Brooks-Corey Model Research Articles

Algebraic model for one-dimensional horizontal water flow with arbitrary initial soil water content

A simple analytical solution of the equation for the one-dimensional horizontal permeability of soil water is important for estimating the hydraulic properties of soil. Our main objective was to develop analytical solutions to the nonlinear Richards equation, with constant-saturation upper boundary and an arbitrary initial soil water content (SWC) for horizontal absorption. We estimated the infiltration rate based on the hypothesis proposed by Parlange and carried out a series of transformations based on the Brooks–Corey model to obtain a theoretical function of the one-dimensional movement of water in unsaturated soil under an arbitrary initial SWC. The algebraic analytical solutions were simple, and the selection of the initial SWC was arbitrary. We assumed three scenarios of linear distributions of initial SWC, and Hydrus-1D software was used to simulate horizontal infiltration. Based on the comparison of algebraic and numerical results, the corrected algebraic model was proposed and verified by the arbitrary initial water content conditions when the maximum SWC was less than the half of saturated water content. The proposed method provides a description of horizontal infiltration for the heterogeneous initial SWCs.

Unsaturated hydraulic conductivity of compacted bio-cemented lateritic soil in municipal solid waste containment application

Most engineering infrastructures, including municipal solid waste containment facilities, are situated in unsaturated zone. The use of chemical additives for soil improvement has been linked to the adverse environmental issues being experienced globally. Research into more sustainable methods of soil improvement has led to the discovery of a novel and innovative method known as microbial induced calcite precipitation (MICP). Lateritic soil was treated with stepped Sporosarcina pasteurii (S. pasteurii) suspension density up to 2.40 x 109 cells/ml at moulding water content (MWC) -2, 0 and +2 % relative to optimum moisture content (OMC) before compaction using Reduced British Standard light (RBSL), British Standard light (BSL), West African Standard (WAS) or Intermediate and British Standard heavy (BSH) energies. Compacted specimens were saturated with cementation reagent in three cycles with 1/3rd pore volume at 6 hours’ interval to induce calcite precipitation at an ambient laboratory temperature of 24±2°C. The soil-water characteristics curves (SWCC) of the specimens were determined using pressure plate extractor over a pressure range of 10-1500 kPa. Unsaturated hydraulic conductivity values were predicted for the S. pasteurii suspension densities considered using Brooks-Corey, van Genuchten as well as Fredlund and Xing curve fitting prediction models. Results show that the unsaturated hydraulic conductivity values of specimens prepared at lower, MWC relative to OMC were generally higher than at higher MWC regardless of compactive efforts and S. pasteurii suspension densities considered. The Brooks-Corey model gave the best predicted unsaturated hydraulic conductivity values which fit the requirements for waste containment facilities over the matric suction range and S. pasteurii suspension densities considered, than the van Genuchten and Fredlund – Xing, when compared with measured values.

Prediction of capillary suction in porous media based on micro-CT technology and B–C model

Abstract Moisture variation in porous media depends mainly on the pore characteristics. This article used the micro-computed tomography (micro-CT) (a non-destructive imaging technique to generate a three-dimensional virtual model) and the Brooks–Corey model to deduce the moisture migration in sand. Relationship between capillary rise height and time (h–t) was achieved by numerical simulation in the capillary suction process, where the parameters fractal dimension, porosity, and air–water interfacial area were obtained by the micro-CT scanning. Meanwhile, experiments of capillary rise in sand column were performed using four different sizes washed sand, and the capillary heights at different times were recorded. Results show that the capillary suction is decided by the aperture size and phase morphology simultaneously, and particle size has obvious effect on capillarity, and the wetting front lowers with the increase in grain size and the decrease in rising rate. Parameters air entry pressure and pore-size distribution index obtained by micro-CT scanning technology and empirical formula are accurate. Method of combing micro-CT images and Brooks–Corey model can predict well the capillary suction of porous media. It is also proved that the capillary suction is decided by the aperture size and phase morphology simultaneously.

