front velocities can be used to identify a fast layer and a slow layer, although in some cases the shock-front velocities are identical even though the layers have contrasting properties. Three crossflow regimes are identified and defined with respect to the fast and slow shock-front mobility ratios, using both theoretical predictions and confirmation from numerical flow simulations. Previous studies have identified only two crossflow regimes. Contrasts in porosity and relative permeability exert a significant influence on contrasts in the shock-front velocities and on storage efficiency, in addition to previously examined contrasts in absolute permeability. Previous studies concluded that the maximum storage efficiency is obtained for unit permeability ratio; this is true only if there are no contrasts in porosity and relative permeability. The impact of crossflow on storage efficiency depends on the mobility ratio evaluated across the fast shock-front and on the time at which the efficiency is measured.

  • Journal article
    Maes J, Muggeridge AH, Jackson MD, Quintard M, Lapene Aet al., 2017,

    Scaling analysis of the In-Situ Upgrading of heavy oil and oil shale

    , FUEL, Vol: 195, Pages: 299-313, ISSN: 0016-2361

    The In-Situ Upgrading (ISU) of heavy oil and oil shale is investigated. We develop a mathematical model for the process and identify the full set of dimensionless numbers describing the model. We demonstrate that for a model with nf fluid components (gas and oil), ns solid components and k chemical reactions, the model was represented by 9+k×(3+nf+ns-2)+8nf+2ns dimensionless numbers. We calculated a range of values for each dimensionless numbers from a literature study. Then, we perform a sensitivity analysis using Design of Experiments (DOE) and Response Surface Methodology (RSM) to identify the primary parameters controlling the production time and energy efficiency of the process. The Damköhler numbers, quantifying the ratio of chemical reaction rate to heat conduction rate for each reaction, are found to be the most important parameters of the study. They depend mostly on the activation energy of the reactions and of the heaters temperature. The reduced reaction enthalpies are also important parameters and should be evaluated accurately. We show that for the two test cases considered in this paper, the Damköhler numbers needed to be at least 10 for the process to be efficient. We demonstrate the existence of an optimal heater temperature for the process and obtain a correlation that can be used to estimate it using the minimum of the Damköhler numbers of all reactions.

  • Journal article
    Al Mahrouqi D, Vinogradov J, Jackson MD, 2016,

    Zeta potential of artificial and natural calcite in aqueous solution

    , Advances in Colloid and Interface Science, Vol: 240, Pages: 60-76, ISSN: 0001-8686

    Despite the broad range of interest and applications, controls on calcite surface charge in aqueous solution, especiallyat conditions relevant to natural systems, remain poorly understood. The primary data source to understandcalcite surface charge comprises measurements of zeta potential. Here we collate and review previousmeasurements of zeta potential on natural and artificial calcite and carbonate as a resource for future studies,compare and contrast the results of these studies to determine key controls on zeta potential and where uncertaintiesremain, and report new measurements of zeta potential relevant to natural subsurface systems.The results show that the potential determining ions (PDIs) for the carbonate mineral surface are the lattice ionsCa2+, Mg2+ and CO32−. The zeta potential is controlled by the concentration-dependent adsorption of these ionswithin the Stern layer, primarily at the Outer Helmholtz Plane (OHP). Given this, the Iso-Electric Point (IEP) atwhich the zeta potential is zero should be expressed as pCa (or pMg). It should not be reported as pH, similarto most metal oxides.The pH does not directly control the zeta potential. Varying the pH whilst holding pCa constant yields constantzeta potential. The pH affects the zeta potential only by moderating the equilibrium pCa for a given CO2 partialpressure (pCO2). Experimental studies that appear to yield a systematic relationship between pH and zeta potentialare most likely observing the relationship between pCa and zeta potential, with pCa responding to the changein pH. New data presented here show a consistent linear relationship between equilibrium pH and equilibriumpCa or pMg irrespective of sample used or solution ionic strength. The surface charge of calcite is weakly dependenton pH, through protonation and deprotonation reactions that occur within a hydrolysis layer immediatelyadjacent to the mineral surface. The Point of Zero Charge (PZC) at which the surface charge is zero could b

  • Journal article
    Al Mahrouqi D, Vinogradov J, Jackson MD, 2016,

    Zeta potential of artificial and natural calcite in aqueous solution.

