Begell House Inc.
Journal of Porous Media
JPM
1091-028X
18
2
2015
ANALYSIS OF SOME MAGNETOHYDRODYNAMIC FLOWS OF THIRD-ORDER FLUID SATURATING POROUS SPACE
89-98
10.1615/JPorMedia.v18.i2.10
Rahmat
Ellahi
Center for Modeling and Computer Simulation, Research Institute, King Fahd University of
Petroleum & Minerals, Dhahran-31261, Saudi Arabia; Department of Mathematics, Faculty of Basic and Applied Sciences, IIU, Islamabad, Pakistan
E.
Shivanian
Department of Mathematics, Imam Khomeini International University, Ghazvin, Iran
Saeid
Abbasbandy
Department of Mathematics, Imam Khomeini International University, Ghazvin, Iran
Tasawar
Hayat
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science,
King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia
porous medium
magnetohydrodynamic
non-Newtonian fluid
numerical solutions
pseudo-spectral collocation method
least square
Newton iteration
Chebyshev method
A hybrid method based on pseudo-spectral collocation in the sense of least-square method is applied to examine the magnetohydrodynamic (MHD) flow of non-Newtonian fluid. The flow equation through constitutive relations of third-order fluid is considered. Four illustrative examples of nonlinear flow, namely (i) plane Couette flow, (ii) Plug flow, (iii) fully developed plane Poiseuille flow, and (iv) generalized plane Couette flow, are considered. An incompressible electrically conducting fluid saturates the porous space between two boundaries. The solutions of governing nonlinear problems are obtained and analyzed through numerical method and graphical illustration.
INVESTIGATION OF THREE-PHASE RELATIVE PERMEABILITIES FOR HEAVY OIL SYSTEMS USING SIMULATED ANNEALING TECHNIQUE; EFFECT OF OIL VISCOSITY
99-111
10.1615/JPorMedia.v18.i2.20
Farshid
Torabi
Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of
Regina, Regina, SK, S4S 0A2, Canada; Department of Petroleum Engineering, School of Chemical and Petroleum Engineering, Shiraz
University, Iran
Manoochehr
Akhlaghinia
Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada S4S 0A2
Christine W.
Chan
Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada S4S 0A2
three-phase relative permeability
displacement experiments
simulated annealing
isoperms
heavy oil
Three-phase relative permeabilities play a crucial role in simulation of thermal heavy oil recovery processes. Obtaining such data is considerably challenging due to the tedious nature of experiments and accuracy of the results. A simulated annealing technique was used to estimate three-phase relative permeabilities in the form of isoperms by utilizing two-and three-phase displacement experiments conducted with a Berea core/heavy oil/brine/CO2 system. After validation of the technique using results obtained from steady-state experiments, the effect of oil viscosity on the three-phase relative permeability was investigated. Results of this study showed that, in a ternary diagram, the three-phase flow zone shifted toward the higher saturations of oil, while no significant change in the size of the three-phase flow zone occurred. Different curvatures were observed for relative permeability isoperms of each phase, indicating dependency of relative permeability to saturation of all phases. Increasing oil viscosity from 1174 to 2658 cP resulted in a decrease in the relative permeability in each phase. Results also indicated that, due to significant difference between the viscosity of the phases, oil relative permeability values are higher than those of brine and CO2 on the order of magnitude of three and five, respectively.
SOLUTIONS FOR COUNTERCURRENT SPONTANEOUS IMBIBITION AS DERIVED BY MEANS OF A SIMILARITY APPROACH
113-124
10.1615/JPorMedia.v18.i2.30
Rasoul
Arabjamaloei
Department of Mechanical & Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 5V6
Douglas W.
Ruth
Department of Mechanical & Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 5V6
Geoffrey
Mason
Department of Chemical Engineering, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
Norman R.
Morrow
Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, WY 82071, USA
spontaneous imbibition
countercurrent
analytical solution
Lagrangian formulation
similarity solution
porous media
A major portion of oil in water-wet fractured reservoirs is produced as a result of countercurrent spontaneous imbibition. Recently, there has been much research in experimental and mathematical analysis of this process. However, the actual physics of this process at the micro-scale is not completely understood. The governing equation of countercurrent spontaneous imbibition is of the diffusion type and is highly nonlinear; therefore, an exact closed-form analytical solution for this equation seems impossible. In the present paper, a basic solution is developed for this process and tested against numerical simulation results. Also, new numerical solution methods are presented to solve the governing equation of this process in one dimension using a similarity variable. Finally, an approximate iteration-based analytical solution is presented that is both stable and accurate.
