Showing papers in "Transport in Porous Media in 2008"

Insights into the Relationships Among Capillary Pressure, Saturation, Interfacial Area and Relative Permeability Using Pore-Network Modeling

Abstract: To gain insight in relationships among capillary pressure, interfacial area, saturation, and relative permeability in two-phase flow in porous media, we have developed two types of pore-network models. The first one, called tube model, has only one element type, namely pore throats. The second one is a sphere-and-tube model with both pore bodies and pore throats. We have shown that the two models produce distinctly different curves for capillary pressure and relative permeability. In particular, we find that the tube model cannot reproduce hysteresis. We have investigated some basic issues such as effect of network size, network dimension, and different trapping assumptions in the two networks. We have also obtained curves of fluid–fluid interfacial area versus saturation. We show that the trend of relationship between interfacial area and saturation is largely influenced by trapping assumptions. Through simulating primary and scanning drainage and imbibition cycles, we have generated two surfaces fitted to capillary pressure, saturation, and interfacial area (P c –S w –a nw ) points as well as to relative permeability, saturation, and interfacial area (k r –S w –a nw ) points. The two fitted three-dimensional surfaces show very good correlation with the data points. We have fitted two different surfaces to P c –S w –a nw points for drainage and imbibition separately. The two surfaces do not completely coincide. But, their mean absolute difference decreases with increasing overlap in the statistical distributions of pore bodies and pore throats. We have shown that interfacial area can be considered as an essential variable for diminishing or eliminating the hysteresis observed in capillary pressure–saturation (P c –S w ) and the relative permeability–saturation (k r –S w ) curves.

Laboratory and Simulation Investigation of Enhanced Coalbed Methane Recovery by Gas Injection

Abstract: Methane/carbon dioxide/nitrogen flow and adsorption behavior within coal is investigated simultaneously from a laboratory and simulation perspective. The samples are from a coalbed in the Powder River Basin, WY. They are characterized by methane, carbon dioxide, and nitrogen sorption isotherms, as well as porosity and permeability measurements. This coal adsorbs almost three times as much carbon dioxide as methane and exhibits significant hysteresis among pure-component adsorption and desorption isotherms that are characterized as Langmuir-like. Displacement experiments were conducted with pure nitrogen, pure carbon dioxide, and various mixtures. Recovery factors are greater than 94% of the OGIP. Most interestingly, the coal exhibited ability to separate nitrogen from carbon dioxide due to the preferential strong adsorption of carbon dioxide. Injection of a mixture rich in carbon dioxide gives slower initial recovery, increases breakthrough time, and decreases the volume of gas needed to sweep out the coalbed. Injection gas rich in nitrogen leads to relatively fast recovery of methane, earlier breakthrough, and a significant fraction of nitrogen in the produced gas at short times. A one-dimensional, two-phase (gas and solid) model was employed to rationalize and explain the experimental data and trends. Reproduction of binary behavior is characterized as excellent, whereas the dynamics of ternary systems are predicted with less accuracy. For these coals, the most sensitive simulation input were the multicomponent adsorption–desorption isotherms, including scanning loops. Additionally, the coal exhibited a two-porosity matrix that was incorporated numerically.

Upscaling of Stochastic Micro Model for Suspension Transport in Porous Media

Abstract: Micro scale population balance equations of suspension transport in porous media with several particle capture mechanisms are derived, taking into account the particle capture by accessible pores, that were cut off the flux due to pore plugging. The main purpose of the article is to prove that the micro scale equations allow for exact upscaling (averaging) in case of filtration of mono dispersed suspensions. The averaged upper scale equations generalise the classical deep bed filtration model and its latter modifications.