Water retention models for soils mixed with waste residues: application of the modified van-Genuchten and Brooks-Corey models

Applying additives (e.g., biochar and rapeseed-oil residue) to soils is a common agronomic practice used to improve water-retaining capacity. An investigation of water availability and an applicability evaluation of traditional soil water retention curve (SWRC) are therefore necessary for the soil mixed with waste residues. We aimed to investigate the impact of additives on water retention and further to develop models for their prediction. Loam and sandy loam were mixed with different amounts of rapeseed-oil residue and biochar, respectively. And results show that the biochar and rapeseed-oil residue retain more water, with a minimum and maximum increase in soil moisture by approximately 26.2% and 92.7%, and 10.2% and 19.4%, respectively, relative to pure soil. Furthermore, based on the soil capillary theory, modified van–Genuchten (M-VG) and Brooks–Corey (M-BC) models were constructed and compared, which indicate that both the modified physics-based models (M-SWRC) have higher accuracy than the traditional SWRC models in soil moisture prediction; furthermore, the M-VG model outperforms the M-BC model, due to larger R2 and smaller MAPE and RMSE. For the field soils mixed with additives, the soil suction density function has potentials for SWRC model modification based on the soil capillary theory.

Vadose Zone Lag Time Effect on Groundwater Drought in a Temperate Climate

An essential factor in the propagation of drought, from meteorological drought to groundwater drought, is the delay between a precipitation event and the groundwater recharge reaching the groundwater table. This delay, which mainly occurs in the vadose zone of the hydrological cycle, is often poorly studied. Therefore, this paper proposes a method for estimating the spatially distributed delay in the vadose zone using the kinematic wave approximation of Richards’ equation combined with the van Genuchten–Burdine and Brooks–Corey parametric model. The modeling was approached (1) using a detailed parametrization of soil and geological layers and (2) using lumped hydraulic and physical properties of geological layers. The results of both approaches were compared against the physically based flow model Hydrus-1D. This analysis shows that using a detailed parametrization of soil and geological layers results in good comparison, with a Nash–Sutcliffe efficiency of 0.89 for Brooks–Corey and 0.80 for van Genuchten–Burdine. The delay result of the Brooks–Corey model was incorporated into the groundwater recharge time series from 1980 to 2013 to analyze the effect of this delay on groundwater drought. The results show that the delay in the vadose zone influences groundwater drought characterization features such as the number, duration, and intensity of drought events.

New fractal-dimension-based relation model for estimating absolute permeability through capillary pressure curves

This paper developed a new general power-law relation model to predict absolute permeability, which innovatively integrating Poiseuille's law and fractal capillary pressure model. The proposed model took into account the assumption of Poiseuille's law and Purcell theory characterizing the porous media as capillary tubes of various radii. Kewen Li fractal capillary pressure model was preferred to characterize capillary pressure curves and derive the new permeability relation model due to its higher fitting accuracy compared with Brooks-Corey model. Further, a randomly collected dataset containing 151 rock samples was used to calibrate the coefficients and another 53 rock samples were used to validate the feasibility of this new model. The proposed permeability model can predict absolute permeability through 5 basic parameters as follows: porosity, displacement pressure, capillary pressure at irreducible wetting phase saturation, irreducible wetting phase saturation and the fractal dimension. The fractal dimension, an indicator of the porous media heterogeneity, has a great impact on flow capacity in natural rock system. For rock samples with fractal dimension Df > 3, the capillary pressure matching results of Kewen Li power-law model are much better than those of Brooks-Corey capillary pressure model. 151 mercury injection capillary pressure (MICP) curves were all well fitted by Kewen Li model to estimate the basic parameters, and the absolute permeability of these rock samples were predicted through the new relation model. Then this study performed a comparison between the measured permeability in laboratory and calculated permeability through the new relation model. The regression Coefficient of Determination (R2) for measured and calculated permeability of 151 rock samples was 0.967. Besides, the new model consistently obtained attractive prediction results for another 53 validation rock samples. The new relation model can be widely used to estimate the absolute permeability for various rock types, including limestone, sandstone, dolomite, and from tight rocks to high permeability rocks.

