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The main goal for this research is to investigate the effect of two composed hybrid nanoparticle materials in heat transfer with account several parameters and in two cases. In addition, exploring how the micropolar hybrid nanofluid (Cu–TiO2) behaves in a shrinking and expansion of the channel. The model considers external factors such as magnetic fields, heat radiation, and solar radiation. The boundary layer approach has been utilized to create transformations that pout the equations of the system in the dimensionless form. The shooting method has been combined with the fourth-order Runge-Kutta-Gill to numerically solve the modified ordinary differential equations. The impacts of the nanoparticles transport on the heat transfer and fluid flow are addressed, and the results are compared to the case of pure water. The velocity, isotherms, angular-velocity, and concentration distributions, are given in tables or graphs. It was found that the effect of heat on the hybrid nanofluids is directly proportional to its velocity and angular velocity. For mass fraction of the two nanofluids φ1 and φ2, the velocity profile f′(η) has a comparable influence for both hybrid nanofluid and nanofluid. The larger quantity of the factors φ1, φ2, M and Q enhance the temperature. For M, φ1 and φ2, the angular velocity profile g(η) has a comparable influence for both hybrid and magnetic parameter. The absorption parameter storing the radiation energy and augmentation of the solar irradiance immersion capacity leads to a greater heat transfer.

In this work the problem of displacing a ganglion of a fluid by another immiscible one in capillaries is investigated. A modeling approach is developed to predict the location of the ganglion with time. The model describes two patterns; namely, when the ganglion totally exists inside the tube, and when the advancing interface of the ganglion has broken through the exit of the tube. The model is valid for the case in which the ganglion is wetting as well as when it is nonwetting to the wall of the tube. It also considers the situation in which both the advancing and the receding interfaces assume, generally, different contact angles. For the special case when the displacement process is quasistatic, both the receding and the advancing contact angles may be considered the same. Under these conditions, interfacial tension force plays no role and the ganglion moves as a plug inside the tube with a constant velocity. When the viscosity ratio between the invading fluid and the ganglion is one (i.e., both phases are having the same viscosity) the motion reduces to the Hagen-Poiseuille flow in pipes. Once the advancing interface breaks through the exit of the tube, interfacial tension starts to take part in the displacement process and the ganglion starts to accelerate or decelerate according to the viscosity ratio. When the ganglion is nonwetting, interfacial tension becomes in the direction of the flow and is opposite to the flow otherwise. The model accounts for external forces such as pressure and gravity in addition to capillarity. A computational fluid dynamics analysis of this system is conducted for both types of wettability scenarios and shows very good match with the results of the developed model during both the two modes of flow patterns. This builds confidence in the developed modeling approach. Other cases have also been explored to highlight the effects of other scenarios. Cited as: Salama, A., Cai, J., Kou, J., Sun, S., EI-Amin, M. F., Wang, Y. Investigation of the dynamics of immiscible displacement of a ganglion in capillaries. Capillarity, 2021, 4(2): 31-44, doi: 10.46690/capi.2021.02.02

Nowadays, enhanced oil recovery using nanoparticles is considered an innovative approach to increase oil production. This paper focuses on predicting nanoparticles transport in porous media using machine learning techniques including random forest, gradient boosting regression, decision tree, and artificial neural networks. Due to the lack of data on nanoparticles transport in porous media, this work generates artificial datasets using a numerical model that are validated against experimental data from the literature. Six experiments with different nanoparticles types with various physical features are selected to validate the numerical model. Therefore, the researchers produce six datasets from the experiments and create an additional dataset by combining all other datasets. Also, data preprocessing, correlation, and features importance methods are investigated using the Scikit-learn library. Moreover, hyperparameters tuning are optimized using the GridSearchCV algorithm. The performance of predictive models is evaluated using the mean absolute error, the R-squared correlation, the mean squared error, and the root mean squared error. The results show that the decision tree model has the best performance and highest accuracy in one of the datasets. On the other hand, the random forest model has the lowest root mean squared error and highest R-squared values in the rest of the datasets, including the combined dataset. Cited as: Alwated, B., El-Amin, M. F. Enhanced oil recovery by nanoparticles flooding: From numerical modeling improvement to machine learning prediction. Advances in Geo-Energy Research, 2021, 5(3): 297-317, doi: 10.46690/ager.2021.03.06

