Prediction Of Relative Permeability Research Articles

Prediction of relative permeability from capillary pressure based on the fractal capillary bundle model

The accurate prediction of relative permeability is one of the most important issues in the study of multiphase flow in porous media and is involved in many fields, such as geothermal energy development and petroleum engineering. Traditional models such as the Purcell model and Burdine model for predicting relative permeability from capillary pressure usually assume that the wetting phase (WP) flows in small pores and that the nonwetting phase (NWP) flows in large pores, which is a limiting assumption, such that these models cannot describe the process of WP being displaced by NWP. In this study, we propose a generalized theoretical model for calculating relative permeability based on the fluid distribution characteristics and the fractal capillary bundle model. The relative location α of the interface between NWP and WP is introduced to characterize the transport of the two-phase interface in porous media. The developed model was validated with relative permeability experimental data of gas–water/oil and compared with the Li model and the Brooks–Corey model. The comparison results show that the new model provides an improved match to experimental data than the Li model and the Brooks–Corey model. The sensitivity analysis results of the model show that tortuosity and pore size distribution play a key role in predicting relative permeability from the capillary pressure curve. The relative permeability of wetting phase decreases significantly with increasing fractal dimension of tortuosity and fractal dimension of pore size distribution. The effect of parameter α, which reflects fluid transport characteristics, on relative permeability of wetting phase is more pronounced in porous media with complex structures and low/ultralow permeability.

Predictive Model for Relative Permeability Using Physically-Constrained Artificial Neural Networks

Summary Hysteresis of transport properties like relative permeability (kr) can lead to computational problems and inaccuracies for various applications including CO2 sequestration and chemical enhanced oil recovery (EOR). Computational problems in multiphase numerical simulation include phase labeling issues and path dependencies that can create discontinuities. To mitigate hysteresis, modeling kr as a state function that honors changes in physical parameters like wettability is a promising solution. In this research, we apply the state function concept to develop a physics-informed data-driven approach for predicting kr in the space of its state parameters. We extend the development of the relative permeability equation-of-state (kr-EoS) to create a predictive physically-constrained model using artificial neural networks (ANNs). We predict kr as a function of phase saturation (S) and phase connectivity (χ^), as well as the specific S-χ^ path taken during the displacement while maintaining other state parameters constant such as wettability, pore structure, and capillary number. We use numerical data generated from pore-network modeling (PNM) simulations to test the predictive capability of the EoS. Physical limits within S-χ^ space are used to constrain the model and improve its predictability outside of the region of measured data. We find that the predicted relative permeabilities result in a smooth and physically consistent estimate. Our results show that ANN can more accurately estimate kr surface compared to using a high-order polynomial response surface. With only a limited amount of drainage and imbibition data with an initial phase saturation greater than 0.7, we provide a good prediction of kr from ANN for all other initial conditions, over the entire S-χ^ space. Finally, we show that we can predict the specific path taken in the S-χ^ space along with the corresponding kr for any initial condition and flow direction, making the approach practical when phase connectivity information is unavailable. This research demonstrates the first application of a physics-informed data-driven approach for the prediction of relative permeability using ANN.

Experimental and Modeling Study of Water Imbibition and Flowback in Shale: Prediction of Relative Permeability and Capillary Pressure Curves

Experimental and Modeling Study of Water Imbibition and Flowback in Shale: Prediction of Relative Permeability and Capillary Pressure Curves

Prediction of gas–water relative permeability in tight rock from movable fluid distribution with nuclear magnetic resonance

The measurement of the relative permeability in tight rock is challenging due to its ultralow permeability and the time-consuming nature of the experiments. Studying the movable and unmovable fluid distribution and establishing a reliable relative permeability prediction model is an urgent problem to be solved. This paper used nuclear magnetic resonance (NMR) to investigate movable and unmovable water distribution in tight sandstone under different centrifugal forces. A new method for predicting gas–water relative permeability in tight rock is established based on movable fluid distribution using the capillary bundle model. The results show that the distribution of movable and unmovable fluids is strongly influenced by the tight rock's pore size distribution and structure. The unmovable fluid saturation increases as the tight rock's permeability and median radius decrease. The nonlinear correlation between the NMR relaxation time and the pore throat size obtained from high-pressure mercury intrusion can be used to derive the pore size of the fluid distribution in tight rocks. The ratio of the movable fluid thickness to pore throat size increases near linearly with the logarithm of the pore throat size. The proposed mathematical model for the prediction of gas-water relative permeability based on movable fluid distribution is verified by comparing with the normalized relative permeability curve measured from experiments. This new model offers an alternative method of estimating the gas–water relative permeability when measurement is unavailable due to the ultralow permeability of the core samples.