Estimating the water characteristic curve for soil containing residual plastic film based on an improved pore-size distribution

Although plastic-film mulching has played an important role in agriculture production in arid areas, the practice has resulted in the accumulation of large amounts of residual plastic film (RPF) in the soil. This intensely impedes the movement of the water and solutes in soil by seriously affecting the physical and hydraulic properties of soil, in particular the soil water characteristic curve (SWCC). Despite the severity of the problem, studies on how RPF affects soil properties and the SWCC remain scarce. This paper thus aims to achieve a better understanding of the influences of RPF on soil pores and SWCC. In this study, SWCCs were measured under five concentrations of RPF (0 kg·hm−2, 50 kg·hm−2, 100 kg·hm−2, 200 kg·hm−2 and 400 kg·hm−2) and three soil textures (sandy soil, sandy loam and loam soil) based on the pressure plate extractor test. A model for estimating SWCC for soil with residual plastic film (RPF-SWCC) based on an improved pore-size distribution is proposed, and its performance was evaluated and compared with those for existing models, including the van Genuchten (VG), Brooks-Corey (BC) and log normal distribution (LND) models. The results showed that there is a clear influence by the RPF in soil on the shape of the SWCC, and the order of the different soil types in regards to soil water holding capacity was loam soil > sandy loam > sandy soil, with or without RPF. The RPF-SWCC model accounted for the effects of water blocking by RPF, thereby achieving improved fitting accuracy compared to that by the VG, BC and LND models, especially for soil with high RPF concentration. The average Nash-Sutcliffe efficiency coefficient (NSE), mean absolute percentage error (MAPE) and symmetric mean absolute percentage error (SMAPE) for achieved for the RPF-SWCC model were 0.9943, 3.37% and 3.43%, respectively, which was an improvement on the 0.9938, 5.94% and 5.06% achieved for the VG model, 0.9926, 4.43% and 4.25% for the BC model and 0.9923, 15.00% and 7.53% for the LND model, respectively. In addition, the correlation between the parameters of the RPF-SWCC model and RPF concentration showed that the saturated soil water content and residual soil water content decreased and increased with increasing RPF concentration, respectively. In addition, soil RPF increased and decreased the proportion of macropores and soil water holding capacity, respectively. This study can provide a theoretical and technical basis for research into soil water movement and the efficient utilization of water and fertilizer in areas with high agricultural film residue.

Comparison of the performance of 22 models describing soil water retention curves from saturation to oven dryness

AbstractSoil water retention curve (SWRC) is key hydraulic property for vadose zone hydrology. Selected 22 SWRC models with different structures were divided into four types: traditional, single‐segment, two‐segment, and three‐segment models. According to the accuracy and model selection criterion, these models were compared and evaluated using water retention data from saturation to oven dryness of 94 soil samples covering almost all soil types. Among the models, the EG model (exponential model combined with the Groenevelt–Grant model) shows the best performance, but the BC (Brooks–Corey) and VG (van Genuchten) models performed the worst. The relationship between model performance and complexity showed that traditional models with residual water content performed worse than segmental models from saturation to oven dryness, and the segmental models performed worse with an increase in the segment number. In general, models with more parameters perform better, but when the parameter number is greater than five, the model performance gradually worsens due to the equifinality of different parameters. The correlation analysis between soil properties on model performance showed that soil texture has a more significant effect on model performance than bulk density and organic matter content, because the models are primarily affected by their mathematical forms rather than the physical significance of the parameters. Each model picks its limitations and may apply to only one or particular group(s) of soil(s). Therefore, the complementarities of different models may be a great choice to improve SWRC fitting and simulation in arid soil.

