Scaling of Transport Properties of Reservoir Material at Low Saturations of a Wetting Phase

1994 ◽  
Vol 367 ◽  
Author(s):  
Y. Carolina Araujo ◽  
Pedro G. Toledo ◽  
Hada Y. Gonzalez
Keyword(s):  
Electrical Conductivity ◽  
Porous Media ◽  
Transport Properties ◽  
Capillary Pressure ◽  
Power Law ◽  
Scaling Laws ◽  
Pore Space ◽  
Conductivity Data ◽  
Phase Saturation ◽  
Electrical Conductivity Data

AbstractTransport properties of natural porous media have been observed to obey scaling laws in the wetting phase saturation. Previous work relates power-law behavior at low wetting phase saturations, i.e., at high capillary pressures, to the thin-film physics of the wetting phase and the fractal character of the pore space of porous media. Here, we present recent combined porousplate capillary pressure and electrical conductivity data of Berea sandstone at low saturations that lend support to the scaling laws. Power law is interpreted in terms of the exponent m in the relation of surface forces and film thickness and the fractal dimension D of the interface between pore space and solid matrix. Simple determination of D from capillary pressure and m from electrical conductivity data can be used to rapidly determine wetting phase relative permeability and capillary dispersion coefficient at low wetting phase saturations.

Numerical estimation of electrical conductivity in saturated porous media with a 2-D lattice gas

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 766-772 ◽  
Author(s):  
Michel Küntz ◽  
Jean Claude Mareschal ◽  
Paul Lavallée
Keyword(s):  
Electrical Conductivity ◽  
Porous Media ◽  
Power Law ◽  
Lattice Gas ◽  
Effective Conductivity ◽  
Pore Space ◽  
Solid Matrix ◽  
Conductivity Ratio ◽  
Saturated Porous Media ◽  
Formation Factor

A 2-D lattice gas is used to calculate the effective electrical conductivity of saturated porous media as a function of porosity and conductivity ratio [Formula: see text] between the pore‐filling fluid and the solid matrix for various microscopic structures of the pore space. The way the solid phase is introduced allows the porosity ϕ to take any value between 0 and 1 and the geometry of the pore structure to be as complex as desired. The results are presented in terms of the formation factor [Formula: see text], with [Formula: see text] the effective conductivity of the saturated rock and [Formula: see text] the conductivity of the fluid. It is shown that the formation factor F as a function of the porosity ϕ follows a power law [Formula: see text], equivalent to the empirical Archie’s law. The exponent m varies with the microgeometry of the pore space and could therefore reflect the microstructure at the macroscopic scale. The prefactor a of the power law, however, is close to 1 regardless of the microstructure. For a given microgeometry of the pore space, the variation of the residual electrical conductivity of the solid matrix induced by a finite conductivity ratio [Formula: see text] does not significantly influence the variation of the effective conductivity of the fluid‐solid binary mixture unless the porosity is low.

Evaluation of Scale-Up Laws for Two-Phase Flow Through Porous Media

1963 ◽  
Vol 3 (02) ◽  
pp. 164-176 ◽  
Author(s):  
Russell L. Nielsen ◽  
M.R. Tek
Keyword(s):  
Porous Media ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Scaling Laws ◽  
Laboratory Model ◽  
Gas Reservoir ◽  
Two Phase ◽  
Phase Saturation ◽  
Water Coning ◽  
Capillary Pressure Curves

The scaling laws as formulated by Rapport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions.Two hypothetical systems - a gas reservoir subject to water drive and the laboratory scaled model of that reservoir - were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these particular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system.This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. Introduction Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models.To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoport and others. Rapoport's scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems.It will be recalled that these scaling laws presuppose three conditions:the relative permeability curves must be identical for the model and prototype;the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; andboundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because:The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media.The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent.Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible.The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible.The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. SPEJ P. 164^

Multiphase-Flow and Reactive-Transport Validation Studies at the Pore Scale by Use of Lattice Boltzmann Computer Simulations

