Porosity-permeability Relationships Research Articles

Simulation of a fluid flow and investigation of a permeability-porosity relationship in porous media with random circular obstacles using the curved boundary lattice Boltzmann method

In this paper, the fluid flow between two parallel flat plates filled with porous media was investigated numerically using the Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM). The obstacles representing porous media were considered as random, circular, rigid and granular ones with uniform diameters and without overlap. The fluid was supposed to be a single-phase viscous Newtonian fluid and the flow to be incompressible, steady and laminar. The uniform velocity profile was considered at the entrance of the canal and the no-slip condition was imposed at solid walls. For applying curved boundary conditions, the linear interpolation method ( $ \Delta$ fraction) was used in this work. The effect of varying the Reynolds number on the pressure gradient and the Darcy drag was studied. The porous medium was supposed to be isotropic and having scalar permeability. The dimensionless permeability was calculated as a function of the Knudsen number. Also, the dimensionless permeability versus porosity was investigated and the results were compared with the Clague equation for different materials. Because of rather low precision of the Clague equation at high porosities, an extension to the Clague equation was presented. The permeability-porosity relationship was surveyed and the corresponding curve was plotted in the LBM scale. It was seen from numerical results that the enhancement of the Knudsen number increases the dimensionless permeability. The change of streamlines tortuosity in terms of porosity was explored and the results were compared with the revised Bruggeman equation. The obtained results demonstrate that the Lattice Boltzmann Method is very useful in the challenging problems of fluid dynamics such as fluid flow simulation through porous media.

Conditions for upscalability of bioclogging in pore network models

In this work, we model the biofilm growth at the microscale using a rectangular pore network model in 2D and a cubic network in 3D. For the 2D network, we study the effects of bioclogging on porosity and permeability when we change parameters like the number of nodes in the network, the network size, and the concentration of nutrients at the inlet. We use a 3D cubic network to study the influence of the number of nodes in the z direction on the biofilm growth and on upscalability. We show that the biofilm can grow uniformly or heterogeneously through the network. Using these results, we determine the conditions for upscalability of bioclogging for rectangular and cubic networks. If there is uniform biofilm growth, there is a unique relation between permeability and porosity, K ∼ ϕ2, this relation does not depend on the volume of the network, therefore the system is upscalable. However, if there is preferential biofilm growth, the porosity-permeability relation is not uniquely defined, hence upscalability is not possible. The Damköhler number is used to determine when upscalability is possible. If the Damköhler number is less than 101, the biofilm grows uniformly and therefore the system is upscalable. However, if the Damköhler number is greater than 103, the biofilm growth exhibits a deviation from uniform biofilm growth and heterogeneous growth is observed, therefore upscalability is not possible. There is a transition from uniform growth to preferential growth if the Damköhler number is between 101 and 103.

Modifications to the Kozeny–Carman model to enhance petrophysical relationships

The most commonly used relationship that relates permeability, porosity, grain size and tortuosity is the Kozeny–Carman equation. When it is used to estimate the permeability behaviour versus porosity, the other two parameters (the grain size and tortuosity) are usually kept constant. In this study, we investigate the deficiency of the Kozeny–Carman assumption and the alternative derived equations for the Kozeny–Carman equation is presented, including equations where the grain size is replaced with the pore size with varying tortuosity. We also introduce relationships for the permeability of shaly sand reservoir that answer the approximately linear permeability decreases in the log-linear permeability–porosity relationships in datasets from different locations.

Effect of Pore-Scale Mineral Spatial Heterogeneity on Chemically Induced Alterations of Fractured Rock: A Lattice Boltzmann Study

Fractures are the main flow path in rocks with very low permeability, and their hydrodynamic properties might change due to interaction with the pore fluid or injected fluid. Existence of minerals with different reactivities and along with their spatial distribution can affect the fracture geometry evolution and correspondingly its physical and hydrodynamic properties such as porosity and permeability. In this work, evolution of a fracture with two different initial spatial mineral heterogeneities is studied using a pore-scale reactive transport lattice Boltzmann method- (LBM-) based model. The previously developed LBM transport solver coupled with IPHREEQC in open-source Yantra has been extended for simulating advective-diffusive reactive transport. Results show that in case of initially mixed structures for mineral assemblage, a degraded zone will form after dissolution of fast-dissolving minerals which creates a resistance to flow in this region. This causes the permeability-porosity relationship to deviate from a power-law behavior. Results show that permeability will reach a steady-state condition which also depends on transport and reaction conditions. In case of initially banded structures, a comb-tooth zone will form and the same behavior as above is observed; however, in this case, permeability is usually less than that of mixed structures.

