Spatial Variability Of Permeability Research Articles

A History Matching Study for the FluidFlower Benchmark Project

In this study, we conduct a comprehensive history matching study for the FluidFlower benchmark model. This benchmark was prepared and organized by the University of Bergen, the University of Stuttgart, and Massachusetts Institute of Technology, for promoting understanding of the complex physics of geological carbon storage (GCS) through in-house experiments and numerical simulations. This paper synthesizes the experiences of history matching the benchmark data encountered by the Delft-DARTS and CSIRO participants. History matching is first performed based on a low-dimensional-zonated structured model using a simple Poisson-like solver. The permeability of six facies and two faults is inferred in this stage to match the digitized concentration data. The history matching is then further enhanced to richer spatial and physical models to capture the spatial variation of permeability and buoyancy effects, using an unstructured grid. Efficient adjoint methods are used to evaluate the gradient used in the optimization of data misfits or equivalent Bayesian log-likelihoods. With efficient optimization methods available for both maximum a posteriori model inference and Randomized Maximum Likelihood methods for model uncertainty, we perform history matching using both binary and continuous concentration observations. The results show that the tracer plumes in the enriched model match the experimental plumes more accurately compared with the results from the parsimonious-zonated model. The history matching results based on the concentration observations provide more similar plume shapes compared with the case based on the binary observations. The permeability difference between the model before and after history matching reveals that the tracer plume zone and the high permeable zone are the regions of high sensitivity in terms of data misfit between the model response and observations. Surprisingly, CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} concentration plume forecasts based on these history-matched models were not especially sensitive to the improvements observed in the enhanced model.

In-field measurement and numerical modelling of air leakage in concrete: From laboratory specimen to structural full-scale

This work estimates air leakage through concrete porosity for structures by using data obtained in field combined with stochastic finite element (SFE) modelling. For this purpose, a methodology is proposed to evaluate permeability under representative over-pressurization conditions based on in-field measurements under vacuum. This makes it possible to investigate the air leakage through the inner wall of a 1:3 scaled nuclear vessel named the VeRCoRs mock-up. Measurements are made for over 80 points scattered on the external face of the inner wall of the structure. Based on the data collected, a statistical analysis quantifies the spatial variation of permeability and contributes to the building of an SFE model of air leakage at the structural scale. Measured and predicted data are in good agreement on the service life of the structure. This shows the relevance of combining in-field measurements during an operational phase and the SFE modelling for better evaluation of the structural performance. The lessons learnt from the present work could be useful for the assessment of all structures with durability or mechanical issues that induce a continuous loss of tightness.

Spatial variation of permeability and consolidation behaviors of soil using ordinary kriging method

The present study is aimed at finding out spatial distribution of permeability characteristic of soil using ordinary kriging method at any location using the data from a few boreholes at NIT (National Institute of Technology) Patna Bihta campus. Kriging is also popularly known as BLUE (i. e. Best Linear Unbiased Estimator) which can be used to interpolate the data obtained from a few locations to get an estimate of any parameter at other locations throughout the study area. In the present work, soil samples collected from eight boreholes have been tested to obtain various geotechnical properties including liquid limit (LL), plastic limit (PL), plasticity index (IP), coefficient of volume compressibility (mv) etc. These values have been used as inputs in an Ordinary Kriging model to calculate coefficient of consolidation (Cv) and coefficient of permeability (k) throughout the NIT Patna, Bihta campus and build contour plots of (Cv) and (k) over the NIT Patna campus to show their spatial variation. The novelty of the current work lies in the first time proposed method for developing the spatial distribution of(Cv) and(k). Markov correlation matrix has been used to develop the correlation behavior of the parameters considering different values of correlation length. In the present study, it is found that the coefficient of consolidation Cv of soil ranges 10−8 (m2/sec). The Kriged values of k are in the range of 10−11 to 10−10 (m/s). Finally, semi-variogram have been shown to display the auto-correlation of the measured data points and cross-validation of data set which establish that the Kriged data are reasonably correlated. Also, various error estimators such as Mean Error, Root Mean Square Error, Average Standard Error, Root Mean Square Standard Error, Mean Standard Error have been calculated using the Kriged data points over the entire area and, it is found that the error level in the predicted Kriged data are reasonably small.