Microscopic Mechanisms of Oil Recovery By Near-Miscible Gas Injection

Abstract: As gas flooding becomes a more viable means of enhanced oil recovery, it is important to identify and understand the pore-scale flow mechanisms, both for the development of improved gas flooding applications and for the predicting phase mobilisation under secondary and tertiary gas flooding. The purpose of this study was to visually investigate the pore-level mechanisms of oil recovery by near-miscible secondary and tertiary gas floods. High-pressure glass micromodels and model fluids representing a near-miscible fluid system were used for the flow experiments. A new pore-scale recovery mechanism was identified which significantly contributed to oil recovery through enhanced flow and cross-flow between the bypassed pores and the injected gas. This mechanism is strongly related to a very low gas/oil interfacial tension (IFT), perfect wetting conditions and simultaneous flow of gas and oil in the same pore, all of which occur as the gas/oil critical point is approached. The results of this study helps us to better understand the pore-scale mechanisms of oil recovery in very low-IFT (near-miscible) systems. In particular we show that in near-miscible gas floods, behind the main gas front, the recovery of the oil continues by cross-flow from the bypassed pores into the main flow stream and as a result almost all of the oil, which has been contacted by the gas, could be recovered. Our observations in high-pressure micromodel experiments have demonstrated that this mechanism can only occur in near-miscible processes (as opposed to immiscible and completely miscible processes), which makes oil displacement by near-miscible gas floods a very effective process.

CO2 injection into saline carbonate aquifer formations I: laboratory investigation

Abstract: Although there are a number of mathematical modeling studies for carbon dioxide (CO2) injection into aquifer formations, experimental studies are limited and most studies focus on injection into sandstone reservoirs as opposed to carbonate ones. This study presents the results of computerized tomography (CT) monitored laboratory experiments to analyze permeability and porosity changes as well as to characterize relevant chemical reactions associated with injection and storage of CO2 in carbonate formations. CT monitored experiments are designed to model fast near well bore flow and slow reservoir flows. Highly heterogeneous cores drilled from a carbonate aquifer formation located in South East Turkey were used during the experiments. Porosity changes along the core plugs and the corresponding permeability changes are reported for different CO2 injection rates and different salt concentrations of formation water. It was observed that either a permeability increase or a permeability reduction can be obtained. The trend of change in rock properties is very case dependent because it is related to distribution of pores, brine composition and thermodynamic conditions. As the salt concentration decreases, porosity and the permeability decreases are less pronounced. Calcite deposition is mainly influenced by orientation, with horizontal flow resulting in larger calcite deposition compared to vertical flow.

Flow Laws in Metal Foams: Compressibility and Pore Size Effects

Abstract: The aim of our experimental work was to establish a simple relation between the flow parameters and the morphological parameters of metallic foam. We used foam samples made from different metals or alloys (Cu, Ni, Ni-Cr, etc) and of various thicknesses. Pore size ranged between 500 and 5000 μm. We measured the pressure profiles in foam samples using a specific experimental set-up of 12 pressure sensors distributed 1 cm apart along the main flow axis. The experimental loop made it possible to use indifferently water or air as working fluid. For the study of the gas (air) flow, velocities ranged roughly from 0 up to 20 m/s and for the liquid (water) flow, velocities ranged between 0 and 0.1 m/s. The measurements of the pressure gradients were performed systematically. We validated the Forchheimer flow model. The influence of the compressibility effects on permeability and inertia coefficient was emphasized. We demonstrated that the pore size Dp in itself is sufficient to describe flow laws in such high porosity material: K and β are respectively proportional to Dp2 and Dp−1.

Visualisation of Residual Oil Recovery by Near-miscible Gas and SWAG Injection Using High-pressure Micromodels

Abstract: We present results of high-pressure micromodel visualizations of pore-scale fluid distribution and displacement mechanisms during the recovery of residual oil by near-miscible hydrocarbon gas and SWAG (simultaneous water and gas) injection under conditions of very low gas–oil IFT (interfacial tension), negligible gravity forces and water-wet porous medium. We demonstrate that a significant amount of residual oil left behind after waterflooding can be recovered by both near-miscible gas and SWAG injection. In particular, we show that in both processes, the recovery of the contacted residual oil continues behind the main gas front and ultimately all of the oil that can be contacted by the gas will be recovered. This oil is recovered by a microscopic mechanism, which is strongly linked to the low IFT between the oil and gas and to the perfect spreading of the oil over water, both of which occur as the critical point of the gas–oil system is approached. Ultimate oil recovery by near-miscible SWAG injection was as high as near-miscible gas injection with SWAG injection using much less gas compared to gas injection. Comparison of the results of SWAG experiments with two different gas fractional flow values (SWAG ratio) of 0.5 and 0.2 shows that fractional flow of the near-miscible gas injected simultaneously with water is not a crucial factor for ultimate oil recovery. This makes SWAG injection an attractive IOR (improved oil recovery) process especially for reservoirs, where continuous and high-rate gas injection is not possible (e.g. due to supply constraint).