In this paper, we introduce an estimation of the random Klinkenberg slip coefficient in the apparent permeability model using a chaos decomposition technique. The apparent permeability expression (Klinkenberg model) is used to describe natural gas transport in low-permeability media. In this process, the Klinkenberg factor is considered as a random parameter that depends on two random variables. The mean and variance (or standard deviation) of the two random variables can be estimated from the empirical data available in the literature. Therefore, the variation in the pressure is related directly to the random variation in the Klinkenberg factor. The polynomial chaos expansion is used to decompose the governing equation into a set of coupled deterministic equations that are solved and then used to compute the mean and variance of the solution. The algorithm of how to solve the deterministic coupled system is also presented. For verification, the model and its solution have been compared with the analytical solution of the basic steady-state version of the model. The comparison shows a very good agreement. The effects of a number of important parameters have been presented in graphs and discussed. It was found that the stochastic model works very well with small values of the liquid equivalent permeability, which meets the characteristics of low-permeability reservoirs. Also, the stochastic model works very well with small values of gas viscosity. On the other hand, the porosity seems to be not engaged well with the low-permeability model. The sensitivity of selection of random parameters is also investigated as well as the transient effect.

This paper focuses on the problem of fractional time derivative of fluid flow and convective heat and mass transfer from a heated semi-infinite wall immersed. We provided two cases of study, one is...

Reservoir permeability is a crucial parameter for reservoir characterization and the estimation of current and future production from hydrocarbon reservoirs. Permeability can be conventionally estimated from traditional approaches such as core analysis and well-test data, which are time-consuming and expensive. Many scientists tried to estimate permeability from nuclear magnetic resonance (NMR) logs utilizing complex mathematical equations that may achieve imprecise approximation of the permeability values. Gradient boosting generates additive regression models by successively fitting a straightforward base learner to present pseudo-residuals using least squares at every iteration. The execution speed and accuracy of gradient boosting can be considerably enhanced by applying randomization process. Besides, the randomization process improves robustness against over fitting of the base learner. So, the novelty of the current study is the development of a Stochastic Gradient Boosting (SGB) regression model to predict the permeability of petroleum reservoirs based on well logs. Besides benchmark machine learning techniques are used to predict reservoir permeability from well logs. The correlation coefficient (R), relative absolute error (RAE), mean-absolute error (MAE), root mean-squared error (RMSE), and root relative squared error (RRSE) are utilized to check the overall fitting between measured permeability versus predicted ones. It is found that Stochastic Gradient Boosting model achieved overall better performance than the other models.

This study aims to investigate the behavior of the micropolar hybrid nanofluid (Cu-TiO2) in a stretching and shrinking channel while maintaining a continuous laminar flow. External effects from magnetic field, thermal and solar radiation are also considered in the model. The governing differential (momentum, micro-rotation, and energy) equations are transformed into dimensionless forms via similarity transformations based on the boundary layer theory. The resulting ordinary differential equations are solved numerically using the fourth-order Runge-Kutta-Gill technique with the shooting method. The effects of nanoparticles transport on fluid flow and heat transfer are discussed and compared to the pure water case. The results are presented in tables or graphs such as velocity, temperature, angular-velocity profiles, and concentration.

The atmosphere contains 3400 trillion gallons of water vapor, which would be enough to cover the entire earth in 1 inch of water. Air humidity is available everywhere, and it acts as a great alternative as a renewable reservoir of water known as atmospheric water. Atmospheric water harvesting system efficiency depends on the sorption capacity of water based on the adsorption phenomenon. Using anhydrous salts is an efficient process for capturing and delivering water from ambient air, especially at a low relative humidity as low as 15%. A lot of water-scarce countries like Saudi Arabia have much annual solar radiation and relatively high humidity. This study is focusing on modeling and simulating the water absorption and release of the anhydrous salt copper chloride (\({CuCl}_{2}\)) under different relative humidity to produce atmospheric drinking water in scarce regions.

Hydrogen leakage is a serious safety issue of pure hydrogen energy usage, since if it mixes with air, fire or explosion can be produced. In this study, the turbulent flow of hydrogen buoyant jet resulting from hydrogen leakage has been investigated using machine learning techniques. A mixed empirical-analytical-numerical model has been developed to describe the problem under consideration. The mass, momentum and concentration fluxes are represented by integral formulae and transformed into a set of ordinary differential equations, which are solved numerically. Therefore, important physical quantities such as the hydrogen mass fraction have been determined. Some machine learning techniques have been selected to forecasting the concentration distribution of hydrogen in air, including Linear Regression (LR), Artificial Neural Networks (ANNs), Support Vector Regression (SVR), k-Nearest Neighbour (k-NN), Random Forest (RF), Random Tree (RT) and REP Tree (REPT) techniques. It was found that the RF method is the best technique to predict the hydrogen leakage distribution in air.