Reactive transport modelling in dual porosity media

A pore-scale model is applied to investigate reactive mass transport in dual porosity media. We use a framework based on the Stokes-Brinkman flow to model reactive flow in porous media with multiscale features. The numerical method involves fluid flow in pore space as well as flow in the rock matrix with microporosity. Reactive transport simulations are performed in a simple fractured porous medium and carbonates. The results are compared against the predictions in regimes of Stokes flow where the microporosity of rocks is excluded. In the fractured porous medium, wormholing dissolution is observed while face dissolution occurs when microporosity is ignored for the same Péclet and Damköhler numbers. This is explained by the penetration of reactive fluid flow through the rock matrix by Stokes-Brinkman flow. Reactive transport is also simulated in a Ketton carbonate. We compare the simulation results with published dynamic micro-CT imaging experiments for dissolution. Inclusion of microporosity leads to more accurate predictions of the pore space structures. The effect of microporosity on pore structure and permeability-porosity relationships is also explored in the carbonate samples with a range of matrix permeability values. The results show that the impact of microporosity on rock permeability variations is dependent on the ratio of matrix permeability to the overall permeability of the porous medium. Greater errors in permeability predictions are observed in the cases with higher ratios. This paper illustrates the significance of microporosity in reactive transport and improves the understanding of reactive transport in porous domains with multiscale features.

New approach towards the classification of microporosity in Miocene carbonate rocks, Central Luconia, offshore Sarawak, Malaysia

Microporosity is recognized as a significant concern in limestone reservoirs throughout the world because it presence can highly complicate the hydrocarbon estimation and production. Numerous studies around the globe emphasises on the physical appearance, occurrence, and abundance of microporosity, but no published study has been emphasises on the presence of microporosity in Miocene carbonate reservoirs. Miocene carbonates from Central Luconia, offshore Sarawak, Malaysia, contains a significant amount of micropores, which occurs in grain, matrix, and cement. For a better understanding of the presence of micropores, it is necessary to consider grains, matrix, cement, and pore types. Based on the qualitative and quantitative knowledge of these components a classification of micropores is proposed and their effect on reservoir quality. These results can reduce the number of the assumption made about the internal rock connectivity and quality.For quantitative analysis, 32 high-resolution images of each thin sections were taken under the transmitted light microscopy. Succeeding these 32 images were stacked together as a photo panel to enable quantifying the amount of grain, matrix, cement, pore types and macroporosity using Digital Image Analysis and J.Microvision software. Furthermore, Field Emission Scanning Electron Microscopy images were also used for the measurement of crystallometry of micrite particles, classification of micrite particles and the micropores.Eight facies scheme is introduced based on the detailed lithofacies study of five wells. The qualitative observation of thin sections unveiled that corals, red algae, green algae, foraminifera, echinoderms, sponge, bivalve, and bryozoans are the most dominant components. Foraminifera, red algae, and corals are the far most dominant components covering almost 50% of the total intervals. Regarding porosity types, the mouldic porosity is the far most dominant pore types with converting the total 50% of the interval. Lithofacies observed in these wells indicate a good reservoir quality, but diagenesis plays a vital role in enhancing or reducing their porosity and permeability. Most of the depositional textures of the reservoir are leached, making this location unique to study facies distribution and diagenetic history.Result exhibits that the micrite particles are classified into five classes, which are very fine, fine, medium, coarse and very coarse, with a diameter of 0.1–2 μm, 2–4 μm, 4–6 μm, 6–8 μm and 8–10 μm respectively. The texture and morphology of micrite microtexture are classified into six classes. Among these six classes, rounded, subrounded, trigonal, rhombic (micro-sub)-polyhedral micrite are representing porous micrite particles, whereas fitted bounded subhedral, and fitted fused anhedral are interpreted as tight micrite particles. Furthermore, five micropores classes are introduced based on the size of these particles. The empirical porosity-permeability relationship is affected by the presence of microporosity and its influences the assessment of ultimate recovery of hydrocarbons in Central Luconia, offshore Sarawak, Malaysia.