From 3D real structure to 3D modelled structure: Modelling water vapor permeability in polypropylene/cellulose composites

A 3D tri-phasic numerical model was developed to predict water vapor permeability in composite materials made of polypropylene (PP) as matrix and cellulose particles as fillers, with existence of an interphase around permeable inclusions. About 70 tri-phasic structures composed of ellipsoidal, heterogenous-size particles were generated to represent composites with four different filler contents (φp=2.96−6.06−12.67−19.91%v/v) with interfacial region at the filler/matrix interface (either 1 or 2 μm thick) displaying its own permeability. The relative permeability (i.e., ratio between composite and neat matrix permeability) was calculated from Finite Element Method (FEM) simulations on these structures. A good prediction of experimental relative permeability for the whole filler content range investigated was observed. The presence of a percolating interphase observed in some structures explains the high permeabilization observed for high φp. The proposed 3D numerical model was confronted to five state-of-the art analytical models and was the only one able to describe the observed complex structures with identification of reliable characteristics for the interphase (thickness, permeability).

Using Nano-XRM and High-Contrast Imaging to Inform Micro-Porosity Permeability During Stokes–Brinkman Single and Two-Phase Flow Simulations on Micro-CT Images

Carbonate rocks have multiscale pore systems that are weakly understood. In this study, we use combined experimental, modeling, and pore space generation methods to tackle the impact of microporosity on the flow properties of Estaillades limestone. First, a nano-core from a microporous grain of Estaillades limestone was scanned using nanotomography (nano-XRM). The information from the nano-XRM scan was then used as input into an object-based pore network generator, on which permeability fields were simulated for a range of porosities, creating a synthetic Kozeny–Carman porosity–permeability relationship targeted for the specific microporous system present in Estaillades. We found a good match between the experimental and simulated Mercury Intrusion Capillary Pressure (MICP) range in the imaged geometry and a good match between the imaged and object-generated permeabilities and MICP. A micro-core of Estaillades was then scanned using X-ray microtomography (μCT), the differential pressure was measured during single-phase flow, and the rock was flooded with doped brine. The contrast between the images was used to assign a porosity to each voxel of connected microporosity. The flow through the pore space was solved using the Stokes–Brinkman (S–B) and Stokes-only solvers, and the differences between the measured permeability and computed permeabilities were evaluated. An agreement was seen between the computed permeability of the Stokes and S–B simulation with the measured permeability. However, the velocity fields with the S–B simulation captured stagnant regions of the pore space that were not present in the Stokes simulations. Additionally, we investigated the implications of including microporosity in the estimation of relative permeability. Nitrogen was experimentally co-injected through the core with doped brine at a 50% fractional flow and imaged to capture the two-phase effective permeability and was compared with the simulated numerical permeability. The Stokes simulation was not able to predict relative permeability with this method due to the major flow paths in the macroporosity being impeded by the injected non-wetting phase. The S–B simulations, however, allowed flow in the microporous regions around these blocked flow paths and were able to achieve a relative permeability prediction that was a reasonable match to the experimental measurement.

