Begell House Inc.
Special Topics & Reviews in Porous Media: An International Journal
STRPM
2151-4798
2
3
2011
PRESSURE BEHAVIOR OF VERTICAL WELLS IN LOW-PERMEABILITY RESERVOIRS WITH THRESHOLD PRESSURE GRADIENT
157-169
10.1615/SpecialTopicsRevPorousMedia.v2.i3.10
Shawket
Ghedan
Computer Modeling Group, Ltd., Calgary T2M 3Y7, Alberta, Canada
Jing
Lu
Northeast Petroleum University
low permeability
pressure drop
threshold pressure gradient
The threshold pressure gradient, which is associated with non-Darcy flow in low permeability reservoirs, is defined as the level of pressure gradient that must be attained to enable the fluid to overcome the viscous forces and start to flow. If the pressure gradient is small, then the flow velocity increases slowly and obeys a nonlinear relationship, but when the pressure gradient starts to exceed the threshold pressure gradient, it increases quickly and starts to obey the linear relationship. With low velocity and non-Darcy flow, the fluid flow boundary is controlled by the threshold pressure gradient and can extend outward continuously, while the fluid beyond this boundary cannot flow. This paper presents analytical solutions to the pressure transient equations of vertical wells in isotropic low-permeability reservoirs with threshold pressure gradient. These solutions are obtained by using Green’s functions method with numerical approximations. A method to determine the location of the moving boundary front is also presented. It is concluded that, at any time, smaller threshold pressure gradient results in smaller resistance to flow; thus, a single-well control radius is larger and the moving boundary front is moving farther away from the wellbore. Furthermore, a greater threshold pressure gradient results in more resistance to flow, meaning a much stronger driving force is required to reach the same flow rate. Unlike the material balance equation, we conclude that both pressure transient radius and pressure drop at the wellbore are approximately linear functions of the cubic root of producing time and not the square root of producing time. Its proposed equations find that the moving boundary front is sensitive to the value of the threshold pressure gradients. Furthermore, at any given value of threshold pressure gradient, we calculate lower bottom-hole pressure than those calculated by the material balance equations. Finally, the solution procedure we propose is a fast tool to evaluate well performance in low permeability reservoirs.
ANALYSIS OF CONVECTIVE HEAT TRANSFER IN A SQUARE CAVITY FILLED WITH A POROUS MEDIUM UNDER A MAGNETIC FIELD
171-180
10.1615/SpecialTopicsRevPorousMedia.v2.i3.20
M.
Sathiyamoorthy
Department of Mathematics, Government Thirumagal Mills College, Gudiyuatham-632 604, India;Department of Mathematics, SSN College of Engineering, Kalavakkam, Chennai 603110
finite element method
MHD convective flow
square cavity
porous medium
non-Darcy
Steady and laminar natural convection flow of electrical conducting fluid in a square cavity filled with a porous medium such as fibrous material, and beds of spheres under a strong magnetic field is investigated numerically. The vertical walls of the cavity are differentially heated, and the horizontal walls are adiabatic while a uniform magnetic field is applied in the normal direction of vertical walls. The Brinkman-Forchheimer extended Darcy model is used to simulate the flow in the porous medium. The penalty finite element method with biquadratic rectangular elements is used to solve the nondimensional governing equations. The companied effects of Hartmann number (Ha = 0−100) and modified Darcy number (Da = 10−5−10−3) on the flow, temperature distributions, and heat transfer rate are investigated in terms of the stream functions, isotherm contours, and average Nusselt number for Ra = 106 and Pr = 0.054 (liquid metals). It has been observed that the heat transfer rate is decreases smoothly as Ha is increases for Da = 10−3 and 10−4, while it is almost constant for Da = 10−5. It also found that effects of the magnetic filed decreases on the heat transfer rate as Darcy number decreases due to domination of Darcy drag in porous medium.
MODELING OF COMBUSTION IN POROUS INERT MEDIA
181-204
10.1615/SpecialTopicsRevPorousMedia.v2.i3.30
Raymond
Viskanta
Heat Transfer Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, USA
porous inert materials
modeling
porous burners
combustion devices
pollutant emissions
Inert porous media are used in advanced combustion devices that are essential to a variety of energy technologies in order to enable the maximum possible power density and power conversion efficiency needed for economic competitiveness and energy conservation with reduction in pollutant emissions. In these and other applications, the desirable characteristics of inert porous media are used to influence the relevant fluid dynamic, thermal, and chemical processes by varying the geometrical and/or physical properties of the porous matrix. In this manner, the flow, the temperature, and the distribution of species concentrations may be controlled. After a brief consideration of the models, the two-energy equation (i.e., local thermal nonequilibrium) model is discussed, and the transport coefficients needed for implementing the model equations to predict premixed combustion in high-porosity porous inert media are briefly reviewed. Despite the fact that some of the fundamental processes taking place in the inert porous media are still not well understood and properties not well known, considerable progress, however, has been made in the numerical modeling of combustion in porous burner-combustors, burner-radiant heaters, and burners-heat exchangers, and these combustion systems are discussed in this paper. Further development of more accurate models and their use in the preliminary design and/or optimization of porous materials-based combustion devices is encouraged.