Existence of convective threshold and its role on temperature in reactive flow through fractured rocks: a simulation study in 2D

A reactive fluid flowing through porous or fractured rocks causes changes in its porosity and permeability. Experimental studies on the effects of reactive flow in porous systems are normally confined to finite size rock samples in laboratories as actual field data is not sufficiently available. Such laboratory data and simulations based on them, may not always correctly predict or explain changes that take place in rock basins in geological time. In this study we simulate two cases- transient and steady. In a transient case, reactions occur as soon as a reactive fluid is injected into the rock, whereas in the steady case, reactions begin only after the injected fluid percolates through the sample length. The transient case is comparable to real rock basins, while the steady case mimics the situation in laboratory experiments. Variation of the hydrodynamic parameters such as porosity, permeability and surface area, and their inter-relationships at different temperatures, are discussed in both cases. We establish that for every temperature, there exists a threshold flux above which the two cases give similar results. Prediction of changes in rock property due to reactive flow in real situations can be made from laboratory experiments provided the flux is kept above this threshold value. When the fluid flux is kept above this threshold value, the porosity-permeability relation follows a power law behaviour. While the threshold flux is independent of temperature and channel width, the exponent of the power law is a slow decreasing function of temperature.

Data mining in the Dutch Oil and Gas Portal: a case study on the reservoir properties of the Volpriehausen Sandstone interval

Abstract This paper presents the results of a data mining exercise on core measurements and reports of the Triassic Lower Volpriehausen Sandstone Member (RBMVL) in The Netherlands. The availability of a large accurate online dataset via the Dutch Oil and Gas Portal (NLOG) enables the definition of general reservoir property trends on a regional–subregional scale. Accurately defined trends are capable of restricting the uncertainty range of key parameters in exploration studies (e.g. porosity and permeability), and thus of reducing risk. Plotting core porosity v. core permeability resulted in a curved data cloud on a log-normal plot. Although porosity–permeability relationships are often defined by straight lines, the dataset in this study shows that a curved relationship results in a better fit with permeability measurements over the entire porosity range. Two methods were applied to define a porosity–depth relationship for sandstones of the RBMVL. The results of both methods confirm, and enable quantification of, the well-known trend of decreasing porosity with depth. By assigning grain density attributes to the core measurements, the dependency of the porosity–depth relationship on sedimentary facies and diagenesis type/grade could be determined. This case study demonstrates the power of this free online dataset in understanding reservoir quality.

Reservoir-condition pore-scale imaging of dolomite reaction with supercritical CO2 acidified brine: Effect of pore-structure on reaction rate using velocity distribution analysis

To investigate the impact of rock heterogeneity and flowrate on reaction rates and dissolution dynamics, four millimetre-scale Silurian dolomite samples were pre-screened based on their physical heterogeneity, defined by the simulated velocity distributions characterising each flow field. Two pairs of cores with similar heterogeneity were flooded with supercritical carbon-dioxide (scCO2) saturated brine under reservoir conditions, 50°C and 10MPa, at a high (0.5ml/min) and low (0.1ml/min) flowrate. Changes to the pore structure brought about by dissolution were captured in situ using X-ray microtomography (micro-CT) imaging. Mass balance from effluent analysis showed a good agreement with calculations from imaging. Image calculated reaction rates (reff) were 5-38 times lower than the corresponding batch reaction rate under the same conditions of temperature and pressure but without mass transfer limitations. For both high (Péclet number=2600-1200) and low (Péclet number=420-300) flow rates, an impact of the initial rock heterogeneity was observed on both reaction rates and permeability-porosity relationships.