    , Adv Colloid Interface Sci, Vol: 240, Pages: 60-76

    Despite the broad range of interest and applications, controls on calcite surface charge in aqueous solution, especially at conditions relevant to natural systems, remain poorly understood. The primary data source to understand calcite surface charge comprises measurements of zeta potential. Here we collate and review previous measurements of zeta potential on natural and artificial calcite and carbonate as a resource for future studies, compare and contrast the results of these studies to determine key controls on zeta potential and where uncertainties remain, and report new measurements of zeta potential relevant to natural subsurface systems. The results show that the potential determining ions (PDIs) for the carbonate mineral surface are the lattice ions Ca(2+), Mg(2+) and CO3(2-). The zeta potential is controlled by the concentration-dependent adsorption of these ions within the Stern layer, primarily at the Outer Helmholtz Plane (OHP). Given this, the Iso-Electric Point (IEP) at which the zeta potential is zero should be expressed as pCa (or pMg). It should not be reported as pH, similar to most metal oxides. The pH does not directly control the zeta potential. Varying the pH whilst holding pCa constant yields constant zeta potential. The pH affects the zeta potential only by moderating the equilibrium pCa for a given CO2 partial pressure (pCO2). Experimental studies that appear to yield a systematic relationship between pH and zeta potential are most likely observing the relationship between pCa and zeta potential, with pCa responding to the change in pH. New data presented here show a consistent linear relationship between equilibrium pH and equilibrium pCa or pMg irrespective of sample used or solution ionic strength. The surface charge of calcite is weakly dependent on pH, through protonation and deprotonation reactions that occur within a hydrolysis layer immediately adjacent to the mineral surface. The Point of Zero Charge (PZC) at which the surface char

  • Journal article
    Salinas P, Pavlidis D, xie Z, Adam A, Pain C, Jackson Met al., 2016,

    Improving the convergence behaviour of a fixed-point-iteration solver for multiphase flow in porous media

    , International Journal for Numerical Methods in Fluids, Vol: 84, Pages: 466-476, ISSN: 1097-0363

    A new method to admit large Courant numbers in the numerical simulation of multiphase flow is presented.The governing equations are discretised in time using an adaptive -method. However, the use of implicitdiscretisations does not guarantee convergence of the non-linear solver for large Courant numbers. In thiswork, a double-fixed point iteration method with backtracking is presented that improves both convergenceand convergence rate. Moreover, acceleration techniques are presented to yield a more robust non-linearsolver with increased effective convergence rate. The new method reduces the computational effort bystrengthening the coupling between saturation and velocity, obtaining an efficient backtracking parameter,using a modified version of Anderson’s acceleration and adding vanishing artificial diffusion.

  • Journal article
    MacAllister DJ, Jackson MD, Butler AP, Vinogradov Jet al., 2016,

    Tidal influence on self-potential measurements

    , Journal of Geophysical Research. Solid Earth, Vol: 121, Pages: 8432-8452, ISSN: 2169-9313

    Long-term surface and borehole self-potential (SP) monitoring was conducted in the UK Chalk aquifer at two sites. The coastal site is ~1.7 km from the coast, and the inland site is ~80 km from the coast. At both sites, power spectral density analysis revealed that SP data contain the main ocean tidal periodic components. However, the principal lunar component (M2), the dominant ocean tidal component, was most significant at the coastal site. The M2 signal in surface-referenced SP data at the inland site was partly due to telluric currents caused by the geomagnetic ocean dynamo. Earth and/or atmospheric tides also contributed, as the SP power spectrum was not typical of a telluric electric field. The M2 component in borehole-referenced data at the inland site was below the significance level of the analysis method and was 2 orders of magnitude smaller than the M2 signal in borehole-referenced SP data at the coastal site. The tidal response of the SP data in the coastal borehole is, therefore, primarily driven by ocean tides. These cause changes in fluid pressure and chemical concentration gradients within the coastal aquifer, leading to time varying electrokinetic and exclusion-diffusion potentials. Borehole-referenced SP measurements could be used to characterize and monitor tidal processes in coastal aquifers such as the intrusion of seawater.

