Begell House Inc.
Journal of Porous Media
JPM
1091-028X
17
4
2014
MATHEMATICAL MODEL AND ANALYTICAL SOLUTIONS FOR UNSTEADY FLOW IN NATURAL GAS RESERVOIRS
279-285
10.1615/JPorMedia.v17.i4.10
Binshan
Ju
School of Energy Resources, China University of Geosciences, Beijing, 100083, China
gas reservoir
flow in porous media
mathematical model
analytical solution
The effects of pressure on the gas viscosity and compressibility factor lead to a nonlinear partial differential equation for the flow in a gas reservoir even if the flow process follows Darcy's law at isothermal conditions. For further study on gas flow performances in gas reservoirs, a mathematical model of gas flow is developed in this article. Exact analytical solutions of one-dimensional unsteady gas flow at low and high pressures in gas reservoirs are obtained by transferring the nonlinear partial differential equation into a nonlinear ordinary differential equation. The numerical solutions obtained by finite difference for two cases of low- and high-pressure condition are given to validate the analytical solutions presented in this work. The key parameters, such as viscosity index, permeability, and porosity, to determine the characteristic of pressure distribution in porous media are analyzed in this work. The solutions at high pressures imply that it leads to obvious errors for prediction pressure distribution when ignoring pressure's effects on gas viscosity and compressibility factor for gas flow at high pressures in deep gas reservoirs. Both the increase in viscosity index and the decrease in permeability lead to an increase in pressure gradients along the distance.
FLOW OF IMMISCIBLE MICROPOLAR FLUIDS BETWEEN TWO POROUS BEDS
287-300
10.1615/JPorMedia.v17.i4.20
J. V. Ramana
Murthy
Department of Mathematics, National Institute of Technology, Warangal-506 004, A.P., India
J.
Srinivas
Department of Mathematics, National Institute of Technology, Warangal-506 004, A.P., India
K. S.
Sai
Department of Mathematics, DMSSVH College of Engineering, Krishna-521 002, A.P., India
micropolar fluid
immiscible fluids
porous beds
Darcy's law
Brinkman's equation
slip boundary condition
The article deals with the flow of two immiscible incompressible micropolar fluids between two homogeneous porous beds at the bottom and top when the beds are of (A) infinite thickness and (B) finite thickness. The flow of two immiscible micropolar fluids is considered in two zones (zone II and zone III). This flow is bounded by zone I at the bottom and zone IV at the top, with saturated porous beds. In case A, zones I and IV are of infinite thickness with low permeability saturated by viscous fluids with the flow modeled by Darcy's law. In case B, zones I and IV are of finite thickness with high permeability saturated by viscous fluids with the flow modeled by Brinkman's law. The effects of the physical parameters on the velocity and microrotation vector are investigated.
GEOMECHANICS OF THERMAL OIL PRODUCTION FROM CARBONATE RESERVOIRS
301-321
10.1615/JPorMedia.v17.i4.30
Ali
Shafiei
Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario, Canada
Maurice B.
Dusseault
Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
thermal viscous oil production
geomechanics
fractured carbonate reservoirs
thermal behavior of reservoir rock
thermally induced stresses
casing shear
Over two trillion barrels of viscous oil (heavy oil, extra heavy oil, and bitumen) are reported in naturally fractured carbonate rocks. Only primary cold production and CO2 flooding with very low recovery factors have achieved some commercial success in these reservoirs. Steam injection in viscous oil carbonates is being piloted in the Middle East and in Canada. This article presents the definitions, geology and origins, geographical distribution, and world endowment of viscous oil in fractured carbonates, then some approaches and physical mechanisms involved in thermal viscous oil production processes are described. High T and p production processes have a profound impact on geomechanical behavior of viscous oil carbonate reservoirs. Thermal-stress-pressure effects on natural fractures can generate changes inflow capacity of several orders of magnitude from wedging to shear dilation around the thermally stimulated zone. Approaches to calculating thermally induced stresses are described. Available experimental data and field evidence of the thermal, physical, and geomechanical behavior of carbonate rocks under elevated temperature and pressure are reviewed, and some of the practical consequences are discussed. Most important, thermal production changes reservoir behavior, generally leading to production enhancement, although thermal stimulation can generate operational issues such as CO2 production, induced casing shear, and seal breaching.
EXPERIMENTAL CHARACTERIZATION OF THERMAL DISPERSION IN FIBROUS POROUS MEDIA
323-336
10.1615/JPorMedia.v17.i4.40
Haoda
Yang
Center for Composite Materials and Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA
Pavel
Simacek
Department of Mechanical Engineering and Center for Composite Materials, University of
Delaware, Newark, DE 19716
Suresh G.
Advani
Department of Mechanical Engineering and Center for Composite Materials, University of
Delaware, Newark, DE 19716
Resin transfer molding
fibrous porous medium
thermal dispersion
When a hot fluid is injected into a cold fibrous porous media or vice versa, energy is convected by the movement of fluid particles not only in the direction of the averaged velocity but also in the transverse direction because of the undulating flow path. This heat dispersion phenomenon can be modeled by increasing the effective transverse thermal conductivity to account for the enhancement in heat transfer. In this work, we have developed a new characterization setup to measure the heat transfer enhancement for a variety of flow rates and fiber volume fractions and introduced a modified Peclet number to describe the heat-transfer enhancement. In the experiment a cold resin is introduced in a heated mold containing fibrous media. The temperature history at the inlet, exit, and at six locations on the mold walls and three locations within the porous media is measured, and the transverse thermal conductivity in the model is varied, until all the temperature profiles recorded from the experiments match with the predicted values at all the thermocouple locations. This is repeated for various fiber volume fractions, flow rates, and two different preform architectures to develop a constitutive relationship between thermal dispersion and the modified Peclet number.