A resistance model for flow through porous media

Abstract: A new model for resistance of flow through granular porous media is developed based on the average hydraulic radius model and the contracting-expanding channel model. This model is expressed as a function of tortuosity, porosity, ratio of pore diameter to throat diameter, diameter of particles, and fluid properties. The two empirical constants, 150 and 1.75, in the Ergun equation are replaced by two expressions, which are explicitly related to the pore geometry. Every parameter in the proposed model has clear physical meaning. The proposed model is shown to be more fundamental and reasonable than the Ergum equation. The model predictions are in good agreement with the existing experimental data.

MHD Peristaltic Transport of a Jeffery Fluid in a Channel With Compliant Walls and Porous Space

Abstract: Here an attempt has been made to investigate the magnetohydrodynamic (MHD) flow of a non-Newtonian fluid filling the porous space in a channel with compliant walls. Constitutive equations of a Jeffery fluid are used in the mathematical modeling. The flow is created due to sinusoidal traveling waves on the channel walls. The resulting problem is solved analytically and series solution for a stream function is derived. The effects of pertinent flow parameters are discussed through graphs.

The transverse permeability of disordered fiber arrays: a statistical correlation in terms of the mean nearest interfiber spacing

Abstract: In the porous media literature, unidirectional fibrous systems are broadly categorized as ordered or disordered. The former class, easily tractable for analysis purposes but limited in its relation to reality, involves square, hexagonal and various staggered arrays. The latter class involves everything else. While the dimensionless hydraulic permeability of ordered fibrous media is known to be a deterministic function of their porosity ϕ, the parameters affecting the permeability of disordered fiber arrays are not very well understood. The objective of this study is to computationally investigate flow across many unidirectional arrays of randomly placed fibers and derive a correlation between K and some measure of their microstructure. In the process, we explain the wide scatter in permeability values observed computationally as well as experimentally. This task is achieved using a parallel implementation of the Boundary Element Method (BEM). Over 600 simulations are carried out in two-dimensional geometries consisting of 576 fiber cross-sections placed within a square unit cell by a Monte Carlo procedure. The porosity varies from 0.45 to 0.90. The computed permeabilities are compared with earlier theoretical results and experimental data. Analysis of the computational results reveals that the permeability of disordered arrays with ϕ < 0.7 is reduced as the non-uniformity of the fiber distribution increases. This reduction can be substantial at low porosities. The key finding of this study is a direct correlation between K and the mean nearest inter-fiber spacing \(\bar{\delta}_{1}\), the latter depending on the microstructure of the fibrous medium.

CO2 Injection into Saline Carbonate Aquifer Formations II: Comparison of Numerical Simulations to Experiments

Abstract: Sequestration of carbon dioxide in geological formations is an alternative way of managing extra carbon. Although there are a number of mathematical modeling studies related to this subject, experimental studies are limited and most studies focus on injection into sandstone reservoirs as opposed to carbonate ones. This study describes a fully coupled geochemical compositional equation-of-state compositional simulator (STARS) for the simulation of CO2 storage in saline aquifers. STARS models physical phenomena including (1) thermodynamics of sub- and supercritical CO2, and PVT properties of mixtures of CO2 with other fluids, including (saline) water; (2) fluid mechanics of single and multiphase flow when CO2 is injected into aquifers; (3) coupled hydrochemical effects due to interactions between CO2, reservoir fluids, and primary mineral assemblages; and (4) coupled hydromechanical effects, such as porosity and permeability change due to the aforementioned blocking of pores by carbonate particles and increased fluid pressures from CO2 injection. Matching computerized tomography monitored laboratory experiments showed the uses of the simulation model. In the simulations dissolution and deposition of calcite as well as adsorption of CO2 that showed the migration of CO2 and the dissociation of CO2 into HCO3 and its subsequent conversion into carbonate minerals were considered. It was observed that solubility and hydrodynamic storage of CO2 is larger compared to mineral trapping.