NUMERICAL STUDY OF LIQUID COMPOSITE MOLDING USING A SMOOTHED PARTICLE HYDRODYNAMICS METHOD
205-216
10.1615/SpecialTopicsRevPorousMedia.v2.i3.40
Di
Su
Department of Mechanical Engineering, University of Maryland Baltimore County, USA
Ronghui
Ma
Department of Mechanical Engineering, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250
Liang
Zhu
Department of Mechanical Engineering, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250; Centennial High School, Ellicott City, MD, 21042
liquid composite molding
smoothed particle hydrodynamics
free surface flow
capillary pressure
continuum surface force method
Liquid composite molding is an important manufacturing process for a variety of composite components. The motion of fluid in a porous preform during a mold-filling process plays an important role in determining the quality of the composite part. In this study, a smoothed particle hydrodynamics (SPH) model is developed based on the Brinkman-Forchheimer-Darcy equation to study the mold-filling process with a special emphasis on the effects of operational conditions on the distributions of the fluid in the preform. The capillary pressure, which is important for a metal-based composite, is included in the model using the continuum surface force method. Two-dimensional simulations were performed to examine the effects of infusion rate, multiple infusion gates, and capillary pressure on the filling process. The results suggest that the SPH model provides an effective tool with sufficient accuracy for simulation, design, and optimization of mold filling for complex components.
ONSET OF PENETRATIVE CONVECTION IN A FERROFLUID-SATURATED POROUS LAYER
217-225
10.1615/SpecialTopicsRevPorousMedia.v2.i3.50
Jinho
Lee
School of Mechanical Engineering, Yonsei University, Seoul 120-749, Korea
I. S.
Shivakumara
Department of Mathematics, Bangalore University, Bangalore-560 056, India
penetrative ferroconvection
porous layer
ferrofluid
internal heat generation
The criterion for the onset of penetrative convection in a horizontal layer of ferrofluid-saturated porous medium in the presence of an applied vertical magnetic field via the internal heating model is studied. The impermeable isothermal boundaries are considered to be either paramagnetic or ferromagnetic, and the eigenvalue problem is solved numerically using the Galerkin method. It is noted that the paramagnetic boundaries with large magnetic susceptibility χ delay the onset of penetrative ferroconvection the most when compared to the low-susceptibility ones, and the system is least stable if the boundaries are ferromagnetic. Increase in the value of magnetic Darcy-Rayleigh number Rm, heat source strength NS, and nonlinearity of magnetization parameter M3 is to hasten the onset of ferroconvection. Further, increase in the value of χ and NS as well as decrease in M3 is to contract the dimension of convection cells.
MIXED CONVECTION OFWATER AT 4°C ALONG A WEDGE WITH A CONVECTIVE BOUNDARY CONDITION IN A POROUS MEDIUM
227-236
10.1615/SpecialTopicsRevPorousMedia.v2.i3.60
Waqar A.
Khan
Department of Mechanical Engineering, College of Engineering, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia
R.S.R.
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
mixed convection
wedge
Robin boundary condition; non similar solution
skin friction
heat transfer rate
In this study, the mixed convection of water at 4°C along a wedge in a porous medium is investigated numerically using an implicit finite difference method. The Robin boundary condition is applied at the wedge surface. In order to explore the effects of mixed convection, both forced and free convection dominated regimes are considered separately. Non similarity solutions are obtained for the variable heat transfer coefficient. Local dimensionless skin friction and Nusselt number are presented in tabular and graphical forms for the selected values of wedge and convective parameters. The wedge angle geometry parameter m range from 0 to 1 in both regimes, whereas different values of mixed convection parameter ε and convective parameter hc are considered for investigating the behavior of skin friction and heat transfer rates.
ROLE OF ANIONS ON SHALE STABILITY: THE NEGLECTED PHENOMENON
237-247
10.1615/SpecialTopicsRevPorousMedia.v2.i3.70
Talal M.
AL-Bazali
College of Engineering & Petroleum, Kuwait University, Saudi Arabia
membrane effeciency
osmostic pressure
shale swelling
chemical potential
low permeability shale
The effect of different anions on the swelling behavior and membrane efficiency of low-permeability shales has been studied using a pressure transmission test. Three different shales obtained from deep formations located in an oil field in the Middle East were used in this study. Three different anions, i.e., chloride, carbonates, and formate anions, were utilized in this study to investigate the impact of anion type, size, and concentration on the swelling behavior and membrane efficiency of low-permeability shales. Experimental results confirm the notion that shales are leaky membranes where they do not completely restrict the flow of ions, and that in turn reduces the osmotic pressure that could be used to induce water out of the shale. The measured membrane efficiencies of shales ranged from 0.62 to 5.23%. In addition, it is shown that different anions impact the swelling behavior and membrane property of shales differently, depending on their relative sizes. Low-permeability shales induce larger osmotic pressure when interacting with larger anions such as carbonates and formate anions. It is also shown that salt solutions with the appropriate ions' (anions and cations) type and concentration could provide an inexpensive product to combat wellbore instability problems in low-permeability shales, given that a large enough chemical potential exists between the shale and the salt solution. This work also shows that a potassium chloride solution can be utilized as an osmotic method for low-permeability shales.