In-situ hydrogen wettability characterisation for underground hydrogen storage

Hydrogen storage in subsurface aquifers or depleted gas reservoirs represents a viable long-term energy storage solution. There is currently a scarcity of subsurface petrophysical data for the hydrogen system. In this work, we determine the wettability and Interfacial Tension (IFT) of the hydrogen-brine-quartz system using captive bubble, pendant drop and in-situ 3D micro-Computed Tomography (CT) methods. Effective contact angles ranged between 29° and 39° for pressures 6.89–20.68 MPa and salinities from distilled water to 5000 ppm NaCl brine. In-situ methods, novel to hydrogen investigations, confirmed the water-wet system with the mean of the macroscopic and apparent contact angle distributions being 39.77° and 59.75° respectively. IFT decreased with increasing pressure in distilled water from 72.45 mN/m at 6.89 MPa to 69.43 mN/m at 20.68 MPa. No correlation was found between IFT and salinity for the 1000 ppm and 5000 ppm brines. Novel insights into hydrogen wetting in multiphase environments allow accurate predictions of relative permeability and capillary pressure curves for large scale simulations. • Comprehensive characterisation of hydrogen-brine-quartz wettability. • Novel investigation of in-situ contact angle for underground hydrogen storage. • Contact angle on smooth rock surface 27–39° and at in situ conditions 39.77–59.75°. • Deficit curvature analysis confirms a water-wet system. • IFT from 72.45 mN/m at 6.89 MPa to 69.43 mN/m at 20.68 MPa.

Intelligent Microfluidics Research on Relative Permeability Measurement and Prediction of Two-Phase Flow in Micropores

Relative permeability is a key index in resource exploitation, energy development, environmental monitoring, and other fields. However, the current determination methods of relative permeability are inefficient and invisible without considering wetting order and pore structure characteristics either. In this study, microfluidic experiments were designed for figuring out key factors impacting on the two-phase relative permeability. The optimized intelligent image recognition was established for saturation extraction. The deep learning was conducted for the prediction of two-phase permeability based on the inputs from microfluidic experiments and image recognition and optimized. Results revealed that phase saturation, wetting order, and pore topology were the key factors influencing the two-phase relative permeability, with the importance of 38.22%, 34.84%, and 26.94%, respectively. The deep learning-based relative permeability model performed well, with MSE < 0.05 and operational efficiency of 3 ms/epoch. Aiming at relative permeability model optimization, on the one hand, the dividing ratio of training set and testing set for flooding phase relative permeability prediction achieved the highest prediction accuracy at 7 : 3, while that for displaced phase was 6 : 4. On the other hand, tanh() activation function performed 40% more accurate than the sigmoid() activation function.

Simple Graphical Prediction of Relative Permeability of Unsaturated Soils under Deformations

At present, there are only a few existing models that can be used to predict the relative permeability of unsaturated soil under deformations, and the calculation process is relatively complex. In order to fit the measured value of the relative permeability coefficient of unsaturated soil before deformation, this work employs the simplified unified model of the relative permeability coefficient of unsaturated soil, and it obtains the index λ before deformation of the soil. In addition, the value of index λ remains unchanged before and after deformation. Based on the actual measured value of the soil–water characteristic curve before deformation, the air-entry value prediction model is used to predict the air-entry value of soil with different initial void ratios. The relative permeability coefficient of unsaturated soil is then conveniently predicted using the graphical method in combination with the simplified unified model. The method is validated by using the test data of silt loam, sandy loam, and unconsoildated sand. The results show that the predicted results are consistent with the measured values. The prediction method in this paper is simple and overcomes the limitations associated with the determination of the index λ. It expands the application range of the unsaturated relative permeability coefficient model while improving the accuracy of predictions.

Pore-scale numerical prediction of three-phase relative permeability in porous media using the lattice Boltzmann method

Three immiscible fluids systems are often encountered in energy and environmental disciplines, especially in the oil exploration field. It is essential to enhance oil recovery (EOR) by identifying the three-phase fluid flow mechanism of oil-gas-water system in complex geological structures. In the present study, a lattice Boltzmann (LB) color gradient model for three immiscible fluid flow in three-dimensional porous media is employed and validated using five benchmarks (i.e., the multiphase spinodal decomposition; the multiphase Young-Laplace test; the liquid lens; contact angles and 3D channel layered three-phase fluid flow). The effects of wettability, viscosity ratio (M) and capillary number (Ca) on the relative permeability curves are analyzed in detail. When the wetting condition is enhanced, the results indicate that the relative permeability of non-wetting phase raises while that for the wetting phase exhibits a decline. When M is not equal 1, the relative permeability of high viscosity phase is significantly increased, while the other two phases are less affected. Meanwhile, the maximal value of relative permeability does not exceed unity because of the low porosity in the porous medium. For the influence of Ca, simulation results indicate the relative permeability shows weak sensitivity to Ca.