Comparison of three models fitting the soil water retention curves in a degraded alpine meadow region

Soil water retention curve (SWRC) plays an important role in simulating soil water movement and assessing soil water holding capacity and availability. Comparison of fitness between different models to determine the best SWRC model of specific regions is required. In this study, three popular models, van Genuchten, Brooks Corey and Gardner model, were selected for comparing in a degraded alpine meadow region on the eastern Tibetan Plateau. Fitness, error distribution along with key parameters were compared. For each soil horizon, the soil moisture content at all soil water potentials decreased consistently with degradation, thereby integrally moving the SWRCs of all soil depths downward with degradation. The differences in SWRCs across various degradation degrees diminished along with soil depth and soil water potential. The Adj.r2 values of van Genuchten, Brooks Corey and Gardner models ranged in 0.971–0.995, 0.958–0.997, and 0.688–0.909, respectively. The van Genuchten and Brooks Corey models significantly (p < 0.05) outperformed the Gardner model, and have no significant differences in fitness. The fitness of all three models showed no significant changes with degradation. Regardless of degradation degree and soil depth, the fitting error of van Genuchten and Brooks Corey models was mainly distributed in the higher (from –100 hPa to –500 hPa) and lower (below –10000 hPa) potential sections. With regard to the parameters of van Genuchten and Brooks Corey models, the field capacity (θs), and permanent wilting moisture were highly coherent with Adj.r2 values of higher than 0.98, while the curve shape parameter (θr), and air entry pressure of the Brooks Corey model were much lower than those of the van Genuchten model with Adj.r2 values of lower than 0.91. The SWRCs with varying degrees of degradation are best fitted by both van Genuchten and Brooks Corey models but cannot be fitted by Gardner model. Soil water holding capacity decreased with degradation especially in the top soil (0 cm to 30 cm), but the curve shape of all SWRCs did not change significantly with degradation.

Bentonite Extrusion into Near-Borehole Fracture

In this paper, we discuss laboratory experiments of bentonite swelling and coupled finite element simulations to explicate bentonite extrusion. For the experiments, we developed a swell cell apparatus to understand the bentonite migration to the near-borehole fracture. We constructed the swell cell using acrylic, which comprised of a borehole and open fracture. Initially, the borehole of the swell cell was filled with bentonite and liquid. Then, the apparatus was sealed for observations. Due to the liquid saturation increase of bentonite, its swelling pressure increased. The developed pressure caused the extrusion of bentonite into the fracture, and the flow of bentonite from the borehole decreased with time. Moreover, for the effectiveness of bentonite-based plugging, there is a limiting condition, which represents the relation between the maximum bentonite migration length with the fracture aperture. Additionally, we also performed the bentonite free swelling test to assess the swelling potential to the fluid salinity, and we observed that with the increase of the salinity, the swelling potential decreased. In addition, we present a fully coupled two-phases fluids flow (e.g., liquid and gas) and deformation flow finite element (FE) model for the bentonite column elements and swell cell model. We also combined the Modified Cam Clay (MCC) model and the swelling model for the bentonite deformation flow model. Then, we also present the validation of the bentonite model. To model other sub-domains, we used the poro-elastic model. Additionally, we obtained the transition between the wetting phase (i.e., liquid) and non-wetting phase (i.e., gas) using the Brooks–Corey model. From the finite element results, we observed that due to the liquid intrusion into the bentonite, the developed capillary pressure gradient results in a change of the hydro-mechanical behavior of the bentonite. Initially, we observed that due to the high capillary pressure gradient, the liquid saturation and the swelling pressure increased, which also decreased with time due to a reduction in the capillary pressure gradient. Thereby, the swelling pressure-induced bentonite migration to the fracture also decreased over time, and after the equilibrium state (for a negligible pressure gradient), there was no significant transport of bentonite into the fracture.