A NUMERICAL APPROACH FOR PERMEABILITY ESTIMATION IN RADIALLY HETEROGENEOUS RESERVOIRS

Analytical solutions are used extensively for pressure transient analysis in radially heterogeneous reservoirs. They are generally used for evaluating variation of reservoir properties along the reservoir radius. However, the available analytical solutions are not sufficiently accurate to determine boundaries of zones. As a result, the interior boundaries of heterogeneous zones are often estimated as a function of the average permeability of zones, which sometimes is a cause of nonunique solutions. As a matter of fact, the skin factor does not provide accurate information about the radius and permeability of an altered zone separately. A new numerical well test procedure is presented in this paper based on the finite element method and a special zonal discretization that utilizes nonlinear regression, which is able to detect the interior boundaries of heterogeneous zones. The results demonstrate that this numerical approach is able to capture the spatial variation of permeability in the radially heterogeneous reservoirs under various boundary conditions. A key advantage of this numerical procedure is quantifying heterogeneity in terms of the radius and permeability of the dissimilar zones, whereas analytical methods generally provide a combination of these parameters.

An approach for modelling spatial variability in permeability of cement-admixed soil

This paper presents a framework for modelling the random variation in permeability in cement-admixed soil based on the binder content variation and thereby relating the coefficient of permeability to the unconfined compressive strength of a cement-admixed clay. The strength–permeability relationship was subsequently implemented in random finite element method (RFEM). The effects of spatial variation in both strength and permeability of cement-admixed clays in RFEM is illustrated using two examples concerning one-dimensional consolidation. Parametric studies considering different coefficient of variation and scale of fluctuation configurations were performed. Results show that spatial variability of the cement-admixed clay considering variable permeability can significantly influence the overall consolidation rate, especially when the soil strength variability is high. However, the overall consolidation rates also depend largely on the prescribed scales of fluctuation; in cases where the variation is horizontally layered, stagnation in pore pressure dissipation may occur due to soft parts yielding.

An extended trajectory-mechanics approach for calculating two-phase flow paths

A technique originating in quantum dynamics is used to derive a trajectory-based, semi-analytical solution for two-phase flow. The partial differential equation governing the evolution of the aqueous phase is equivalent to a family of ordinary differential equations defined along a path through the porous medium. The trajectories may be found by solving the differential equations directly or by post-processing the output of a numerical solution to the full set of governing equations. The trajectories, which differ from conventional streamlines, are found to bend downward in response to gravitational forces. The curvature is more pronounced as the dip of the porous layer containing the flow increases. Subtle changes in the relative permeability curve can lead to significant variations in the trajectories. The ordinary differential equation for the trajectory provides an expression for the travel time along the path. The expression produces a semi-analytical approximation to the model parameter sensitivities, the partial derivatives of the travel times with respect to changes in the permeability model. The semi-analytical trajectory-based sensitivities generally agree with those computed using a numerical reservoir simulator and a perturbation approach. The sensitivities are useful in tomographic imaging algorithms designed to estimate the spatial variation in permeability within a porous medium using multiphase observations.

Small-scale diagenetic facies heterogeneity controls porosity and permeability pattern in reservoir sandstones

The fluvial-aeolian Upper Rotliegend sandstones from the Bebertal outcrop (Flechtingen High, Germany) are the famous reservoir analog for the deeply buried Upper Rotliegend gas reservoirs of the Southern Permian Basin. While most diagenetic and reservoir quality investigations are conducted on a meter scale, there is an emerging consensus that significant reservoir heterogeneity is inherited from diagenetic complexity at smaller scales. In this study, we utilize information about diagenetic products and processes at the pore- and plug-scale and analyze their impact on the heterogeneity of porosity, permeability, and cement patterns. Eodiagenetic poikilitic calcite cements, illite/iron oxide grain coatings, and the amount of infiltrated clay are responsible for mm- to cm-scale reservoir heterogeneities in the Parchim formation of the Upper Rotliegend sandstones. Using the Petrel E&P software platform, spatial fluctuations and spatial variations of permeability, porosity, and calcite cements are modeled and compared, offering opportunities for predicting small-scale reservoir rock properties based on diagenetic constraints.