Improved quantification of the porosity–permeability relationship of limestones using petrographical texture

The relationship between porosity and permeability in limestones is a fundamental constitutive equation in subsurface fluid flow modelling, and is essential in quantifying a range of geological processes. For a given porosity, the permeability of limestones varies over a range of up to five orders of magnitude. Permeability of a given rock sample depends on the total amount of pore space, characterized by porosity, as well as how the pore space is distributed within the rock, which can be expressed as a probability density function of pore sizes. We investigate in this study whether the information about pore-size distribution can be sufficiently captured by the bulk petrographical properties extracted from thin sections. We demonstrate that most of the uncertainty can be explained by variations in texture, which is defined by the mud content (mass fraction of particles less than 0.06 mm in diameter). Using mud content as a quantitative texture descriptor, we used multivariable regression and neural network models to predict permeability from porosity. For a given porosity, inclusion of mud content reduces the uncertainty in permeability prediction from five to two orders of magnitude.

Porosity, permeability and compaction trends for Scandinavian regoliths

Abstract Weathered crystalline and metamorphic basement are proven as hydrocarbon reservoir rock in many areas of the world, including the Norwegian Continental Shelf. The reservoir properties of these rocks vary laterally and vertically as a function of the burial history, initial basement lithologies, sub-aerial exposure to weathering processes, chemical weathering, fault patterns, and these properties are relatively unknown. In this work, laboratory measurements are performed on different regolith types applying varying confining pressures representative for different degrees of basement weathering and burial depth. Porosity and permeability are measured on coherent samples (altered basement) and incoherent samples (disintegrated basement rock and saprolites) from the Utsira High (offshore Norway), and outcrop samples from Bomlo (southwestern Norway) and Ivo Klack (southern Sweden). Coherent samples from Utsira High (well 16/1-15 and 16/1-12) give porosities between 5.10% and 7.95% and permeabilities between 1.08 and 3.30 mD at 5.1 MPa, and indicate a relation between observed micro-fractures and decreasing permeabilities. In general, permeability increases with increasing amount of micro-fractures. The permeability is varying from 0.15 mD at 30 MPa to 3.30 mD at 5.1 MPa. This work presents the first published compaction curves for weathered basement (saprock and saprolites), and to our knowledge first permeability-porosity relationships for saprock and saprolites from three locations (Bomlo, Ivo Klack and Utsira High). The new porosity and permeability measurements of weathered basement rocks can be used as input parameters for reservoir modelling, basin modelling, field planning and hydrocarbon exploration in areas with regoliths. It can also serve as important input into hydrogeology, geothermal modelling, planning of tunnels, and as help to understand landslides and hillslope gullies in weathered basement.

Numerical Simulation Modeling of Carbonate Reservoir Based on Rock Type

There are many types of carbonate reservoir rock spaces with complex shapes, and their primary pore structure changes dramatically. In order to describe the heterogeneity of K carbonate reservoir, equations of porosity, permeability and pore throat radii under different mercury injection saturations are fitted, and it shows that 30% is the best percentile. R30 method is presented for rock typing, and six rock types are divided according to R30 value of plugs. The porosity-permeability relationship is established for each rock type, and their relevant flow characteristics of each rock type have been studied. Logs are utilized to predict rock types of noncored wells, and a three-dimensional (3D) rock type model has been established based on the well rock type curves and the sedimentary facies constraint. Based on the relationship between J function and water saturation, the formula of water saturation, porosity, permeability, and oil column height can be obtained by multiple regressions for each rock type. Then, the water saturation is calculated for each grid, and a 3D water saturation model is established. The model can reflect the formation heterogeneity and the fluid distribution, and its accuracy is verified by the history matching.

An innovative technique for estimating water saturation from capillary pressure in clastic reservoirs

A major drawback of old resistivity tools is the poor vertical resolution and estimation of hydrocarbon when applying water saturation (Sw) from historical resistivity method. In this study, we have provided an alternative method called saturation height function to estimate hydrocarbon in some clastic reservoirs in the Niger Delta. The saturation height function was derived from pseudo capillary pressure curves generated using modern wells with complete log data. Our method was based on the determination of rock type from log derived porosity-permeability relationship, supported by volume of shale for its classification into different zones. Leverette-J functions were derived for each rock type. Our results show good correlation between Sw from resistivity based method and Sw from pseudo capillary pressure curves in wells with modern log data. The resistivity based model overestimates Sw in some wells while Sw from the pseudo capillary pressure curves validates and predicts more accurate Sw. In addition, the result of Sw from pseudo capillary pressure curves replaces that of resistivity based model in a well where the resistivity equipment failed. The plot of hydrocarbon pore volume (HCPV) from J-function against HCPV from Archie shows that wells with high HCPV have high sand qualities and vice versa. This was further used to predict the geometry of stratigraphic units. The model presented here freshly addresses the gap in the estimation of Sw and is applicable to reservoirs of similar rock type in other frontier basins worldwide.