Spatial variability of the parameters of soil-water characteristic curves in gravel-mulched fields

Abstract Knowledge of the soil-water characteristic curve (SWCC) and its spatial variability is essential for many agricultural, environmental, and engineering applications. We analyzed the spatial variability of the parameters of SWCC in gravel-mulched fields using classical statistics and geostatistical methods. Soil samples were collected from the layer in 64 evenly distributed 1 × 1 m quadrats 4 m apart, center to center. SWCC in the gravel-mulched fields could be fitted well by both the van Genuchten and Brooks–Corey models, but the fit was better with the van Genuchten model. The type of fitting three parameters was tested. The model parameters θs and n of each type of soil were weakly variable, and α was moderately variable. The results indicate that the gravel-mulched field has better water retention, and the water retention effect of the new gravel-mulched fields is most obvious. The spatial variation of the parameters in SWCC can therefore be used to infer soil hydraulic properties, which is important for simplifying the calculation of SWCC and quantitatively determining the retention of soil water and for managing the capacity of soil to retain water in gravel-mulched fields in arid regions.

An Experimental Study on the Hydromechanical Behaviours of the Evolution of Postearthquake Landslide Deposits

In this study, a series of experiments of the full-scale physical model was employed to investigate the hydromechanical behaviours of the postearthquake landslide evolution, in forms of rill erosion and shallow headward failure on the rill bank slopes under unsaturated conditions. Soil-water characteristic curves (SWCC) were established using the Brooks-Corey (BC) and van Genuchten (VG) models. The stability of the shallow failure was then analyzed via a one-dimensional and unsaturated stability analysis model of the infinite slope. This measurement revealed that the preferential flow and the matrix flow coexisted when infiltration occurred and the VG model performs better in fitting the SWCC than the BC model. Consistent feedback between stability calculations and experimental observations enables the analysis of mechanisms of rill erosion and slope failure of postseismic landslide under the impact of preferential flow. Furthermore, the seepage-induced internal erosion phenomenon was observed in the experiment. This work thus provides a new perspective on the triggering mechanisms of debris flow during the postseismic period.

Characterising the role of parametric functions in the van Genuchten empirical model on CO2 storage performance

In the application of two-phase flow in porous media within the context of CO2 sequestration, a non-wetting phase is used to displace a wetting phase residing in-situ to the maximum extent through a network of pore conduits. The storage performance of this physical process can be assessed through numerical simulations where transport properties are usually described using the Brooks & Corey (BC) or van Genuchten (vG) model. The empirical constant, namely the pore geometry index, is a primary parameter in both of these models and experimental evidence shows a variation in the value of this empirical constant. It is, therefore, essential to cast this empirical constant into a ternary diagram for all types of clastic porous media to demarcate the efficiency of two-phase flow processes in terms of the pore geometry index (PGI). In doing so, this approach can be used as a tool for designing more efficient processes, as well as for the normative characterisation of two-phase flow, taking into consideration the predominance of capillary pressure or relative permeability effects. This concept is based on the existence of a PGI estimation for clastic sediments, for which the value for 12 sediment mixtures fall between 1.01 and 3.00. Statistical data obtained from soil physics is used for developing and validating numerical models where a good match is observed in numerical simulations. In this context, a new methodology for the effective characterisation of PGI for different clastic rocks is proposed. This paper presents theoretical observations and continuum-scale numerical simulation results of a PGI characterisation for the prediction of the hydraulic properties of clastic reservoir rocks. The effect of key parameters in the vG empirical model, such as the pressure strength coefficient and the PGI, is incorporated into the simulation analysis. In particular, the model is used to investigate the effects of parameter representation on CO2 storage performance in a saline aquifer. Subsequent analysis shows that the PGI is a very important parameter for defining the flow characteristics of simulation models. It can also be flexibly changed for each rock type and this approach may thus be practical when simulating the evolution of CO2 plume in reservoirs with sedimentary heterogeneities, such as intra-aquifer aquitard layers or graded beds. The use of the realistic PGI boundaries promises a more precise description of the hydraulic behaviour in sandstones and shale when using either the BC or vG model.