Estimates for the Effective Permeability of Intact Granite Obtained from the Eastern and Western Flanks of the Canadian Shield

Granitic rock from the western part of the Canadian Shield is considered as a potential host rock for the siting of a deep geological repository for the storage of heat-emitting high-level nuclear fuel waste. The research program focused on the use of surface permeability measurements conducted at 54 locations on a 300 mm cuboid of granite, obtained from the Lac du Bonnet region in Manitoba, to obtain an estimate for the effective permeability of the cuboid. Companion experiments are conducted on a 280 mm cuboid of granite obtained from Stanstead, Quebec, located in the eastern part of the Canadian Shield. The surface permeabilities for the cuboids of granite are developed from theoretical relationships applicable to experimental situations where steady flow is initiated at a sealed annular surface region with a pressurized central domain. The experimental values for the surface permeability are used with a kriging procedure to estimate the permeability variations within the cuboidal region. The spatial variations of permeability are implemented in computational models of the cuboidal regions to determine the one-dimensional permeabilities in three orthogonal directions. The effective permeability of the granite cuboids is estimated by appeal to the geometric mean. The research provides a non-destructive methodology for estimating the effective permeability of large specimens of rock and the experiments performed give estimates for the effective permeability of the two types of granitic rock obtained from the western and eastern flanks of the Canadian Shield.

A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels.

Mechanical interactions between flowing and coagulated blood (thrombus) are crucial in dictating the deformation and remodeling of a thrombus after its formation in hemostasis. We propose a fully-Eulerian, three-dimensional, phase-field model of thrombus that is calibrated with existing in vitro experimental data. This phase-field model considers spatial variations in permeability and material properties within a single unified mathematical framework derived from an energy perspective, thereby allowing us to study effects of thrombus microstructure and properties on its deformation and possible release of emboli under different hemodynamic conditions. Moreover, we combine this proposed thrombus model with a particle-based model which simulates the initiation of the thrombus. The volume fraction of a thrombus obtained from the particle simulation is mapped to an input variable in the proposed phase-field thrombus model. The present work is thus the first computational study to integrate the initiation of a thrombus through platelet aggregation with its subsequent viscoelastic responses to various shear flows. This framework can be informed by clinical data and potentially be used to predict the risk of diverse thromboembolic events under physiological and pathological conditions.

Effect of the spatial variation of permeability on air bubble creation and compression

Tow bundles inside a quasi-unidirectional non-crimp fabric are maintained by sewing threads that induce variation in the bundles’ shape. Indeed, the sewing threads apply a light clamping force that gives a periodical and sinusoidal shape to the tow’s cross-sectional area. This tow cross-sectional area heterogeneity, as a function of position in the fabric, induces a variation of the permeability values. Consequently, while injecting liquid into the fibrous bed, preform's impregnation is influenced as well as the fabric’s void content. The aim of this paper is to consider the effect of tow cross-sectional area heterogeneity on the quality of the manufactured composite part. It leads to reveal the influence of the fibrous reinforcement’s microstructure on the air bubble creation and compression phenomena, especially in terms of process time and the micro and macro air bubble distribution.

Investigating Fine‐Scale Permeability Structure and Its Control on Hydrothermal Activity Along a Fast‐Spreading Ridge (the East Pacific Rise, 9°43′–53′N) Using Seismic Velocity, Poroelastic Response, and Numerical Modeling

AbstractAlong with the intracrustal heat source, crustal permeability is considered as the controlling factor for hydrothermal circulation within zero‐age oceanic crust. To obtain fine‐scale, 2‐D models of upper crustal permeability along the East Pacific Rise 9°50′N, known for prolific hydrothermal activity, we use recently derived high‐resolution seismic velocity and examine a number of the existing velocity‐permeability relationships. To constrain our preferred permeability model, we compare thus derived permeability models with collocated permeability estimates from poroelastic response to tidal loading at L‐vent. Furthermore, using the preferred permeability result, we model hydrothermal convection in 2‐D and find that the distributions of recharge and discharge zones are in good agreement with seafloor observations, including locations of the vent fields. Our results suggest that seismic velocities can be used as a tool for deriving spatial variation of permeability, which must be considered in modeling of hydrothermal flow.