In this paper, machine learning techniques are utilized to predict the temperature distribution in a vertical buoyant turbulent jet. Experimental results for five cases with different flow rates are reported. The results show that temperature behaves linearly along the vertical axis of the jet. Also, the thermal stratification phenomenon has been observed. Different machine learning techniques have been used to predict the temperature distribution in the induced vertical buoyant turbulent jet. The used machine learning including k-nearest neighbor algorithm (k-NN), artificial neural networks (ANNs), Support Vector Regression (SVR), and random forest (RF). It was found both SVR and RF methods are the best machine learning techniques to predict the temperature distribution in a vertical buoyant turbulent jet.

In this paper, the problem of nonisothermal two-phase flow in a porous cavity has been investigated numerically. The conservation laws of energy, momentum, and mass are used to model the problem. The mixed Dirichlet-Neumann boundary conditions are used to describe the cavity boundaries. The equations system is converted into a dimensionless system in terms of Prandtl, Reynolds, Bond, capillary, and Darcy numbers. A time-splitting multiscale scheme has been developed to treat the time derivative discretization. Also, the Courant-Friedrichs-Lewy stability condition is utilized to adapt the time step size. Darcy’s law and continuity equation are coupled to compute the pressure, then, the energy equation is solved implicitly. The effects of Prandtl, Reynolds, Bond, capillary, and Darcy numbers on the pressure, velocity, temperature, saturation, and local Nusselt number have been investigated.

The universal dimensionless time is an important parameter to predict a real oil field behavior from a scaled laboratory experiment. The dimensionless time uses a group of parameters that are inherited to the properties of both fluids and rocks of the reservoirs. In addition to the injection velocity which dynamics of the process depends on. In this work, we proposed a new power-law scaling velocity as a function of characteristic injection velocities, which can be linked into the dimensionless time. Based on machine learning techniques, namely, k-nearest neighbor algorithm (k-NN), artificial neural networks (ANNs), support vector machine (SVM), and random forest (RF) for experimental oil recovery data and real time is employed to estimate the dimensionless time of oil recovery. It was found the SVM method is the best machine learning technique to predict dimensionless time-scale based on the primary physical data of the oil and rock.

In this paper, an approximate similarity solution of a fractional laminar boundary layer of viscous fluid flow over an infinite vertical plate has been presented. We introduce new fractional similarity transformations to convert the partial differential equation into a similarity ordinary differential equation with a fractional context. The viscous term of the flow momentum equation is written based on the Caputo fractional derivative. The proposed analytical solution has been developed using fractional power-series technique, and the convergence of the solution has been examined. The velocity distributions with the similarity variable are plotted against different values of the fractional order to illustrate the effects of fractional argument on the velocity behavior.

Vernacular measures, such as courtyard, wind catcher “Malqaf”, wooden lattice “Mashrabia”, and lantern—which can help buildings to depend on natural energy from the sun and the wind—have started to be abandoned in the last decades. However, wind pressure and stack effects are becoming more popular in modern buildings design and the primary method in most domestic buildings to achieve the desired cross ventilation and minimize the air temperature to reach the required cooling loads. This paper aims to revive one of the vernacular measures “the windcatcher”, quantifying the effectiveness of the inward/outward opening properties on the air temperature and airflow inside the buildings. Analytical literature review, context analysis, and numerical simulations are performed. The computer fluid dynamics (CFD) is utilized to simulate both the temperature distribution and the flow field within the windcatcher model. Simulations are carried out in the fluent environment, which uses the control volume method for solving the conservation law. The Reynolds-averaged Navier–Stokes (RANS) and energy equation with the realizable k-ϵ turbulent model are employed. The research uses a parametric analysis to test different scenarios of windcatcher designs in terms of dimensions, proportions, and opening ratios. The results of this study confirm that windcatcher has a significant effect in lowering the air temperature inside the different floors. However, it is recommended to use a wind-catcher for not more than two floors, increase the area of the outward opening to 200% relative to the inward opening and apply side opening in the upper floors.

Throughout this study, we present a dual-continuum model of transport of the natural gas in shale formations. The model includes several physical mechanisms such as diffusion, adsorption and rock stress sensitivity. The slippage has a clear effect in the low-permeability formations which can be described by the apparent permeability. The adsorption mechanism has been modeled by the Langmuir isotherm. The porosity-stress model has been used to describe stress state of the rocks. The thermodynamics deviation factor is calculated using the equation of state of Peng–Robinson. The governing differential system has been solved numerically using the mixed finite element method (MFEM). The stability of the MFEM has been investigated theoretically and numerically. A semi-implicit scheme is employed to solve the two coupled pressure equations, while the thermodynamic calculations are conducted explicitly. Moreover, numerical experiments are performed under the corresponding physical parameters of the model. Some represented results are shown in graphs including the rates of production as well as the pressures and the apparent permeability profiles.