SPE Journal ◽  
2017 ◽  
Vol 22 (03) ◽  
pp. 940-949 ◽  
Author(s):  
Edo S. Boek ◽  
Ioannis Zacharoudiou ◽  
Farrel Gray ◽  
Saurabh M. Shah ◽  
John P. Crawshaw ◽  
...  
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Capillary Pressure ◽  
Computer Simulations ◽  
Relative Permeability ◽  
Lattice Boltzmann ◽  
Reactive Transport ◽  
Pore Space ◽  
Processing Unit ◽  
Space Images

Summary We describe the recent development of lattice Boltzmann (LB) and particle-tracing computer simulations to study flow and reactive transport in porous media. First, we measure both flow and solute transport directly on pore-space images obtained from micro-computed-tomography (CT) scanning. We consider rocks with increasing degree of heterogeneity: a bead pack, Bentheimer sandstone, and Portland carbonate. We predict probability distributions for molecular displacements and find excellent agreement with pulsed-field-gradient (PFG) -nuclear-magnetic-resonance (NMR) experiments. Second, we validate our LB model for multiphase flow by calculating capillary filling and capillary pressure in model porous media. Then, we extend our models to realistic 3D pore-space images and observe the calculated capillary pressure curve in Bentheimer sandstone to be in agreement with the experiment. A process-based algorithm is introduced to determine the distribution of wetting and nonwetting phases in the pore space, as a starting point for relative permeability calculations. The Bentheimer relative permeability curves for both drainage and imbibition are found to be in good agreement with experimental data. Third, we show the speedup of a graphics-processing-unit (GPU) algorithm for large-scale LB calculations, offering greatly enhanced computing performance in comparison with central-processing-unit (CPU) calculations. Finally, we propose a hybrid method to calculate reactive transport on pore-space images by use of the GPU code. We calculate the dissolution of a porous medium and observe agreement with the experiment. The LB method is a powerful tool for calculating flow and reactive transport directly on pore-space images of rock.

Coulometric Titration Studies of Nonstoichiometric Nanocrystalline Ceria

1996 ◽  
Vol 457 ◽  
Author(s):  
O. Porat ◽  
H. L. Tuller ◽  
E. B. Lavik ◽  
Y.-M. Chiang
Keyword(s):  
Electrical Conductivity ◽  
Oxygen Vacancies ◽  
Coulometric Titration ◽  
Surface Adsorption ◽  
Oxygen Nonstoichiometry ◽  
Conductivity Data ◽  
Nanocrystalline Ceria ◽  
Electrical Conductivity Data

ABSTRACTOxygen nonstoichiometry measurements in nanocrystalline ceria, x in CeO2-x, were performed using coulometric titration. The measurements reveal large apparent deviations from stoichiometry, of the order of 10−3 − 10−4 at T = 405 − 455 °C and Po2 = 0.21 − 10−5 atm, as compared to levels of ∼10−9 for coarsened materials under the same conditions. The level of nonstoichiometry is, however, larger then expected from previous electrical conductivity data of nanocrystalline ceria. In addition, x ∝ Po2−½ while Σ ∝po2−1/6. The observed dependence of x(Po2, T) can be explained by either the formation of neutral oxygen vacancies at or near the interface, or by surface adsorption.

Electrical conductivity data of alkanols from 273 to 333 K

2003 ◽  
Vol 102 (1-3) ◽  
pp. 83-91 ◽  
Author(s):  
M. Prego ◽  
E. Rilo ◽  
E. Carballo ◽  
C. Franjo ◽  
E. Jiménez ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Conductivity Data ◽  
Electrical Conductivity Data

Amazonian floodplain water balance based on modelling and analyses of hydrologic and electrical conductivity data

2017 ◽  
Vol 31 (9) ◽  
pp. 1702-1718 ◽  
Author(s):  
Marie-Paule Bonnet ◽  
Sébastien Pinel ◽  
Jérémie Garnier ◽  
Julie Bois ◽  
Géraldo Resende Boaventura ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Water Balance ◽  
Conductivity Data ◽  
Electrical Conductivity Data
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