LOCAL THERMAL NON-EQUILIBRIUM AND HETEROGENEITY EFFECTS ON THE ONSET OF CONVECTION IN A LAYERED POROUS MEDIUM WITH VERTICAL THROUGHFLOW
125-136
10.1615/JPorMedia.v18.i2.40
D A
Nield
University of Auckland
Auckland, New Zealand
Andrey V
Kuznetsov
Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA
local thermal non-equilibrium
throughflow
porous medium
instability
natural convection
We investigated the combined effects of throughflow and local thermal non-equilibrium on the onset of convection in a porous medium consisting of two horizontal layers. In our analytical study, which is performed using linear stability theory, we considered variations of permeability, fluid thermal conductivity, solid thermal conductivity, interphase heat transfer coefficient, and porosity. It is found that heterogeneity of permeability and fluid thermal conductivity have a major effect, heterogeneity of the interphase heat transfer coefficient and porosity have a lesser effect, while heterogeneity of solid thermal conductivity is relatively unimportant.
PETROPHYSICAL AND MICROSTRUCTURAL EVALUATION OF THE THERMAL CYCLE LOADING EFFECT ON GEOTHERMAL WELLBORE CEMENTS
137-151
10.1615/JPorMedia.v18.i2.50
Kolawole S.
Bello
Mileva
Radonjic
LSU
wellbore cement thermal cyclic loading
wellbore cement strength retrogression
wellbore cement/brine interaction
wellbore cement permeability
liquid pressure/pulse decay permeameter
geothermal wellbore cements
Five wellbore cement designs with a range of additives and fibers were subjected to 100 thermal cycles of ΔT ~50°C at 100% relative humidity in salt brine. The experimental results show leaching of portlandite will occur from the cement irrespective of wellbore cement slurry design, which causes the porosity and hydraulic conductivity to increase and the mechanical strength to decrease. Furthermore, the study shows the presence of steel fibers can improve the mechanical properties of the cement sheath under thermal cycle loading conditions; although it would not prevent it from completely degrading as the well ages.
MODELING OF MULTISTEP DRAINAGE PROCESS USING THE EXTENDED INTERACTIVE TUBE-BUNDLE MODEL
153-164
10.1615/JPorMedia.v18.i2.60
Shengdong
Wang
Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB, T2N 1N4, Canada
Mingzhe
Dong
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao
266580, People's Republic of China; Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
gas/liquid drainage
porous plate method
tube-bundle model
saturation profiles
multistep drainage process
network model
The relative permeabilities at low saturation and high capillary pressure are important for any drainage process such as CO2 storage and steam-assisted gravity drainage. The relative permeabilities can be estimated by analyzing the wetting phase production histories at each step in a multistep drainage process. Different from the conventional porous plate method, the multistep drainage process applies a plastic membrane to significantly reduce experiment time while prevent the nonwetting phase from being discharged from the porous medium The conventional tubebundle model has some difficulties in modeling this process because in a drainagetype process the sealing effect of the membrane significantly changes the multiphase flow pattern. In this paper, an extended interactive tubebundle model (ITBM) was developed to model this process. First, in order to qualitatively model this process, a new threetube interacting capillary model was developed and the reverse flood and bidirectional flood were properly modeled. This model also explains in concept why, in this process, the phase with lower mobility determines the wetting phase production history. After that, the threetube interacting capillary model was extended to a complex ITBM, consisting of hundreds of tubes. The saturation profiles along the porous medium, the wetting phase production curves, and the multistep drainage process were all successfully modeled. The application of the ITBM indicates that it can better represent the pore structure of a porous medium and potentially be applied to history match a multistep drainage process.
INSTABILITY OF POISEUILLE FLOW IN A CHANNEL FILLED WITH MULTILAYER POROUS MEDIA
165-177
10.1615/JPorMedia.v18.i2.70
Chuanshan
Dai
Key Laboratory of Effi cient Utilization of Low and Medium Grade Energy, Ministry of Education,
Tianjin 300072, China; School of Mechanical Engineering, Tianjin University, Tianjin 300072, China
Qi
Li
Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, School of Mechanical Engineering, Tianjin University, 300072 Tianjin, China
Haiyan
Lei
Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, School of Mechanical Engineering, Tianjin University, 300072 Tianjin, China
porous media linear stability multilayer porous media channel flow
We performed a linear stability analysis of Poiseuille flow in a parallel-plate channel filled with fluid-saturated multilayer porous media. To investigate the effect of the porous layer number, np, two ways of increasing the number of porous layers have been considered based on an identical three-layer model, which are referred to as the constant Re and ψ conditions, respectively. When the inertial effects are ignored, the numerical results show that at the constant Re condition, with an increase in the value of dimensionless permeability, u, the number of migration paths for the upper wall modes on the left branch in Orr−Sommerfeld spectra for np = 1, 2, 3, and 4 is identical to the number of open fluid layers, while the number of new inducing lower wall modes is just twice the number of porous layers placed in the channel. The number of modes on the lower-left branch also depends on the positions of the porous layers. In addition, we present the behaviors of the critical Re number against wave number α, and np for the constant Re and constant ψ conditions. By comparing the stability characteristics between the two conditions, we observed that both have less stability as the number of porous layers increases. At the same number of porous layers, np the value of Rec at the constant ψ condition is much less than that at the constant Re condition.