In this article, we consider a two-phase immiscible incompressible flow including nanoparticles transport in fractured heterogeneous porous media. The system of the governing equations consists of water saturation, Darcy’s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat, as well as, porosity and permeability variation due to the nanoparticles deposition/entrapment on/in the pores. The discrete-fracture model (DFM) is used to describe the flow and transport in fractured porous media. Moreover, multiscale time-splitting strategy has been employed to manage different time-step sizes for different physics, such as saturation, concentration, etc. Numerical examples are provided to demonstrate the efficiency of the proposed multi-scale time splitting approach.

In the present paper, an adaptive time-splitting scheme is introduced to investigate the problem of two-phase flow in heterogeneous porous media. The pressure and saturation equations are coupled by the capillary pressure which is linearized in terms of saturation. An IMplicit Pressure Explicit Saturation scheme is used to solve the problem under consideration. We use the time schemes for the pressure and saturation equations. The external time interval is divided into two levels, the first level is for the pressure, the second one is for the saturation. This method can reduce the computational cost arisen from the implicit solution of the pressure equation and the rapid changes in saturation. The time-step size for saturation equation is adaptive under computing and satisfying the Courant–Friedrichs–Lewy (CFL

Purpose This paper aims to introduce modeling, numerical simulation and convergence analysis of the problem of nanoparticles’ transport carried by a two-phase flow in a porous medium. The model consists of equations of pressure, saturation, nanoparticles’ concentration, deposited nanoparticles’ concentration on the pore-walls and entrapped nanoparticles concentration in pore-throats. Design/methodology/approach A nonlinear iterative IMPES-IMC (IMplicit Pressure Explicit Saturation–IMplicit Concentration) scheme is used to solve the problem under consideration. The governing equations are discretized using the cell-centered finite difference (CCFD) method. The pressure and saturation equations are coupled to calculate the pressure, and then the saturation is updated explicitly. Therefore, the equations of nanoparticles concentration, the deposited nanoparticles concentration on the pore walls and the entrapped nanoparticles concentration in pore throats are computed implicitly. Then, the porosity and the permeability variations are updated. Findings Three lemmas and one theorem for the convergence of the iterative method under the natural conditions and some continuity and boundedness assumptions were stated and proved. The theorem is proved by induction states that after a number of iterations, the sequences of the dependent variables such as saturation and concentrations approach solutions on the next time step. Moreover, two numerical examples are introduced with convergence test in terms of Courant–Friedrichs–Lewy (CFL) condition and a relaxation factor. Dependent variables such as pressure, saturation, concentration, deposited concentrations, porosity and permeability are plotted as contours in graphs, whereas the error estimations are presented in a table for different values of the number of time steps, number of iterations and mesh size. Research limitations/implications The domain of the computations is relatively small; however, it is straightforward to extend this method to the oil reservoir (large) domain by keeping similar definitions of CFL number and other physical parameters. Originality/value The model of the problem under consideration has not been studied before. Also, both solution technique and convergence analysis have not been used before with this model.

In this paper, we explore the possibility of specifying the ideal hypothetical positions of matrices blocks and fractures in fractured porous media as a single-continuum reservoir model in a way that mimics the dual-porosity dual-permeability (DPDP) configuration. In order to get an ideal mimic, we use the typical configuration and geometrical hypotheses of the DPDP model for the SDFM. Unlike the DPDP model which consists of two equations for the two-continuum coupled by a transfer term, the proposed single-domain fracture model (SDFM) model consists of a single equation for the single-continuum. Each one of the two models includes slippage effect, adsorption, Knudsen diffusion, geomechanics, and thermodynamics deviation factor. For the thermodynamics calculations, the cubic Peng-Robinson equation of state is employed. The diffusion model is verified by calculating the total mass flux through a nanopore by combination of slip flow and Knudsen diffusion and compared with experimental data. A semi-implicit scheme is used for the time discretization while the thermodynamics equations are updated explicitly. The spatial discretization is done using the cell-centered finite difference (CCFD) method. Finally, numerical experiments are performed under variations of the physical parameters. Several results are discussed such as pressure, production rate and cumulative production. We compare the results of the two models using the same dimensions and physical and computational parameters. We found that the DPDP and the SDFM models production rate and cumulative production behave similarly with approximately the same slope but with some differences in values. Moreover, we found that the poroelasticity effect reduces the production rate and consequently the cumulative production rate but in the SDFM model the reservoir takes more time to achieve depletion than the DPDP model. The normal fracture factor which appears in the transfer term of the DPDP model is adjusted against the SDFM.