Permeability sensitivity functions and rapid simulation of multi-point pressure measurements using perturbation theory

We introduce a perturbation method for the forward modeling of transient diffusion phenomena in aquifers with pressure measurements acquired at arbitrary observation points. Our numerical approach requires only two simulations to compute the Permeability Sensitivity Function (PSF) at an observation point under multi-source and multi-rate conditions; one simulation captures the pressure solution due to the flow history of the sources, while the second simulation is required to extract the Green's function of the groundwater system. The PSF is calculated on the spatial-temporal domain by convolving the gradients of the pressure solution and of the Green's function. The first-order term in the perturbation expansion is obtained by weighting the spatial variations of permeability with a flow-history-dependent PSF.Our work confirms the flexibility and reliability of the method after successful validation with forward numerical simulations in cylindrical and Cartesian coordinates. Multidimensional synthetic studies including multi-well and formation testing conditions, were examined for diverse anisotropy-dominated fluid-flow regimes. Against perturbations of more than one order of magnitude in background permeability, results show that first-order approximations can be computed in tens of CPU seconds with relative errors in pressure of < 7%. Results indicate that sensitivity functions enable improved qualitative understanding of permeability-pressure correlations and local Darcy flow dynamics.

Impact of Spatial Variations in Permeability of Liquefiable Deposits on Seismic Performance of Structures and Effectiveness of Drains

AbstractSand deposits are often stratified with thin layers of low-permeability silt. Previous studies have shown that the presence of sharp variations in permeability could slow down the dissipati...

Stochastic prediction of fractured caprock by history matching pressure monitoring data

In this study, a novel method to stochastically characterize the effective permeability of a fractured caprock (typically fine-grained sedimentary rock or natural mudstones) is presented. The method requires pressure monitoring data from above and below the caprock, which are used in combination with other readily-available data from laboratory and outcrop observations in a history-matching process that maintains the distribution of underlying fracture attributes to characterize the spatial variation in permeability of the caprock. A “best-fitting” geological model of caprock, representing a most-likely scenario, is selected from an ensemble of stochastic realizations generated using optimized parameters. The method is demonstrated using a representative, moderately permeable, heterogeneous caprock, as a reference “truth” to compare accuracy of caprock predicted using pressures from injection and post-injection phases. The accuracy of “best-fitting” caprock is assessed by studying its sensitivity to four variables, which are caprock thickness, leakage intensity, time length of available pressure history, and injection rate.Improved characterization of effective caprock permeability allows more confident prediction of flux through the sealing interval, over time. That information is useful in quantifying potential impacts of fluid migration, evaluating monitoring designs, and designing mitigation alternatives, should they be needed. It has value both during active injection and in building confidence that a site can be safely closed after injection is complete.

Simultaneous prediction of dryout heat flux and local temperature for thin film evaporation in micropillar wicks

Porous wicks are of great interest in thermal management because they are capable of passively supplying liquid for thin film evaporation, a promising method to reliably dissipate heat in high performance electronics. While dryout heat flux has been well-characterized for many wick configurations, key design information is missing as many previous models cannot determine the distribution of evaporator surface temperature. Temperature gradients are inherent to the passive capillary pumping mechanism since the shape of the liquid/vapor interface is a function of the local liquid pressure, causing spatial variation of permeability and heat transfer coefficient (HTC). Here, we present a comprehensive modeling framework for thin film evaporation in micropillar wicks that can predict dryout heat flux and local temperature simultaneously. Our numerical approach captures the effect of varying interfacial curvature across the micropillar evaporator to determine the spatial distributions of temperature and heat flux. Heat transfer and capillary flow in the wick are coupled in a computationally efficient manner via incorporation of parametric studies to relate geometry and interface shape to local permeability and HTC. This model predicts notable variations of HTC (∼30%) across the micropillar wick, highlighting the significant effects of interfacial curvature. Further, we are able to quantify the tradeoff associated with enhancing either dryout heat flux or HTC by optimizing geometry. Our model provides all of the information needed to guide the design and optimization of micropillar wicks by resolving evaporator temperature distributions in addition to dryout heat flux.