  • Journal article
    Mostaghimi P, Kamali F, Jackson MD, Muggeridge AH, Pain CCet al., 2016,

    Adaptive mesh optimization for simulation of immiscible viscous fingering

    , SPE Journal, Vol: 21, Pages: 2250-2259, ISSN: 1086-055X

    Viscous fingering can be a major concern when waterflooding heavy-oil reservoirs. Most commercial reservoir simulators use low-order finite-volume/-difference methods on structured grids to resolve this phenomenon. However, this approach suffers from a significant numerical-dispersion error because of insufficient mesh resolution, which smears out some important features of the flow. We simulate immiscible incompressible two-phase displacements and propose the use of unstructured control-volume finite-element (CVFE) methods for capturing viscous fingering in porous media. Our approach uses anisotropic mesh adaptation where the mesh resolution is optimized on the basis of the evolving features of flow. The adaptive algorithm uses a metric tensor field dependent on solution-interpolation-error estimates to locally control the size and shape of elements in the metric. The mesh optimization generates an unstructured finer mesh in areas of the domain where flow properties change more quickly and a coarser mesh in other regions where properties do not vary so rapidly. We analyze the computational cost of mesh adaptivity on unstructured mesh and compare its results with those obtained by a commercial reservoir simulator on the basis of the finite-volume methods.

  • Journal article
    Jackson MD, Al-Mahrouqi D, Vinogradov J, 2016,

    Zeta potential in oil-water-carbonate systems and its impact on oil recovery during controlled salinity water-flooding

    , Scientific Reports, Vol: 6, ISSN: 2045-2322

    Laboratory experiments and field trials have shown that oil recovery from carbonate reservoirs can be increased by modifying the brine composition injected during recovery in a process termed controlled salinity water-flooding (CSW). However, CSW remains poorly understood and there is no method to predict the optimum CSW composition. This work demonstrates for the first time that improved oil recovery (IOR) during CSW is strongly correlated to changes in zeta potential at both the mineral-water and oil-water interfaces. We report experiments in which IOR during CSW occurs only when the change in brine composition induces a repulsive electrostatic force between the oil-brine and mineral-brine interfaces. The polarity of the zeta potential at both interfaces must be determined when designing the optimum CSW composition. A new experimental method is presented that allows this. Results also show for the first time that the zeta potential at the oil-water interface may be positive at conditions relevant to carbonate reservoirs. A key challenge for any model of CSW is to explain why IOR is not always observed. Here we suggest that failures using the conventional (dilution) approach to CSW may have been caused by a positively charged oil-water interface that had not been identified.

  • Journal article
    Al-Mahrouqi, Vinogradov J, Jackson MD, 2016,

    Temperature-dependence of the zeta potential in intact natural carbonates

    , Geophysical Research Letters, Vol: 43, Pages: 11578-11587, ISSN: 1944-8007

    The zeta potential is a measure of the electrical charge on mineral surfaces and is an important control on subsurface geophysical monitoring, adsorption of polar species in aquifers, and rock wettability. We report the first measurements of zeta potential in intact, water-saturated, natural carbonate samples at temperatures up to 120°C. The zeta potential is negative and decreases in magnitude with increasing temperature at low ionic strength (0.01 M NaCl, comparable to potable water) but is independent of temperature at high ionic strength (0.5 M NaCl, comparable to seawater). The equilibrium calcium concentration resulting from carbonate dissolution also increases with increasing temperature at low ionic strength but is independent of temperature at high ionic strength. The temperature dependence of the zeta potential is correlated with the temperature dependence of the equilibrium calcium concentration and shows a Nernstian linear relationship. Our findings are applicable to many subsurface carbonate rocks at elevated temperature.