International audience; In this work, we introduce a theoretical foundation of the stability analysis of the mixed finite element solution to the problem of shale-gas transport in fractured porous media with geomechanical effects. The differential system was solved numerically by the Mixed Finite Element Method (MFEM). The results include seven lemmas and a theorem with rigorous mathematical proofs. The stability analysis presents the boundedness condition of the MFE solution.

The present article investigates the non-isothermal nanofluids flow in a squared porous cavity. The model consists of the conservation laws of energy, momentum, and mass. The cavity boundaries are modeled by mixed Dirichlet-Neumann boundary conditions. The discretization of time derivatives is developed by a time-splitting multiscale technique. The momentum and continuity equations are solved implicitly to find the pressure, then the velocity of the field is explicitly calculated. Therefore, both energy equation is solved implicitly. The Courant-Friedrichs-Lewy condition has been used to achieve the time step-size adaptation. Two numerical cases are considered for different boundary conditions. The effects of the nanofluid volume fraction of the on pressure, velocity, temperature and Nusselt number have been investigated. It was found that the temperature decreases as the volume fraction increases. We also found that the pressure and velocity increase while the local Nusselt number decreases as the volume fraction increases.

The problem fractional derivative of flow and heat transfer by natural convection from a heated semi-infinite wall immersed in a fluid is studied numerically. The time derivative terms in both the momentum and energy equations are assumed fractional. Fractional derivative is a generalization to the normal derivative and it would be interesting to study its possible effects on both velocity and temperature fields. For accurate implementation, it is important that the results obtained by fractional derivative formulations reduce to the results obtained by normal derivative when the order of differentiation becomes the same. In this work, it is found that both the velocity and temperature profiles using fractional derivatives around first order (i.e., smaller and larger than one) encompass those obtained using first order time derivative. Nusselt number variations as well as friction coefficient profiles follow a similar pattern.

In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space. Keywords: Fractional derivative, Porous media, Natural gas, Reservoir modeling, Infinite series solutions

In this paper, the problem of two-phase flow in porous media including dynamic capillary pressure has been studied numerically. The IMplicit Pressure Explicit Saturation (IMPES) scheme has been modified to solve the governing equations. The pressure equation is treated implicitly with the saturation equation to obtain the pressure, while the saturation equation is solved explicitly to update the saturation at each time step. We introduce stability analysis of the modified scheme and its stability condition has been derived. Comparison between the static and the dynamic capillary pressure has been introduced to illustrate the efficiency of the modified scheme.

In this paper, the problem of magnetic nanoparticles injection into a water–oil two–phase flow under an external permanent magnetic field is investigated. The mathematical model of the problem under consideration has been developed. We treat the water-nanoparticles suspension as a miscible mixture while it is immiscible with the oil phase. The magnetized phase pressure includes an additional pressure term with the conventional thermodynamic pressure. The countercurrent imbibition flow problem is taken as an example. Physical variables including water–nanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat deposited nanoparticles are investigated under the influence of the magnetic field.

In this work, the heat transport phenomena coupled with melting process are studied by using the enthalpy-based lattice Boltzmann method (LBM). The proposed model is a modified version of thermal LB model, where could avoid iteration steps and ensures high accuracy. The Bhatnagar–Gross–Krook (BGK) approximation with a D1Q2 lattice was used to determine the temperature field for one-dimensional melting by conduction and multi-distribution functions (MDF) with D2Q9 lattice was used to determine the density, velocity and temperature fields for two-dimensional melting by natural convection. Different boundary conditions including Dirichlet, adiabatic and bounce-back boundary conditions were used. The influence of increasing Rayleigh number (from 103 to 105) on temperature distribution and melting process is studied. The obtained results show that a good agreement with the analytical solution for melting by conduction case and with the benchmark solution for melting by convection.

The present work is dedicated to studying the transfer of natural gas in shale formations. The governing model was developed on the basis of the model of dual-porosity dual-permeability (DPDP). The mixed finite element method (MFEM) is employed to solve the governing equations numerically. Numerical example is presented and results discussed such as production cumulative rate, pressure and apparent permeability.