Viscous Fingering Instability in Porous Media : Effect of Anisotropic Velocity-Dependent Dispersion Tensor

Abstract: The viscous fingering of miscible flow displacements in a homogeneous porous media is examined to determine the effects of an anisotropic dispersion tensor on the development of the instability. In particular, the role of velocity-dependent transverse and longitudinal dispersions is investigated through linear stability analysis and nonlinear simulations. It is found that an isotropic velocity-dependent dispersion tensor does not affect substantially the development of the instability and effectively has the same effect as molecular diffusion. On the other hand, an anisotropic velocity-dependent dispersion tensor results in different instability characteristics and more intricate finger structures. It is shown that anisotropic dispersion has profound effects on the development of the fingers and on the mechanisms of interactions between neighboring fingers. The development of the new finger structures is explained by examining the velocity field and characterized qualitatively through a spectral analysis of the average concentration and an analysis of the variations of the sweep efficiency and relative contact area.

Effect of reactive surface areas associated with different particle shapes on chemical-dissolution front instability in fluid-saturated porous rocks

Abstract: In this article, the effect of reactive surface areas associated with different particle shapes on the reactive infiltration instability in a fluid-saturated porous medium is investigated through analytically deriving the dimensionless pore-fluid pressure-gradient of a coupled system between porosity, pore-fluid flow and reactive chemical-species transport within two idealized porous media consisting of spherical and cubic grains respectively. Compared with the critical dimensionless pore-fluid pressure-gradient of the coupled system, the derived dimensionless pore-fluid pressure-gradient can be used to assess the instability of a chemical dissolution front within the fluid-saturated porous medium. The related theoretical analysis has demonstrated that (1) since the shape coefficient of spherical grains is greater than that of cubic grains, the chemical system consisting of spherical grains is more unstable than that consisting of cubic grains, and (2) the instability likelihood of a natural porous medium, which is comprised of irregular grains, is smaller than that of an idealized porous medium, which is comprised of regular spherical grains. To simulate the complicated morphological evolution of a chemical dissolution front in the case of the chemical dissolution system becoming supercritical, a numerical procedure is proposed for solving this kind of problem. The related numerical results have demonstrated that the reactive surface area associated with different particle shapes can have a significant influence on the morphological evolution of an unstable chemical-dissolution front within fluid-saturated porous rocks.

Competitive Methane Desorption by Supercritical CO2 Injection in Coal

Abstract: A large diameter (∼70 mm) dry coal sample was used to study the competitive displacement of CH4 by injection of supercritical CO2, and CO2–CH4 counter-diffusion in coal matrix. During the test, a staged loading procedure, which allows the calibration of the key reservoir modelling parameters in a sequential and progressive manner, was employed. The core-flooding test was history matched using an Enhanced Coalbed Methane (ECBM) simulator, in which Fick’s Law for mixed gas diffusion and the extended Langmuir equations are implemented. The system pressure rise during the two loading stages and the CO2 breakthrough time in the final production stage were matched by using the pair of constant sorption times (9 and 3.2 days) for CH4 and CO2, respectively. The corresponding diffusion coefficients for CH4 and CO2 were estimated to be 1.6 × 10−12 and 4.6 × 10−12 m2/s, respectively. Comparison was made with published gas diffusion coefficients for dry ground samples (ranging from < 0.063 to ∼3 mm) of the same coal at relatively low pressures (< 4 MPa). The CO2/CH4 gas diffusion coefficient ratio was well within the reported range (2–3), whereas the CH4 diffusion coefficient obtained from history matching of the core-flooding test is approximately 15 times smaller than that arrived by curve-fitting the measured sorption uptake rate using a unipore diffusion model. The calibrated model prediction of the effluent gas composition was in good agreement with the test data for CO2 mole fraction of up to 20%.

Analytic solution for flow of Sisko fluid through a porous medium

Abstract: This paper presents the analytic solution for flow of a magnetohydrodynamic (MHD) Sisko fluid through a porous medium. The non-linear flow problem in a porous medium is formulated by introducing the modified Darcy’s law for Sisko fluid to discuss the flow in a porous medium. The analytic solutions are obtained using homotopy analysis method (HAM). The obtained analytic solutions are explicitly expressed by the recurrence relations and can give results for all the appropriate values of material parameters of the examined fluid. Moreover, the well-known solutions for a Newtonian fluid in non-porous and porous medium are the limiting cases of our solutions.