NON-DARCIAN AND ANISOTROPIC EFFECTS ON THE CONJUGATE HEAT TRANSFER IN A POROUS ENCLOSURE WITH FINITE THICKNESS WALLS
337-345
10.1615/JPorMedia.v17.i4.50
Sameh Elsayed
Ahmed
Department of Mathematics, Faculty of Science, Abha, King Khalid University, Saudi Arabia; Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
Abdelraheem M.
Aly
Department of Mathematics, Faculty of Science, Abha, King Khalid University, Saudi Arabia;
Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
conjugate heat transfer
anisotropy
natural convection
non-Darcy flow
finite volume method
In this article, the conjugate natural convection in an anisotropic fluid-filled porous enclosure has been investigated using Brinkman extended non-Darcy flow model. The finite volume method is applied to solve the dimensionless partial differential equations governing the flow and heat transfer. The governing parameters considered are the ratio of the wall thickness to its height (0.05 ≤ D ≤ 0.2), the wall to porous thermal conductivity ratio (1 ≤ Kr ≤ 10), the permeability ratio (0.5 ≤ K* ≤ 5), the modified Darcy number (0.001 ≤ Da ≤ 0.1), and the Rayleigh number (100 ≤ Ra ≤ 1000). It is found that increasing either the Rayleigh number or the permeability ratio can increase the rates of heat transfer for both the wall and the porous medium. However, increasing the modified Darcy number decreases the average Nusselt numbers for the wall and the porous medium.
STUDY ON TEMPERATURE MEASUREMENT IN WATER-SATURATED POROUS MEDIA USING MRI
347-358
10.1615/JPorMedia.v17.i4.60
Lanlan
Jiang
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116024, China; Research Institute of Innovative Technology for the Earth, Kizugawa City, Kyoto 619-0292, Japan
Minghao
Yu
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education
Yongchen
Song
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, No.2 Linggong Rd. Ganjingzi District, Liaoning 116024, China
Yu
Liu
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian, Liaoning 116024, China
Mingjun
Yang
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116024, P.R. China
Xinhuan
Zhou
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian, Liaoning 116024, China
Yuechao
Zhao
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, No.2 Linggong Rd. Ganjingzi District, Liaoning 116024, China
Binlin
Dou
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian, Liaoning 116024, China
Bohao
Wu
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian, Liaoning 116024, China
Ziqiu
Xue
Research Institute of Innovative Technology for the Earth, Kizugawa City, Kyoto 619-0292, Japan
Weizhong
Li
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education,
School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, China
MRI
temperature maps
T1 method
chemical shift method
An attractive approach for MRI thermograph has been used to investigate temperature distribution in watersaturated porous media. A range of temperaturesensitive MRI parameters (T1 and chemical shift) were evaluated to measure temperature distribution induced heating and cooling in water and watersaturated porous media samples. The SPRG and SE sequences were used for the T1 method. For the SPRG sequence, the T1 dependence is about 0.0283 and 0.001 for water and watersaturated porous media, respectively. The error results from the T1 measurement. The T1 dependence for porous media was smaller than that for water, so the temperature measurement in porous media was more difficult. For the SE sequence, the relationship varied with TR. Generally, the relationship dependence of temperature is higher than that with the SPGR sequence. But the method with the spin echo sequence needs a long acquisition time, which is not useful to measurement temperatures changing quickly. For the chemical shift method, there was excellent linearity for water and porous media samples. The linearity relationship was independence with respect to physical or chemical structure, in addition to good temperature sensitivity. Also the chemical shift method gave promising results even at low magnetic fields. In contrast, the chemical shift method was currently accepted as the method of choice for MR thermometry in water-based homogeneous media. The T1 method is used for temperature measurement during fluid flow.
NUMERICAL SIMULATIONS OF REVERSIBLE REACTIVE FLOWS IN HOMOGENEOUS POROUS MEDIA
359-372
10.1615/JPorMedia.v17.i4.70
Hesham
Alhumade
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada T2N1N4
Jalel
Azaiez
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada T2N1N4
viscous fingering
reversible reaction
porous media
numerical simulation
The effects of reversibility on the viscous fingering of miscible reactive flow displacements in homogeneous porous media are examined through numerical simulations. A model in which the viscosities mismatch between the reactants and the chemical product triggers the instability is adopted. The problem is governed by the continuity equation, Darcy's law, and the convection-diffusion-reaction equations, which are solved using a pseudo-spectral method. It was found that in general, chemical reversibility tends to attenuate the instability at the fronts, resulting in less complex fingers than in the nonreversible case. However, stronger chemical reversibility also leads to less diffuse and thinner finger structures. Furthermore, the chemical product was found to be homogeneously distributed in the porous medium in the case of the reversible reaction, while strong concentration gradients are observed in the nonreversible case. The study has also revealed that chemical reversibility is capable of enhancing the instability of a stable reactive front. It is also found that the rate of production can be the same for different cases of frontal instability for a period of time that increases with the increase in the magnitude of chemical reversibility.