Application of the Brooks-Corey model in the conditions of lower cretaceous deposits in terrigenous reservoirs of Western Siberia

The paper deals with the issues of determining Brooks-Corey model parameters in the approximation of capillary curves under the conditions of productive strata of Western Siberia. It was emphasized that in the conditions of reservoirs of Western Siberia, there are close correlations between current water saturation of capillary curves at fixed values of capillary pressure and reservoir properties (absolute permeability, residual water saturation). Using these correlations, the approximation model parameters (initial capillary pressure and capillary curve steepness) were accurately assessed.

PORE CHANNELS DISTRIBUTION DENSITY BY THE WESTERN SIBERIA RESERVOIR ROCK SIZES

The paper discusses the relationship between the filtration properties and the reservoir filter channels distribution density. In this case, the Brooks-Corey model was used, allowing the capillary curves obtained in laboratory conditions for the Las-Egansk field BV6 reservoir approximating with good accuracy. It is shown that the pore channels of collectors in Western Siberia distribution moments are completely determined by the approximation model parameters. With a known absolute permeability, the parameters of the Brooks-Corey model are estimated first, and then the filtration channels moments of distribution are determined. The paper presents expressions that allow one to proceed from the Brooks-Corey model parameters to the pore channels distribution moments over radii. Graphs of pore channels distribution density are presented for various absolute permeability values.

Performance evaluation of different soil water retention functions for modeling of water flow under transient condition

ABSTRACT ABSTRACT: Description and prediction of water flow through unsaturated soils is necessary to understand their hydraulic properties, including soil water retention curve (SWRC). Many models have been developed for estimation of SWRC and many researchers compared water retention curve derived from these models with the measured values. In this paper, in addition to comparing measured and derived SWRC, a functional evaluation of SWRC for modeling of soil water movement was carried out using van Genuchten, Brooks-Corey, Campbell and Hutson-Cass models in three sites including Loamy sand, Loam and Clay loam soils. Therefore, the functional behavior of SWRC was quantitatively compared by applying mentioned SWRC to numerical code (HydroGeoSphere) to simulate soil profile drainage under steady-state and transient conditions. The agreement between simulated and measured free drainages values was evaluated using statistical criteria including mean absolute error (MAE), modified index of agreement (d’), modified coefficient efficiency (E’), and t-test. The results demonstrated that the van Genuchten model was slightly better than the other models for estimation of SWRC (MAE 0.014 – 0.016,E’ 0.80 – 0.87 and d’ 0.90 – 0.93) while according to t-test, it was found that the measured and estimated SWRC using various models did not differ significantly. Therefore, it is expected that the simulated free drainage using mentioned SWRC models did not differ significantly with observed values. But the results demonstrated that the simulated free drainage using Brooks-Corey model for Loamy sand soil and van Genuchten and Brooks-Corey models for Loam soil differed significantly (p ≤ 0.05) with measured values.

Exponential Capillary Pressure Functions in Sedimentary Rocks

The Brooks-Corey power-law capillary pressure model is commonly imposed on core analysis data without verifying the validity of its underlying assumptions. The Brooks-Corey model, originally developed to model the pressure head during the drainage of soil, is only valid at low wetting phase saturations. However, such models are often applied in petroleum production simulations and may lead to erroneous recovery factors when the saturation range of interest is far from the end points. We demonstrate that exponential models work much better for capillary pressure compared to the Brooks-Corey model over a wide saturation range. Mercury injection porosimetry, petrographic image analysis, and magnetic resonance studies suggest that the pore and throat size distribution in many rocks are log-normally distributed. This fact was previously employed to calculate the capillary pressure function as a function of saturation for pore size distributions described by atruncated log-normal distribution. Employing a Taylor series expansion, we simplify the random fractal capillary pressure model of Hunt to Pc = exp(a − bS), where S is the wetting phase saturation, and a and b characteristic of the porous medium. An extensive dataset of seventeen centrifuge capillary pressure measurements were used in this research to demonstrate the merit of the new method. For both sandstones and carbonates, the logarithm of capillary pressure showed a linear relationship with saturation as observed by magnetic resonance imaging centrifuge capillary pressure measurements over a wide saturation range. This work demonstrates that: (a) in semi-log plots of capillary pressure as a function of saturation, capillary pressurewill vary linearly over a wide saturation range, (b) such a plot as described in (a) will show the uni-or bimodal pore size distribution of the rock, (c) the exponential capillary pressure function simplifies analytical modelsthat use the capillary pressure function, for example oil recovery models for fractured reservoirs.

