Begell House Inc.
Special Topics & Reviews in Porous Media: An International Journal
STRPM
2151-4798
10
1
2019
A MATHEMATICAL MODEL OF IMBIBITION PHENOMENON IN HOMOGENEOUS POROUS MEDIA
1-13
10.1615/SpecialTopicsRevPorousMedia.2018021445
Bhumika G.
Choksi
Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat-395007, Gujarat, India
Twinkle R.
Singh
Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat-395007, Gujarat, India
mathematical modeling
counter-current imbibition phenomenon
homotopy perturbation sumudu transform method (HPSTM)
successive linearization method (SLM)
In this article, the phenomenon of counter-current imbibition in a particular displacement method concerning two immiscible fluids through a dipping homogeneous porous medium has been discussed under certain conditions. This
phenomenon plays a very essential role in the oil recovery process. A nonlinear partial differential equation was given
out as the governing equation of this phenomenon, whose exact analytical solution is almost impossible to find.Here we have solved it by two different methods: homotopy perturbation sumudu transform method and successive linearization method (a newly developed method). By comparison of solution using these two methods, it has been concluded that by the successive linearization method, a good amount of oil can be produced during a secondary oil recovery process in the petroleum technology. Also, the fraction of oil recovered to dimensionless time is studied, which is the main goal of any oil recovery process and the proposed method can be used to optimize the oil recovery rate.
INVESTIGATION OF VISCOUS FINGERING INSTABILITY IN HETEROGENEOUS POROUS MEDIA
15-29
10.1615/SpecialTopicsRevPorousMedia.2018022882
Mohammad Reza
Shahnazari
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
I. Maleka
Ashtiani
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
fingering
porous media
miscible fluid
channeling
Fourier space
Viscous fingering instability in porous media has various applications and models in industry, processes, and natural
issues. Several studies on the stability in porous media have been done by researchers in recent years. In this paper, a solution is introduced to stabilize the viscous fingering instability, which is described as "channeling". In this solution, narrow channels were placed next to the walls, and an exponential function was used to represent it. In linear stability analysis the governing equations are transferred to Fourier space. By introducing a novel numerical method, the transferred equations are analyzed. The results show that when the ratio of maximum to minimum permeability is approximately equal to one, the channeling has no significant effect. By increasing the permeability ratio, the channeling effect increases, more fluid flows near the walls, and the system becomes more stable at the center and unstable along the walls. Also increasing the mobility ratio increases the system instability. In nonlinear simulation, by using stream function and vortices, new equations have been rewritten and because of no slip boundary condition, the direct solution method is conducted and concentration contours are presented. Similar results for nonlinear simulation are found, which are in good agreement with linear stability analysis.
AN ANALYTICAL MODEL ON PRODUCTION PERFORMANCE OF MULTIPLE WELLS PRODUCING AT CONSTANT BOTTOMHOLE PRESSURES
31-48
10.1615/SpecialTopicsRevPorousMedia.2018026034
Jing
Lu
Northeast Petroleum University
Jalal Farhan
Owayed
Department of Petroleum Engineering, Kuwait University, Kuwait
Jiaxing
Xu
Department of Petroleum Engineering, Khalifa University of Science and Technology, Abu
Dhabi, UAE
Md. Motiur
Rahman
Department of Petroleum Engineering, Khalifa University of Science and Technology, Abu
Dhabi, UAE
analytical model
production performance
multiple wells
constant bottomhole pressure
This paper presents an analytical model with numerical approximation on production performance of multiple wells
producing at constant bottomhole pressures during boundary-dominated flow period in a closed rectangular reservoir.
It is obtained through a series of mathematical methods such as Laplace transform, Dirac delta function, convolution,
Green's function, and superposition principle. Computer Modeling Group Ltd. (CMG) simulation is used to validate
the new proposed model and it is found that the model is accurate enough to predict the production performance of
multi-well system producing under different bottomhole pressures during boundary-dominated flow period in a closed
rectangular reservoir. We conclude that at a given time the flow rate of a well decreases as the total well numbers
increases and bottomhole pressures of adjacent wells decrease, while the total reservoir production increases as the bottomhole pressure of reservoir wells decreases. And, at a given time the greater distance between the observation well and adjacent wells, the bigger flow rate and cumulative production the observation well has. In terms of the decline
rate of flow rate, it depends on well numbers, bottomhole pressures of adjacent wells, as well as the size of the reservoir. Compared with the empirical or semi-analytical models in the literature, our proposed model is fully analytical which has solid theoretical basis; it is accurate enough to predict the production performance of multiple wells under constant bottomhole pressures.
NANOFLUID TRANSPORT IN POROUS MEDIA: A REVIEW
49-64
10.1615/SpecialTopicsRevPorousMedia.2018027168
Younes
Menni
Unite of Research on Materials and Renewable Energies - URMER - Department of Physics,
Faculty of Sciences, Abou Bekr Belkaid University, BP 119-13000-Tlemcen, Algeria
Ali J.