Laboratory Experiments on Environmental Friendly Means to Improve Coalbed Methane Production by Carbon Dioxide/Flue Gas Injection

Abstract: Scaled in situ laboratory core flooding experiments with CO2, N2 and flue gas were carried out on coal in an experimental high P,T device. These experiments will be able to give an insight into the design of the injection system, management, control of the operations and the efficiency of an ECBM project. Although the experience gained by the oil industry represents a valuable starting point, several problems are still to be studied and solved before CO2 improved deep coalbed methane production may be operationally feasible. These are all related to the heterogeneous nature of the pore structure of coal, and in particular to the presence of fractures. More specifically, a number of questions need to be addressed, e.g. what are the conditions under which the fluid in the micro pores of the coal is displaced by the CO2 in the presence of competitive adsorption; what is the role of compositional heterogeneity and fracture anisotropy of coal for the injection design and the efficiency of the sequestration in relation to the swelling and shrinkage characteristics of coal; how does the mobile and the immobile water in the coal affect the exchange process. These questions can be answered by means of downscaled laboratory experiments that are capable of accurately describing the coupled process of multiphase flow, competitive adsorption and geo-mechanics. The laboratory conditions have been simulated to match pressure and temperature at depths of 800 to 1,000 m. Under those conditions the injected CO2 remains supercritical. Upto now, the results show that dewatering will be an essential step for successful ECBM combined with a CO2 sequestration process.

Two-Phase Flow in Porous Media with Slip Boundary Condition

Abstract: Flow in porous media described by Darcy’s law extended to two-phase flow using the concept of relative permeabilities k r naturally assumes a maximum value of 0 ≤ k r ≤ 1. Reports in literature and our own experimental data show endpoint relative permeabilities k r > 1. In the porous medium, the flux of the non-wetting phase is in many cases about 2-4 times higher when a small amount of the wetting phase is present. Here, we draw an analogy between k r > 1 and a slip-boundary condition for the pore scale flow. We use a model description assuming flow in capillary tubes with a slip boundary condition. This model predicts that the flux increase due to slip depends on the equivalent capillary radius of the flow channels. Our k r data specifically follows this dependence indicating that slip is a plausible explanation for the observation of k r > 1.

A Semi-empirical Correlation for Pressure Drop in Packed Beds of Spherical Particles

Abstract: The effect of a confining wall on the pressure drop of fluid flow through packed beds of spherical particles with small bed-to-particle diameter ratios was investigated to develop an improved pressure drop correlation. The dependency of pressure loss on both wall friction and increased porosity near the wall was accounted for by using a theoretical approach. A semi-empirical model was created based upon the capillary-orifice model, which included a wall correction factor for the inertial pressure loss. In this model, packed beds were treated as a bundle of capillary tubes whose orifice diameter in the core region was different from that of the wall region. Using this model, a new pressure drop correlation was obtained, based on the Ergun equation and applicable for a wide range of Reynolds numbers (10−2–103). The proposed correlation was compared with previous correlations, as well as with experimental data. This correlation showed close agreement with the experimental data for both low- and high-Reynolds number regimes and for a wide range of bed-to-particle diameter ratios. The ratio of the pressure drop in finite packing to that in homogeneous packing was then calculated. This ratio clearly shows how the wall effect depends on the Reynolds number and the bed-to-particle diameter ratio.

Nonisothermal moisture transport in hygroscopic building materials: modeling for the determination of moisture transport coefficients

Abstract: A mathematical model for calculating the nonisothermal moisture transfer in building materials is presented in the article. The coupled heat and moisture transfer problem was modeled. Vapor content and temperature were chosen as principal driving potentials. The coupled equations were solved by an analytical method, which consists of applying the Laplace transform technique and the Transfer Function Method. A new experimental methodology for determining the temperature gradient coefficient for building materials was also proposed. Both the moisture diffusion coefficient and the temperature gradient coefficient for building material were experimentally evaluated. Using the measured moisture transport coefficients, the temperature and vapor content distribution inside building materials were predicted by the new model. The results were compared with experimental data. A good agreement was obtained.