Prediction of three-phase relative permeabilities of Berea sandstone using lattice Boltzmann method

Three-phase flows through a pore network of Berea sandstone are studied numerically under critical interfacial tension conditions. Results show that the relative permeability of each fluid increases as its own saturation increases. The specific interfacial length between wetting and nonwetting fluids monotonously decreases with increasing the saturation of intermediate-wetting fluid, while the other two specific interfacial lengths exhibit a nonmonotonous variation. As the wetting (nonwetting) fluid becomes less wetting (nonwetting), the relative permeability of wetting fluid monotonously increases, while the other two relative permeabilities show a nonmonotonous trend. Due to the presence of a spreading layer, the specific interfacial length between wetting and nonwetting fluids always stabilizes at a low level. As the viscosity ratio of wetting (nonwetting) to intermediate-wetting fluids increases, the relative permeability of wetting (nonwetting) fluid increases. With the viscosity ratio deviating from unity, the phase interfaces become increasingly unstable, leading to an increased specific interfacial length.

Effects of Water Retention Curves and Permeability Equations on the Prediction of Relative Air Permeability

AbstractAppropriate simulation of air flow in porous media needs an accurate estimate of relative air permeability (RAP). Combining 2 traditional and 2 fractal water retention curves (WRCs) respectively with 6 permeability equations, we obtained 12 statistical and 12 fractal RAP models. All these models were subsequently tested with 31 experimental datasets of disturbed soils to examine their predictive ability for RAP. Results showed that irrespective of using traditional or fractal WRCs, the six permeability equations exhibit consistent performances for RAP prediction. The modified Burdine (Yang & Mohanty, 2015, https://doi.org/10.1002/2014wr016190) permeability equation best fits the published soil data. In addition, the selection of a proper permeability equation is critical for accurately predicting the RAP, whereas the choice of WRCs has little effect on RAP prediction. This finding suggests that for disturbed soils, air permeability is primarily dictated by the pore tortuosity‐connectivity but not the pore size distribution inferred from the WRCs.

Artificial Neural Network Models and Predicts Reservoir Parameters

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 19854, “Modeling and Prediction of Resistivity, Capillary Pressure, and Relative Permeability Using Artificial Neural Network,” by Mustafa Ba alawi, SPE, King Fahd University of Petroleum and Minerals; Salem Gharbi, SPE, Saudi Aramco; and Mohamed Mahmoud, King Fahd University of Petroleum and Minerals, prepared for the 2020 International Petroleum Technology Conference, Dhahran, Saudi Arabia, 13–15 January. The paper has not been peer reviewed. Copyright 2020 International Petroleum Technology Conference. Reproduced by permission. Capillary pressure and relative permeability are essential measurements that affect multiphase fluid flow in porous media directly. The processes of measuring these parameters, however, are both time-consuming and expensive. Artificial-intelligence methods have achieved promising results in modeling extremely complicated phenomena in the industry. In the complete paper, the authors generate a model by using an artificial-neural-network (ANN) technique to predict both capillary pressure and relative permeability from resistivity. Capillary Pressure and Resistivity Capillary pressure and resistivity are two of the most significant parameters governing fluid flow in oil and gas reservoirs. Capillary pressure, the pressure difference over the interface of two different immiscible fluids, traditionally is measured in the laboratory. The difficulty of its calculation is related to the challenges of maintaining reservoir conditions and the complexity of dealing with low-permeability and strong heterogeneous samples. Moreover, unless the core materials are both available and representative, a restricted number of core plugs will lead to inadequate reservoir description. On the other hand, resistivity can be obtained by either lab-oratory analysis or through typical and routine well-logging tools in real time. Both parameters have similar attributes, given their dependence on wetting-phase saturation. Despite many studies in the literature that are reviewed in the complete paper, improvement of capillary pressure and resistivity modeling remains an open research area. Artificial Intelligence in Petroleum Engineering In addition to labor and expense concerns, conventional methods to measure resistivity, capillary pressure, and relative permeability depend primarily, with the exception of resistivity from well logs, on the availability of core samples of the desired reservoir. The literature provides several attempts to model these parameters in order to avoid many of the requirements of measurement. However, the performance of many of these models is restricted by assumptions and constraints that require further processing. For example, the accuracy of prediction of capillary pressure from resistivity is highly dependent on the tested core permeability, which requires measuring it as well to achieve the full potentiality of the model.