  • Journal article
    Al Mahrouqi D, Vinogradov J, Jackson MD, 2016,

    Temperature dependence of the zeta potential in intact natural carbonates

    , GEOPHYSICAL RESEARCH LETTERS, Vol: 43, Pages: 11578-11587, ISSN: 0094-8276
  • Conference paper
    Salinas P, Pavlidis D, Xie Z, Adam A, Pain C, Jackson Met al., 2016,

    Dynamic unstructured mesh adaptivity for improved simulation of near­wellbore flow in reservoir ­scale models

    , 15th European Conference on the Mathematics of Oil Recovery, Publisher: EAGE

    It is well known that the pressure gradient into a production well increases with decreasing distanceto the well and may cause downwards coning of the gaswater interface, or upwards coning ofwateroil interface, into oil production wells; it can also cause downwards coning of the water table,or upwards coning of a saline interface, into water abstraction wells. To properly capture the localpressure drawdown into the well, and its effect on coning, requires high grid or mesh resolution innumerical models; moreover, the location of the well must be captured accurately. In conventionalsimulation models, the user must interact with the model to modify grid resolution around wells ofinterest, and the well location is approximated on a grid defined early in the modelling process.We report a new approach for improved simulation of nearwellbore flow in reservoirscale modelsthrough the use of dynamic unstructured adaptive meshing. The method is novel for two reasons.First, a fully unstructured tetrahedral mesh is used to discretize space, and the spatial location of thewell is specified via a line vector. Mesh nodes are placed along the line vector, so the geometry ofthe mesh conforms to the well trajectory. The well location is therefore accurately captured, and theapproach allows complex well trajectories and wells with many laterals to be modelled. Second,the mesh automatically adapts during a simulation to key solution fields of interest such as pressureand/or saturation, placing higher resolution where required to reduce an error metric based on theHessian of the field. This allows the local pressure drawdown and associated coning to be capturedwithout userdriven modification of the mesh. We demonstrate that the method has wideapplication in reservoirscale models of oil and gas fields, and regional models of groundwaterresources.

  • Journal article
    Jackson MD, Vinogradov J, Hamon G, Chamerois Met al., 2016,

    Evidence, mechanisms and improved understanding of controlled salinity waterflooding part 1: Sandstones

    , FUEL, Vol: 185, Pages: 772-793, ISSN: 0016-2361
  • Journal article
    Gomes JLMA, Pavlidis D, Salinas P, Xie Z, Percival JR, Melnikova Y, Pain CC, Jackson MDet al., 2016,

    A force-balanced control volume finite element method for multi-phase porous media flow modelling

    , International Journal for Numerical Methods in Fluids, Vol: 83, Pages: 431-445, ISSN: 1097-0363

    A novel method for simulating multi-phase flow in porous media is presented. The approach is based on acontrol volume finite element mixed formulation and new force-balanced finite element pairs. The novelty ofthe method lies in: (a) permitting both continuous and discontinuous description of pressure and saturationbetween elements; (b) the use of arbitrarily high-order polynomial representation for pressure and velocityand (c) the use of high-order flux-limited methods in space and to time avoid introducing non-physicaloscillations while achieving high-order accuracy where and when possible. The model is initially validatedfor two-phase flow. Results are in good agreement with analytically obtained solutions and experimentalresults. The potential of this method is demonstrated by simulating flow in a realistic geometry composed ofhighly permeable meandering channels.

  • Journal article
    Adam A, Pavlidis D, Percival J, Salinas P, Xie Z, Fang F, Pain C, Muggeridge A, Jackson Met al., 2016,

    Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity

    , Journal of Computational Physics, Vol: 321, Pages: 512-531, ISSN: 1090-2716

    A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.

  • Journal article
    Massart BYG, Jackson MD, Hampson GJ, Johnson HD, Legler B, Jackson CA-Let al., 2016,

    Effective flow properties of heterolithic, cross-bedded tidal sandstones: Part 1. Surface-based modeling

    , AAPG Bulletin, Vol: 100, Pages: 697-721, ISSN: 0149-1423

    Tidal heterolithic sandstones are commonly characterized by millimeter- to centimeter-scale intercalations of mudstone and sandstone. Consequently, their effective flow properties are poorly predicted by (1) data that do not sample a representative volume or (2) models that fail to capture the complex three-dimensional architecture of sandstone and mudstone layers. We present a modeling approach in which surfaces are used to represent all geologic heterogeneities that control the spatial distribution of reservoir rock properties (surface-based modeling). The workflow uses template surfaces to represent heterogeneities classified by geometry instead of length scale. The topology of the template surfaces is described mathematically by a small number of geometric input parameters, and models are constructed stochastically. The methodology has been applied to generate generic, three-dimensional minimodels (9 m3 volume) of cross-bedded heterolithic sandstones representing trough and tabular cross-bedding with differing proportions of sandstone and mudstone, using conditioning data from two outcrop analogs from a tide-dominated deltaic deposit. The minimodels capture the cross-stratified architectures observed in outcrop and are suitable for flow simulation, allowing computation of effective permeability values for use in larger-scale models. We show that mudstone drapes in cross-bedded heterolithic sandstones significantly reduce effective permeability and also impart permeability anisotropy in the horizontal as well as vertical flow directions. The workflow can be used with subsurface data, supplemented by outcrop analog observations, to generate effective permeability values to be derived for use in larger-scale reservoir models. The methodology could be applied to the characterization and modeling of heterogeneities in other types of sandstone reservoirs.