Instabilities in viscosity-stratified two-fluid channel flow over an anisotropic-inhomogeneous porous bottom

A linear stability analysis of a pressure driven, incompressible, fully developed laminar Poiseuille flow of immiscible two-fluids of stratified viscosity and density in a horizontal channel bounded by a porous bottom supported by a rigid wall, with anisotropic and inhomogeneous permeability, and a rigid top is examined. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the liquid-porous interface. The formulation is within the framework of modified Orr-Sommerfeld analysis, and the resulting coupled eigenvalue problem is numerically solved using a spectral collocation method. A detailed parametric study has revealed the different active and coexisting unstable modes: porous mode (manifests as a minimum in the neutral boundary in the long wave regime), interface mode (triggered by viscosity-stratification across the liquid-liquid interface), fluid layer mode [existing in moderate or O(1) wave numbers], and shear mode at high Reynolds numbers. As a result, there is not only competition for dominance among the modes but also coalescence of the modes in some parameter regimes. In this study, the features of instability due to two-dimensional disturbances of porous and interface modes in isodense fluids are explored. The stability features are highly influenced by the directional and spatial variations in permeability for different depth ratios of the porous medium, permeability and ratio of thickness of the fluid layers, and viscosity-stratification. The two layer flow in a rigid channel which is stable to long waves when a highly viscous fluid occupies a thicker lower layer can become unstable at higher permeability (porous mode) to long waves in a channel with a homogeneous and isotropic/anisotropic porous bottom and a rigid top. The critical Reynolds number for the dominant unstable mode exhibits a nonmonotonic behaviour with respect to depth ratio. However, it increases with an increase in anisotropy parameter ξ indicating its stabilizing role. Switching of dominance of modes which arises due to variations in inhomogeneity of the porous medium is dependent on the permeability and the depth ratio. Inhomogeneity arising due to an increase in vertical variations in permeability renders short wave modes to become more unstable by enlarging the unstable region. This is in contrast to the anisotropic modulations causing stabilization by both increasing the critical Reynolds number and shrinking the unstable region. A decrease in viscosity-stratification of isodense fluids makes the configuration hosting a less viscous fluid in a thinner lower layer adjacent to a homogeneous, isotropic porous bottom to be more unstable than the one hosting a highly viscous fluid in a thicker lower layer. An increase in relative volumetric flow rate results in switching the dominant mode from the interface to fluid layer mode. It is evident from the results that it is possible to exercise more control on the stability characteristics of a two-fluid system overlying a porous medium in a confined channel by manipulating the various parameters governing the flow configurations. This feature can be effectively exploited in relevant applications by enhancing/suppressing instability where it is desirable/undesirable.

Iterative filter based estimation of fully 3D heterogeneous fields of permeability and Mualem-van Genuchten parameters

The accurate modeling of flow and transport in the vadose zone for agricultural and environmental applications requires knowledge about soil parameters. Soil parameters vary in space depending on soil texture and structure. In the present synthetic study we considered spatial variation of permeability (k), inverse of capillary entry pressure head (αVG) and exponent (n) of the Mualem-van Genuchten model. The iterative Ensemble Kalman filter (IEnKF) can estimate the spatially variable soil parameters if measurements of water saturation at different locations and times are available. We used as input daily precipitation data from the Berambadi catchment (southern India). We first considered that the parameters vary horizontally but are constant in the vertical direction. In this case log (k) and log (αVG) can be estimated satisfactorily with 30%–40% reduction of RMSE (compared to open loop runs), if the initial guess of the spatial correlation lengths of the heterogeneous fields is equal to or larger than the unknown, true values. The estimation of exponent n is poorer as the reduction of RMSE is just 20%. If vertical heterogeneity of the parameters is considered the estimation of log (k) and log (αVG) is only improved for the upper 1.5 m and estimation of n is not improved. We also demonstrate that the estimation problem can be simplified when flow in the unsaturated zone is predominantly vertical. If in this case soil hydraulic parameters are estimated with IEnKF at measurement locations and afterwards interpolated with kriging, results are produced with a similar quality as with 3D-IEnKF.