Multiphase flow modeling in multiscale porous media: An open-source micro-continuum approach

A multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume averaging principles, where a unique set of partial differential equations is used to represent flow in both regions and scales. The crux of the proposed model is that it tends asymptotically towards the Navier-Stokes volume-of-fluid approach in solid-free regions and towards the multiphase Darcy equations in porous regions. Unlike existing multiscale multiphase solvers, it can match analytical predictions of capillary, relative permeability, and gravitational effects at both the pore and Darcy scales. Through its open-source implementation, hybridPorousInterFoam, the proposed approach marks the extension of computational fluid dynamics (CFD) simulation packages into porous multiscale, multiphase systems. The versatility of the solver is illustrated using applications to two-phase flow in a fractured porous matrix and wave interaction with a porous coastal barrier.

On the prediction of three-phase relative permeabilities using two-phase constitutive relationships

The predictions of two recent and two classical mathematical models are compared with experimentally measured three-phase relative permeabilities. Experimentally determined constitutive relationships in two-phase systems were used as model input parameters to numerically predict relative permeabilities (kr) in three-phase systems. Then the estimated results were compared with experimental three-phase permeabilities measured along decreasing water saturation/decreasing oil saturation/increasing gas saturation (DDI) paths. The results of the individual models to each of the three fluids involved (water, oil, and gas) were analyzed in detail. The simulated results showed that the Total Differential (TD) compatible model overestimates significantly both the global mobilities as well as the relative phase permeabilities in the three-phase system. There was improvement in the prediction with the TD compatible model when experimental data were used to locally impose the global mobility and fractional water and gas fluxes in the ternary diagram. Globally, the best prediction of the measured kr values was obtained with the so-called mechanistic model. However, its numerical implementation requires a preliminary calibration of the relative phase permeabilities in a three-phase system against experimental data along one DDI path to quantify the required six characteristic coefficients. In contrast to the TD compatible model, which by construction does not exhibit any numerical instabilities, elliptic zones in the water-oil (NAPL)-gas ternary diagram were identified in the mechanistic model.

Pore-by-pore modeling, analysis, and prediction of two-phase flow in mixed-wet rocks.

A pore-network model is an upscaled representation of the pore space and fluid displacement, which is used to simulate two-phase flow through porous media. We use the results of pore-scale imaging experiments to calibrate and validate our simulations, and specifically to find the pore-scale distribution of wettability. We employ energy balance to estimate an average, thermodynamic, contact angle in the model, which is used as the initial estimate of contact angle. We then adjust the contact angle of each pore to match the observed fluid configurations in the experiment as a nonlinear inverse problem. The proposed algorithm is implemented on two sets of steady state micro-computed-tomography experiments for water-wet and mixed-wet Bentheimer sandstone. As a result of the optimization, the pore-by-pore error between the model and experiment is decreased to less than that observed between repeat experiments on the same rock sample. After calibration and matching, the model predictions for capillary pressure and relative permeability are in good agreement with the experiments. The proposed algorithm leads to a distribution of contact angle around the thermodynamic contact angle. We show that the contact angle is spatially correlated over around 4 pore lengths, while larger pores tend to be more oil-wet. Using randomly assigned distributions of contact angle in the model results in poor predictions of relative permeability and capillary pressure, particularly for the mixed-wet case.

Permeability determination of hydrate sediments and a new reduction model considering hydrate growth habit

The saturation (SH) and growth habit of hydrates in sediments directly affect the evaluation of permeability. This work was devoted to evaluating the growth habit of hydrates in sediments by permeability measurements. The water effective permeability of hydrate sediments with different SH was obtained, and these permeability data were excellent in stability and accuracy. The change of differential pressure of hydrate sediments with water injection was completely recorded, it was a new found that the differential pressure was unstable in the first few minutes, and it is not recommended to employ short–term data to evaluate the permeability of the hydrate sediments. Based on the hypothesis of wedge tetrahedral filling of sediment particles, the growth habits of hydrates were compered in the models of hydrate coating grain and occupying pore center respectively. By analyzing the experimental data with the reduction models in different hydrate growth habits, it was founded that the hydrates were more likely to form in the pore centers rather than coating grains. Finally, the ratio of the internal surface area of pore space with and without hydrate was simplified to an expression related to SH in a new model of water relative permeability. This model could distinguish the growth habits of hydrate in porous media and provide a more accurate prediction of water relative permeability.