Chamkha
Faculty of Engineering, Kuwait College of Science and Technology, Doha District, Kuwait;
Center of Excellence in Desalination Technology, King Abdulaziz University, P.O. Box 80200,
Jeddah 21589, Saudi Arabia; Mechanical Engineering Department, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Saudi Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, P.O. Box
10021, Ras Al Khaimah, United Arab Emirates
Ahmed
Azzi
Unit of Research on Materials and Renewable Energies – URMER, Abou Bekr Belkaid
University, BP 119-13000-Tlemcen, Algeria; Department of Mechanical Engineering, Faculty of Technology, Abou Bekr Belkaid University,
BP 230-13000-Tlemcen, Algeria
nanofluids
porous media
natural convection
forced convection
mixed convection
Convection heat transfer mode is the principal topic in thermal transfer. So, it is the matter of many numerical and
experimental studies. In recent years, much attention was given to the use of free/forced/mixed convection heat transfer with nanofluids in geothermal engineering, storage of radioactive nuclear waste, solar collectors, transpiration cooling, performance of cold storage, separation processes in chemical industries, thermal insulation of buildings, filtration, space technology, transport processes in aquifers, nuclear reactor cooling system, groundwater pollution, underground nuclear wastes disposal, geothermal extraction, and fiber insulation, etc, and many researches were reported in this topic. This paper presents a detailed review of the numerical and experimental studies carried out by various researchers in order to obtain enhanced heat transfer in free, forced, and mixed convection by using nanofluids in porous media. Critical information of all studies in three categories (analytical, experimental. and numerical) has been collected.
STABILITY OF AN ANISOTROPIC POROUS LAYER WITH INTERNAL HEAT SOURCE AND BRINKMAN EFFECTS
65-87
10.1615/SpecialTopicsRevPorousMedia.2018025396
Amit
Mahajan
Department of Applied Sciences, National Institute of Technology, Narela, Delhi 110040, India
Reena
Nandal
Christ (Deemed to be University)
anisotropy
internal heat source
Darcy–Brinkman model
energy method
The effects of the internal heat source and anisotropy in permeability on the onset of convection in a fluid layer modeled using modified Darcy's equation are analyzed using linear and nonlinear analysis for impermeable and isothermal
boundaries. Normal mode technique is used for linear analysis and energy method is used for nonlinear stability
analysis. The presence of heat generation and anisotropy of the medium leads to the possibility of the existence of a
subcritical instability. Effects of Darcy–Brinkman number, anisotropic parameter, and internal heat parameter on the
value of critical Rayleigh numbers were analyzed using Chebyshev-QZ method.
A NEW CALCULATING METHOD FOR RELATIVE PERMEABILITY OF BRANCHED PREFORMED PARTICLE GEL FLOODING IN MULTIPHASE COMPOSITE SYSTEM
89-98
10.1615/SpecialTopicsRevPorousMedia.2018025439
Weiyao
Zhu
School of Civil and Resource Engineering, University of Science and Technology Beijing,
Beijing, BJ 100083, China
Bingbing
Li
School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo, 454000,
China
Yajing
Liu
School of Civil and Resource Engineering, University of Science and Technology Beijing,
Beijing, BJ 100083, China
Hongqing
Song
College of Petroleum Engineering, Xi'an Shiyou University, Xi'an, China; School of Civil and Environmental Engineering, University of Science and Technology Beijing, China
Ming
Yue
School of Civil and Resource Engineering, University of Science and Technology Beijing,
Beijing, BJ 100083, China
Nan
Wu
National Engineering Research Center of China United Coalbed Methane, Beijing, BJ 100095,
China
mathematical model
relative permeability
B-PPG suspension
particle mesh
particle size distribution
Relative permeability curve of Branched-preformed particle gel (B-PPG) suspension/oil two-phase system is one of the
most effective means to acquire percolation characteristics in reservoirs. Based on the Buckley–Leverett equation, a
new mathematical model with rheological properties for B-PPG suspension/oil relative permeability was established.
Firstly, this new model was reliable by comparison with the traditional unsteady-state model through experiments.
Then, the effects of particle mesh and size distribution on relative permeability with different permeability levels were comparatively investigated. The results showed that the permeability value of the derived formula was below that of
the traditional formula, regardless of displaced and displacing term. In addition, the displacement efficiency boosted with an increment of particle mesh. In terms of the decrement of residual oil saturation, the effect of particle mesh on low permeability reservoir (3.4%) was more distinct than that of high permeability reservoir (2.9%). The displacement efficiency was higher when the particle size distribution was more uneven. Besides, the effect of particle size distribution on low permeability reservoir (2.0%) was almost similar to that of high permeability reservoir (1.9%). This research not only provides important basic information for the numerical simulation, but also lays a foundation for the development of the reservoir.