Forecast of Reactive CO2 Injection into a Carbonate Formation, Middle East

This paper describes the results of reservoir and reactive transport modelling using MoReS-PHREEQC to study the long-term fate of CO2 injection in a carbonate aquifer. The heterogeneous model is based on a geological model built in Petrel, contains faults, various rock types, and various porosity-permeability relationships. The mineralogy of the target formation is dominated by calcite, but also contains dolomite. The results show that CO2 predominantly migrates along the high permeability zones at the top and the bottom of the target formation where CO2 is injected into. Impermeable layers (aquitards) on top of the target formation effectively block upwards migration. However, the plume reaches a conductive fault at the end of the injection (after 30 years), causing upward migration of CO2. Migration of CO2 into the fault appeared to be sensitive to the injection well location and different realizations of the geological model. Accurate mapping of faults and choice of injection well locations are therefore important for controlling CO2 conformance with time. Dissolution and dissociation of CO2 lowers the pH, leading to buffering by calcite and dolomite dissolution, as well as precipitation of anhydrite and celestine. The mineral amounts that dissolved or precipitated are relatively small and lead to porosity increase up to 0.03% within the impacted zone after 1,000 years. The geochemical impact of CO2 injection into the carbonate aquifer is therefore relatively low.

Numerical Simulation of the CO2 Behavior to Obtain a Detailed Site Characterization: A Case Study at Nagaoka Pilot-scale Injection Site

This paper discusses a methodology for the site characterization of deep saline reservoirs evaluated through dynamic flow simulations. Not only the detailed site characterization techniques, but also the injection and monitoring data are useful for the characterization of geological storage. Adopting the Nagaoka site as a test field, we constructed a geological model based on a seismic attribute data. Core and logging data analyses suggested that the petrophysical properties had facies dependency and heterogeneity. After building a model, we conducted flow simulations by TOUGH2/ECO2N. The model was calibrated by the bottom-hole pressure and breakthrough time at the observation wells. We selected porosity-permeability relationships, vertical/horizontal permeability ratio, and pore compressibility as the parameter for the history matching. For the systematic search of the best matched model, we used design of experience techniques and obtained a best matched model. Using the model, we investigated long-term fate of injected CO2 up to 1000 years. In this simulation we considered a reactive transport model. These results demonstrated that temporal change of trapping mechanisms at the Nagaoka site.

Characterisation of reactive transport in pore-scale correlated porous media

We apply a reactive transport model to study the effect of correlation length on dissolution and to characterise reactive transport in pore-scale correlated porous media. Porous media with different correlation lengths are derived from correlated fields. An efficient numerical model is employed to simulate dissolution on these geometries for a range of Péclet and Damköhler numbers. The solute concentration distribution is presented in porous media for both low and high correlation lengths. Four types of dissolution patterns are observed in various correlated porous media: face dissolution, uniform dissolution, wormholing and mixed dissolution. The permeability-porosity relationships are also studied in simulations of porous media with different correlation lengths. The permeability in larger correlation length media increases faster at the same Damköhler number. Dissolution patterns of all cases are plotted in a diagram and the effect of correlation length on reaction regimes are analysed. The findings show that larger correlation lengths can result in more uniform and wormholing types of dissolution but less face dissolution. Correlation length plays a critical role in characterising the reaction regimes during reactive transport.