  • Journal article
    Alroudhan A, Vinogradov J, Jackson MD, 2016,

    Zeta potential of intact natural limestone: Impact of potential-determining ions Ca, Mg and SO4

    , Colloids and Surfaces A - Physicochemical and Engineering Aspects, Vol: 493, Pages: 83-98, ISSN: 0927-7757

    We report measurements of the zeta potential on intact limestone samples obtained using the streaming potential method (SPM), supplemented by the more ubiquitous electrophoretic mobility method (EPM). The effect of the potential-determining ions (PDI) Ca, Mg and SO4, and the total ionic strength controlled by NaCl concentration, is investigated over the range typical of natural brines. We find that the zeta potential varies identically and linearly with calcium and magnesium concentration expressed as pCa or pMg. The zeta potential also varies linearly with pSO4. The sensitivity of the zeta potential to PDI concentration, and the IEP expressed as pCa or pMg, both decrease with increasing NaCl concentration. We report considerably lower values of IEP than most previous studies, and the first observed IEP expressed as pMg. The sensitivity of the zeta potential to PDI concentration is lower when measured using the SPM compared to the EPM, owing to the differing location of the shear plane at which the zeta potential is defined. SPM measurements are more appropriate in natural porous samples because they reflect the mineral surfaces that predominantly interact with the adjacent fluids. We demonstrate that special cleaning procedures are required to return samples to a pristine zeta potential after exposure to PDIs. We apply our results to an engineering process: the use of modified injection brine composition to increase oil recovery from carbonate reservoirs. We find a correlation between an increasingly negative zeta potential and increased oil recovery.

  • Journal article
    Massart BYG, Jackson MD, Hampson GJ, Johnson HDet al., 2016,

    Effective flow properties of heterolithic, cross-bedded tidal sandstones: Part 2. Flow simulation

    , AAPG Bulletin, Vol: 100, Pages: 723-742, ISSN: 0149-1423

    Tidal heterolithic sandstone reservoirs are heterogeneous at the sub-meter scale, due to the ubiquitous presence of intercalated sandstone and mudstone laminae. Core-plug permeability measurements fail to sample a representative volume of this heterogeneity. Here we investigate the impact of mudstone drape distribution on the effective permeability of heterolithic, cross-bedded tidal sandstones using three-dimensional (3D) surface-based “mini-models” that capture the geometry of cross-beds at an appropriate scale. The impact of seven geometric parameters has been determined: (1) mudstone fraction, (2) sandstone laminae thickness, (3) mudstone drape continuity, (4) toeset dip, (5) climb angle of foreset-toeset surfaces, (6) proportion of foresets to toesets, and (7) trough or tabular geometry of the cross-beds.We begin by identifying a representative elementary volume (REV) of 1 m3, confirming that the model volume of 9 m3 yields representative permeability values. Effective permeability decreases as the mudstone fraction increases, and is highly anisotropic: vertical permeability falls to c. 0.5% of the sandstone permeability at a mudstone fraction of 25%, while the horizontal permeability falls to c. 5% and c. 50% of the sandstone value in the dip (across mudstone drapes) and strike (parallel to mudstone drapes) directions, respectively. There is considerable spread around these values, because each parameter investigated can significantly impact effective permeability, with the impact depending upon the flow direction and mudstone fraction. The results yield improved estimates of effective permeability in heterolithic, cross-bedded sandstones, which can be used to populate reservoir-scale model grid blocks using estimates of mudstone fraction and geometrical parameters obtained from core and outcrop-analog data.

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