Compositional Space Parametrization for Miscible Displacement Simulation

Abstract: Thermodynamic equilibrium computations are the most time-consuming part of a compositional flow simulation. We describe a compositional space parameterization approach for dealing with gas injection displacement processes. This tie-line-based parameterization can be used to replace existing compositional simulation methods completely. We illustrate our approach using numerical examples of challenging multi-component miscible gas injection problems.

The Effect of Rotation on the Onset of Double Diffusive Convection in a Horizontal Anisotropic Porous Layer

Abstract: The effect of rotation and anisotropy on the onset of double diffusive convection in a horizontal porous layer is investigated using a linear theory and a weak nonlinear theory. The linear theory is based on the usual normal mode technique and the nonlinear theory on the truncated Fourier series analysis. Darcy model extended to include time derivative and Coriolis terms with anisotropic permeability is used to describe the flow through porous media. The effect of rotation, mechanical and thermal anisotropy parameters, and the Prandtl number on the stationary and overstable convection is discussed. It is found that the effect of mechanical anisotropy is to allow the onset of oscillatory convection instead of stationary. It is also found that the existence of overstable motions in case of rotating porous medium is not restricted to a particular range of Prandtl number as compared to the pure viscous fluid case. The finite amplitude analysis is performed to find the thermal and solute Nusselt numbers. The effect of various parameters on heat and mass transfer is also investigated.

A New Method for Calculating Two-Phase Relative Permeability from Resistivity Data in Porous Media

Abstract: Many resistivity data from laboratory measurements and well logging are available. Papers on the relationship between resistivity and relative permeability have been few. To this end, a new method was developed to infer two-phase relative permeability from the resistivity data in a consolidated porous medium. It was found that the wetting phase relative permeability is inversely proportional to the resistivity index of a porous medium. The proposed model was verified using the experimental data in different rocks (Berea, Boise sandstone, and limestone) at different temperatures up to 300°F. The results demonstrated that the oil and water relative permeabilities calculated from the experimental resistivity data by using the model proposed in this article were close to those calculated from the capillary pressure data in the rock samples with different porosities and permeabilities. The results demonstrated that the proposed approach to calculating two-phase relative permeability from resistivity data works satisfactorily in the cases studied.

Efficiency of diffusion controlled miscible displacement in fractured porous media

Abstract: Experiments were performed to study the diffusion process between matrix and fracture while there is flow in fracture. 2-inch diameter and 6-inch length Berea sandstone and Indiana limestone samples were cut cylindrically. An artificial fracture spanning between injection and production ends was created and the sample was coated with heat-shrinkable teflon tube. A miscible solvent (heptane) was injected from one end of the core saturated with oil at a constant rate. The effects of (a) oil type (mineral oil and kerosene), (b) injection rates, (c) orientation of the core, (d) matrix wettability, (e) core type (a sandstone and a limestone), and (f) amount of water in matrix on the oil recovery performance were examined. The process efficiency in terms of the time required for the recovery as well as the amount of solvent injected was also investigated. It is expected that the experimental results will be useful in deriving the matrix–fracture transfer function by diffusion that is controlled by the flow rate, matrix and fluid properties.

Wetting Phase Bridges Establish Capillary Continuity Across Open Fractures and Increase Oil Recovery in Mixed-Wet Fractured Chalk

Abstract: The effect of fractures on oil recovery and in situ saturation development in fractured chalk has been determined at near neutral wettability conditions. Fluid saturation development was monitored both in the matrix and in the fractures and the mechanisms of fracture crossing were determined using high spatial resolution MRI. Capillary continuity across open oil-filled fractures was verified by imaging the water bridges established within the fracture. Despite an alternate escape fracture for the water, separate water bridges were shown to be stable for the entire duration of the experiments. The established capillary contact resulted in oil recovery exceeding the spontaneous imbibition potential in the outlet-isolated cores by ca. 10% PV. This is explained by viscous recovery provided by water bridges across open fractures. The size of the bridges seemed to be controlled by the wettability of the rock and not by the differential pressure applied across the open fracture.