On the prediction of permeability and relative permeability from pore size distributions

This paper addresses the calculation of the relative permeability of concrete and rocks with a model that is aimed at being implemented in large scale computations for evaluating the tightness of vessels. To this end, it is necessary to rely on some fast procedure and a random hierarchical capillary approach is used. It is based on the extension of an existing model proposed initially to describe the evolution of the intrinsic permeability of mortar undergoing micro-cracking. First, the efficiency of this existing model is tested on several types of concretes and rocks, with permeability spanning over 6 orders of magnitude. Then, the model is adapted to obtain the relative permeability to gas and liquid as a function of the saturation of the porous solid with respect to the liquid phase. The extended model is shown to provide reasonably accurate predictions for several concretes and rocks tested in the literature.

A Novel Relative Permeability Model for Gas and Water Flow in Hydrate-Bearing Sediments With Laboratory and Field-Scale Application

In a producing gas hydrate reservoir the effective porosity available for fluid flow constantly changes with dissociation of gas hydrate. Therefore, accurate prediction of relative permeability using legacy models (e.g. Brooks-Corey (B-C), van Genuchten, etc.) that were developed for conventional oil and gas reservoirs would require empirical parameters to be calibrated at various Sh over its range of variation, but such calibrations are precluded because of lack of experimental relative permeability data. This study proposes a new relative permeability model for gas hydrate-bearing media that is a function of maximum capillary pressure, capillary entry pressure, pore size distribution index, residual saturations, hydrate saturation, and four other constants. The three novel features of the proposed model are: (i) requires fitting its six empirical parameters only once using experimental data from any single Sh, and the same set of empirical parameters predict relative permeability at all Sh, (ii) includes the effect of capillarity, and (iii) includes the effect of pore-size distribution. From practical standpoint, the model can be used to simulate multiphase flow in gas hydrate-bearing sediments where the proposed relative permeability can account for the evolving hydrate saturation. The proposed model is implemented in a numerical simulator and the wall time required to perform simulations using the proposed model is shown to be similar to the time it takes to run same simulations with the B-C model. The proposed model is a step forward towards achieving the goal of physically accurate modeling of multiphase flow for gas hydrate-bearing sediments that accounts for the effect of gas hydrate saturation change on relative permeability.

A Hybrid Approach for the Prediction of Relative Permeability Using Machine Learning of Experimental and Numerical Proxy SCAL Data

Summary Accurate estimation of relative permeability is one of the key parameters for decision making in upstream applications from project appraisal to field development and evaluation of various field development options. In this study, we identify Euler number (Arns et al. 2001) (a quantitative measure of fluid connectivity/distribution) and saturation as being the first-order predictors of relative permeability and develop a reliable correlation between them using machine learning of experimental special core analysis (SCAL) data and pore network simulation results. In order to achieve our objective, first, we developed a machine-learning model based on the random forest algorithm (Breiman 2001) to analyze specific SCAL data that indicates a key missing feature in the traditional saturation-based relative permeability prediction. We identified this missing feature and proposed the Euler characteristic as a potential first-order predictor of relative permeability in combination with in-situ fluid saturations. We generated “artificial” relative permeability data using pore network simulation (Valvatne and Blunt 2004) by systematically varying a set of key parameters such as pore geometry, wettability, and saturation history. Subsequently, we used machine learning to rank the importance of each parameter and identify possible correlative responses to those selected variables. At a fixed saturation (zero-dimensional volumetric abundance) and Euler number coordinates, the relative permeability is very consistent and varies insignificantly across different cases, suggesting these two parameters as first-order predictors. Euler number characterizes the fluid connectivity/distribution, while saturation represents the net volumetric fluid quantity. We believe that Euler number could be the missing first-order predictor in traditional saturation-based predictive relative permeability models, especially for connected pathway dominated flow regime. Finally, we identified the quantitative relationship between relative permeability and Euler characteristic, and present a reliable correlation to determine the relative permeability on the basis of Euler number and saturation.