A rock physics and seismic reservoir characterization study of the Rock Springs Uplift, a carbon dioxide sequestration site in Southwestern Wyoming

We present a reservoir geophysics study, including rock physics modeling and seismic inversion, of a carbon dioxide sequestration site in Southwestern Wyoming, namely the Rock Springs Uplift, and build a petrophysical model for the potential injection reservoirs for carbon dioxide sequestration. Our objectives include the facies classification and the estimation of the spatial model of porosity and permeability for two sequestration targets of interest, the Madison Limestone and the Weber Sandstone. The available dataset includes a complete set of well logs at the location of the borehole available in the area, a set of 110 core samples, and a seismic survey acquired in the area around the well. The proposed study includes a formation evaluation analysis and facies classification at the well location, the calibration of a rock physics model to link petrophysical properties and elastic attributes using well log data and core samples, the elastic inversion of the pre-stack seismic data, and the estimation of the reservoir model of facies, porosity and permeability conditioned by seismic inverted elastic attributes and well log data. In particular, the rock physics relations are facies-dependent and include granular media equations for clean and shaley sandstone, and inclusion models for the dolomitized limestone. The permeability model has been computed by applying a facies-dependent porosity-permeability relation calibrated using core sample measurements. The study shows that both formations show good storage capabilities. The Madison Limestone includes a homogeneous layer of high-porosity high-permeability dolomite; the Weber Sandstone is characterized by a lower average porosity but the layer is thicker than the Madison Limestone.

Integration of depositional, petrophysical, and petrographic facies for predicting permeability in tight gas reservoirs

Understanding the linkages between grain mineralogy and diagenetic and sedimentary processes enhances the reliability of petrophysical models to predict reservoir deliverability from permeability. Petrographic data within well-defined depositional facies reveal the diagenetic evolution of porosity-permeability relationships. Formation evaluation methods relying solely on petrophysical rock typing are seriously limited when predicting ultimate reservoir performance in complex pore structures. The Almond Formation, Wyoming, is characterized by three depositional facies associations — shoreface, deltaic (bay head and flood tide), and fluvial-coastal plain — which present three distinctive porosity-permeability trends. Textural features resulting from depositional processes, such as grain size and sorting, vary little between facies associations, yet permeability can vary by up to four orders of magnitude for the same porosity value. Differences between petrophysical facies are primarily driven by diagenetic (cementation and grain dissolution) effects on different framework grain compositions (petrographic facies). Therefore, the main difference between the facies associations is diagenetic, due to provenance and transport mechanisms. The characterization of depositional and diagenetic controls on pore geometry allows the narrowing of uncertainty in absolute permeability prediction. We have quantified the relationship between depositional facies, with their specific mineral composition and diagenetic overprint, and the steepness functions in porosity-permeability space. This analysis allowed us to effectively reduce the uncertainty in the prediction of initial gas production from wireline logs.

Longitudinal and radial permeability analysis of additively manufactured porous scaffolds: Effect of pore shape and porosity

While in practice cell ingrowth in scaffolds mostly occurs radially, the recent literature has mainly emphasized on modeling permeability under unidirectional flows. In this article, we attempt to introduce the radial flow direction as another important factor for scaffold internal architecture design, and thereby show its trade-off with the conventionally studied longitudinal permeability. To this end, a set of computational models is developed for different lattice and triply periodic minimal surface-based geometries to predict the corresponding structure-property relationships with respect to different porosity levels. Also, permeability is experimentally investigated for different values of porosity through 3D-printing of the selected critical structures as identified by the numerical models; namely Hexagonal and Rhombic Dodecahedron. Relative to the longitudinal permeability, the normalized radial permeability is shown to change by −51.2% and 39.4% for Hexagonal and Rhombic Dodecahedron, respectively, implying the necessity of including radial permeability as a more realistic computational tool for the design of scaffold pore architecture. Moreover, the permeability-porosity relationship was developed through both the power law as well as the Kozeny-Carman models and the effects of experimental conditions on the permeability values were discussed.

The estimation of permeability of a porous medium with a generalized pore structure by geometry identification

The paper presents an approach for estimating the permeability of a porous medium that is based on the characteristics of the porous structure. The pressure drop in different fluid flow passages is estimated and these are combined to evaluate the overall reduction. The theory employed is presented and the level of accuracy for different cases is discussed. The successive steps in the solution algorithm are described. The accuracy and computational efficiency of the approach are compared with results obtained from a finite-element-based multiphysics formulation. It is shown that for a comparable accuracy, the computational efficiency of the approach can be two orders of magnitude faster. Finally, the model predictions are examined with conventional relationships that have been reported in the literature and are based on permeability-porosity relationships. It is shown that estimating the permeability of a porous medium using porosity can lead to an order of magnitude error and the expected permeability range in different porosities is presented using 10 000 random structures.