Integration of genetic algorithm and a coactive neuro-fuzzy inference system for permeability prediction from well logs data

Abstract: Permeability is one of the reservoir fundamental properties, which relate to the amount of fluid contained in a reservoir and its ability to flow. These properties have a significant impact on petroleum fields operations and reservoir management. The most reliable data of local permeability are taken from laboratory analysis of cores. Extensive coring is very expensive and this expense becomes reasonable in very limited cases. Thus, the proper determination of the permeability is of paramount importance because it affects the economy of the whole venture of development and operation of a field. In this study, we introduce a new hybrid network based on Coactive Neuro-Fuzzy Inference System (CANFIS). CANFIS is a dependable and robust network that developed to identify a non-linear relationship and mapping between petrophysical data and core samples. Then to improve the system performance, genetic algorithm (GA) was integrated in order to search of optimal network parameters and decrease of noisy data in training samples. An Iranian offshore gas field is located in the Persian Gulf, has been selected as the study area in this paper. Well log data are available on substantial number of wells. Core samples are also available from a few wells. It was shown that the new proposed strategy is an effective method in predicting permeability from well logs.

The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium: double diffusive case

Abstract: The effects of both horizontal and vertical hydrodynamic, thermal and solutal heterogeneity, on the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below, are studied analytically using linear stability theory for the case of weak heterogeneity. The Brinkman model is employed. It is found that the effect of such heterogeneity on the critical value of the Rayleigh number Ra based on mean properties is of second order if the properties vary in a piecewise constant or linear fashion. The effects of horizontal heterogeneity and vertical heterogeneity are then comparable once the aspect ratio is taken into account, and to a first approximation are independent.

Upscaling and Simulation of Waterflooding in Heterogeneous Reservoirs Using Wavelet Transformations: Application to the SPE-10 Model

Abstract: We have developed an accurate and highly efficient method for upscaling and simulation of immiscible displacements in three-dimensional (3D) heterogeneous reservoirs, which is an extension of the technique that we developed previously for 2D systems. The method utilizes wavelet transformations (WTs) to upscale the geological model of a reservoir, based on the spatial distribution of the single-phase permeabilities and the locations of the wells in the reservoir. It generates a non-uniform grid in which the resolved structure of the fine grid around the wells, as well as in the high-permeability sectors, are preserved, but the rest of the grid is upscaled. A robust uplayering procedure is used to reduce the number of the layers, and the WTs are used to upscale each layer areally. To demonstrate the method’s accuracy and efficiency, we have applied it to the geological model of a highly heterogeneous reservoir put forward in the tenth Society of Petroleum Engineers comparative solution project (the SPE-10 model), and carried out simulation of waterflooding in the upscaled model. Various upscaling scenarios were examined, and although some of them resulted in efficient simulations and accurate predictions, the results when non-uniform upscaling is used based on the WT technique are in excellent agreement with the solution of the same problem in the fine grid of the SPE-10 model. Most importantly, the speed-up factors that we obtain are several orders of magnitude. Hence, the method renders it unnecessary to use massively parallel computations for such problems.

Two-Phase Inertial Flow in Homogeneous Porous Media: A Theoretical Derivation of a Macroscopic Model