Calculating Trajectories Associated With Solute Transport in a Heterogeneous Medium

AbstractWe present a trajectory‐based technique for calculating solute transport in a porous medium that has several advantages over existing methods. Unlike streamlines, the extended trajectories are influenced by each of the important parameters governing transport, including molecular diffusion and transverse dispersion. The approach is complete and does not require any additional techniques, such as operator splitting or particle tracking, in order to account for the full dispersion tensor. The semianalytic expressions make it clear how the flow field, the concentration distribution, and the dispersion tensor contribute to the velocity field of an injected solute. The equations are valid for an arbitrary porous medium, including those with rapid spatial variations in properties, overcoming limitations faced by previous approaches based upon asymptotic techniques. A test on a layered model with sharp boundaries indicates that the extended trajectories are compatible with the results of a numerical simulator and differ from streamlines. We also describe a new form of the dispersion tensor that incorporates a known asymmetry. The trajectories indicate that the modifications of the dispersion tensor lead to more focused transport within regions of high conductivity. Finally, the trajectories are used to define a semianalytic relationship between solute travel times and variations in solute velocities along a path that may be used for tomographic imaging. In an application to the injection of a radioactive tracer into a Berea sandstone core, monitored using micropositron emission tomographic (micro‐PET) observations, the sensitivities are used to map the spatial variations of permeability within the core.

Heterogeneity-assisted carbon dioxide storage in marine sediments

Global climate change is a pressing problem caused by the accumulation of anthropogenic greenhouse gas emissions in the atmosphere. Carbon dioxide (CO2) capture and storage is a promising component of a portfolio of options to stabilize atmospheric CO2 concentrations. Meaningful capture and storage requires the permanent isolation of enormous amounts of CO2 away from the atmosphere. We investigate the effectiveness of heterogeneity-induced trapping mechanism, in potential synergy with a self-sealing gravitational trapping mechanism, for secure CO2 storage in marine sediments. We conduct the first comprehensive study on heterogeneous marine sediments with various thicknesses at various ocean depths. Prior studies of gravitational trapping have assumed homogeneous (deep-sea) sediments, but numerous studies suggest reservoir heterogeneity may enhance CO2 trapping. Heterogeneity can deter the upward migration of CO2 and prevent leakage through the seafloor into the seawater. Using geostatistically-based Monte Carlo simulations of CO2 transport in heterogeneous sediment, we show that strong spatial variability in permeability is a dominant physical mechanism for secure CO2 storage in marine sediments below 1.2 km water depth (less than half of the depth needed for the gravitational trapping). We identify thresholds for sediment thickness, mean permeability and porosity, and their relationships to meaningful injection rates. Our results for the U.S. Gulf of Mexico suggest that heterogeneity-assisted trapping has a greater areal extent with more than three times the CO2 storage capacity for secure offshore CO2 storage than with gravitational trapping. These characteristics offer CO2 storage opportunities that are closer to coasts, more accessible, and likely to be less costly.

Permeability Sensitivity Functions and Rapid Simulation of Hydraulic‐Testing Measurements Using Perturbation Theory

AbstractSingle‐well pressure‐diffusion simulators enable improved quantitative understanding of hydraulic‐testing measurements in the presence of arbitrary spatial variations of rock properties. Simulators of this type implement robust numerical algorithms which are often computationally expensive, thereby making the solution of the forward modeling problem onerous and inefficient. We introduce a time‐domain perturbation theory for anisotropic permeable media to efficiently and accurately approximate the transient pressure response of spatially complex aquifers. Although theoretically valid for any spatially dependent rock/fluid property, our single‐phase flow study emphasizes arbitrary spatial variations of permeability and anisotropy, which constitute key objectives of hydraulic‐testing operations. Contrary to time‐honored techniques, the perturbation method invokes pressure‐flow deconvolution to compute the background medium's permeability sensitivity function (PSF) with a single numerical simulation run. Subsequently, the first‐order term of the perturbed solution is obtained by solving an integral equation that weighs the spatial variations of permeability with the spatial‐dependent and time‐dependent PSF. Finally, discrete convolution transforms the constant‐flow approximation to arbitrary multirate conditions. Multidimensional numerical simulation studies for a wide range of single‐well field conditions indicate that perturbed solutions can be computed in less than a few CPU seconds with relative errors in pressure of 5%, corresponding to perturbations in background permeability of up to two orders of magnitude. Our work confirms that the proposed joint perturbation‐convolution (JPC) method is an efficient alternative to analytical and numerical solutions for accurate modeling of pressure‐diffusion phenomena induced by Neumann or Dirichlet boundary conditions.