Functional Extremum Solution and Parameter Estimation for One‐Dimensional Vertical Infiltration using the Brooks–Corey Model

Core Ideas Least action and variational principles were used to simulate unsaturated vertical infiltration. A functional extremum explicit solution to Richards' equation was obtained. A new method describes nonlinear relationships between cumulative infiltration, infiltration rate and wetting‐front depth. The method could be used to accurately predict soil water content and estimate soil hydraulic parameters. A simple analytical solution of one‐dimensional vertical infiltration of soil water is of great importance for the estimation of soil hydraulic properties and for precision irrigation. We use a new approximate analytical method based on the principle of least action and the variational principle for simulating the vertical infiltration of water in unsaturated soil for a constant‐saturation upper boundary and for estimating infiltration parameters. The method proposes the functional extremum problem of one‐dimensional vertical infiltration of water in unsaturated soil using the Brooks–Corey model. A functional extremum solution (FES) to Richards' equation was obtained using the Euler–Lagrange equation and the integral mean‐value theorem. A modified functional extremum solution (MFES) was also proposed empirically to improve precision based on the FES of horizontal absorption and numerical data simulated by Hydrus‐1D. The relationships between a parameter derived by the value theorem of the integral (α), the air‐entry suction (hd), and the wetting front depth (zf) were analyzed by comparing MFES with the numerical distribution of soil water content. The MFES was used to describe the nonlinear relationship between cumulative infiltration and zf, with the relative error (Re) of &lt; 4.1% and the coefficient of determination (R2) &gt; 0.986. The MFES was also used to describe the nonlinear relationship between the infiltration rate (i) and the reciprocal of zf for soils with hd ≥10 cm, with Re &lt; 6.0% and R2 &gt; 0.8453. A simple method for estimating soil saturated hydraulic conductivity (Ks) was proposed from the nonlinear relationship between i and zf, and the sensitivities of parameters in the Brooks–Corey model were also analyzed.

Finite element method for modelling of two phase fluid flow in porous media

Petroleum and gas industry is doing enormous research to investigate new process and methods for the extraction of oil and gas from natural reservoirs after primary and secondary recovery, these processes are named as Enhanced Oil Recovery (EOR). A lot of simulation techniques have been adopted to study the behaviour and predict the physical mechanisms of oil recovery. Different characteristic functions including capillary pressures, relative permeabilities and fluid saturations are helpful in predicting the effects of wettability alteration, viscosity, and surface tension on oil recovery. In this work, simulations have been carried out by using finite element method (FEM), for two-phase fluid flow in porous media. A 3-dimensional cylindrical shaped porous media was designed, same as the laboratory-scale setup for EOR. Brooks-Corey model and Ban Genuchten models were used for the calculation of capillary pressure with changing the saturation of water and oil. The proposed model is capable to predict capillary pressure, relative permeability and speed of fluid at different positions in porous media with random wettability conditions.

Permeability function for unsaturated soil

This paper proposes a permeability function to estimate the water permeability coefficient of unsaturated soil. It is derived on the basis of the equilibrium equation of the water phase. Only one parameter is required in the proposed function, which is similar to the Brooks–Corey model. However, this parameter can be more easily obtained by using permeability tests of saturated soil with different porosity values. A number of test results in the literature are employed to validate the proposed permeability function, and the model prediction exhibits good agreement with the experimental data.