Abstract: The purpose of this article is to derive a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. Starting from the continuity and Navier–Stokes equations in each phase β and γ, the method of volume averaging is employed subjected to constraints that are explicitly provided to obtain the macroscopic mass and momentum balance equations. These constraints are on the length- and time-scales, as well as, on some quantities involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The resulting macroscopic momentum equation relates the phase-averaged pressure gradient \( abla \langle p_{\alpha}\rangle^{\alpha}\) to the filtration or Darcy velocity \(\langle {\mathbf{v}}_{\alpha}\rangle\) in a coupled nonlinear form explicitly given by $$\langle {\mathbf{v}}_{\alpha}\rangle =-\frac{{\mathbf{K}}_{\alpha \alpha}^{{\mathbf{\ast}}}}{\mu _{\alpha}} \,\cdot\, ( abla \langle p_{\alpha}\rangle^{\alpha}-\rho _{\alpha}{\mathbf{g}})-{\mathbf{F}}_{\alpha \alpha} \,\cdot\, \langle {\mathbf{v}}_{\alpha} \rangle -\frac{{\mathbf{K}}_{\alpha \kappa}^{{\mathbf{\ast}}}}{\mu_{\kappa}} \,\cdot\, ( abla \langle p_{\kappa}\rangle^{\kappa}-\rho_{\kappa}{\mathbf{g}})-{\mathbf{F}}_{\alpha \kappa}\,\cdot\, \langle {\mathbf{v}}_{\kappa}\rangle \qquad\alpha ,\kappa =\beta, \gamma \quad\alpha eq \kappa$$ or equivalently $$\langle {\mathbf{v}}_{\alpha}\rangle =-\frac{{\mathbf{K}}_{\alpha}}{\mu _{\alpha}}\,\cdot\, ( abla \langle p_{\alpha} \rangle^{\alpha}-\rho _{\alpha}{\mathbf{g}})-{\mathbf{F}}_{\alpha \alpha} \,\cdot\, \langle {\mathbf{v}}_{\alpha}\rangle +\,{\mathbf{K}}_{\alpha \kappa}\,\cdot\, \langle {\mathbf{v}}_{\kappa}\rangle - {\mathbf{F}}_{\alpha \kappa} \,\cdot\, \langle {\mathbf{v}}_{\kappa}\rangle\qquad \alpha ,\kappa =\beta ,\gamma \quad\alpha eq \kappa$$ In these equations, \({\mathbf{F}}_{\alpha \alpha}\) and \({\mathbf{F}}_{\alpha \kappa}\) are the inertial and coupling inertial correction tensors that are functions of flow-rates. The dominant and coupling permeability tensors \({\mathbf{K}}_{\alpha \alpha}^{{\mathbf{\ast}}}\) and \({\mathbf{K}}_{\alpha \kappa}^{{\mathbf{\ast}}}\) and the permeability and viscous drag tensors \({\mathbf{K}}_{\alpha}\) and \({\mathbf{K}}_{\alpha \kappa}\) are intrinsic and are those defined in the conventional manner as in (Whitaker, Chem Eng Sci 49:765–780, 1994) and (Lasseux et al., Transport Porous Media 24(1):107–137, 1996). All these tensors can be determined from closure problems that are to be solved using a spatially periodic model of a porous medium. The practical procedure to compute these tensors is provided.

New criteria for the validity of steady-state upscaling

Abstract: We present new dimensionless criteria to determine the validity of steady-state upscaling techniques in the limit that capillary (capillary limit, CL) or viscous (viscous limit, VL) forces dominate flow in a simple, layered geological system. We begin by identifying a suit of dimensionless groups which characterize the balance of capillary and viscous forces, then use numerical experiments to determine empirically the threshold values of these dimensionless groups for which each upscaling method is valid. Our criteria capture the effects of capillary trapping and are valid regardless of fluid mobility, wettability, or end-point saturation. They can be used to determine the reservoir conditions for which each upscaling method is valid. Previous studies have used a single dimensionless number to characterize the balance of forces, so have failed to properly identify the range of validity. We apply our new criteria to explain cases when the upscaling methods have been observed to do unexpectedly well or poorly. We also demonstrate that the CL method can be valid for a wider range of reservoir conditions than previously thought, particularly in mixed- and oil-wet systems where capillary trapping is minimal.

The effects of filtration on the injection of cement-based grouts in sand columns

Abstract: This article presents injection experiments and modeling of cement based grout in sand. In particular, it focuses on the role of filtration during the sand impregnation by the grout. One-dimensional injection tests in sand columns are performed. In these, the mass intake of the sample and the injection pressure are measured to quantify the effects of filtration during grouting. The cement-to-water ratio of the grout and the initial density of the soil are also studied. The modeling of these tests is achieved by incorporating the filtration and the damage coefficients in the classical transport in porous media equations. A method is proposed to determine these coefficients. The method simultaneously relies on both analytical analysis and experimental measurements. Density and viscosity effects are also considered in the model equations which are solved using the finite element method. The simulation of an injection test proves that the model is suitable to recover the injection pressure obtained experimentally. Finally, both experimental and numerical results reveal the importance of including filtration when analyzing one-dimensional injections of cement based grouts in sand.