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Research Papers: Energy Systems Analysis

Dimensionless Scaling Parameters During Thermal Flooding Process in Porous Media

[+] Author and Article Information
M. Enamul Hossain

Professor
Mem. ASME
School of Mining and Geoscience,
Department of Petroleum Engineering,
Nazarbayev University,
Astana 010000, Kazakhstan
e-mails: dr.mehossain@gmail.com; enamul.hossain@nu.edu.kz

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received January 30, 2015; final manuscript received November 6, 2017; published online March 15, 2018. Assoc. Editor: Antonio J. Bula.

J. Energy Resour. Technol 140(7), 072004 (Mar 15, 2018) (15 pages) Paper No: JERT-15-1041; doi: 10.1115/1.4039266 History: Received January 30, 2015; Revised November 06, 2017

The scaling concept is important, effective, and consistent in any application of science and engineering. Scaled physical models have inimitable advantages of finding all physical phenomena occurring in a specific process by transforming parameters into dimensionless numbers. This concept is applicable to thermal enhanced oil recovery (EOR) processes where continuous alteration (i.e., memory) of reservoir properties can be characterized by various dimensionless numbers. Memory is defined as the continuous time function or history dependency which leads to the nonlinearity and multiple solutions during modeling of the process. This study critically analyzed sets of dimensionless numbers proposed by Hossain and Abu-Khamsin in addition to Nusselt and Prandtl numbers. The numbers are also derived using inspectional and dimensional analysis (DA), while memory concept is used to develop some groups. In addition, this article presents relationships between different dimensionless numbers. Results show that proposed numbers are measures of thermal diffusivity and hydraulic diffusivity of a fluid in a porous media. This research confirms that the influence of total absolute thermal conductivities of the fluid and rock on the effective thermal conductivity of the fluid-saturated porous medium diminishes after a certain local Nusselt number of the system. Finally, the result confirms that the convective ability of the fluid-saturated porous medium is apparently more pronounced than its conductive ability. This study will help to better understand the modeling of the EOR process thus improving process design and performance prediction.

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Figures

Grahic Jump Location
Fig. 1

Variation of NHA1 with αH and αTe at (NPr)f=56.4214, respectively: (a) αH is calculated by varying ct and αTe is calculated by varying ρfcpf, while other parameters are constant for both calculations and (b) αTe is calculated by varying ρfcpf and αH is calculated by varying μ, while other parameters are constant for both calculations

Grahic Jump Location
Fig. 2

Variation of NHA1 with NAH for various values of υ at (NPr)f= 56.4214 and αTe = 0.006

Grahic Jump Location
Fig. 3

Variation of NHA1 with (NPr)fs for different (NPr)f (a) and (NPr)f for different (NPr)s (b)

Grahic Jump Location
Fig. 4

Variation of NHA2 with αTe for various values of αTb (a) or with αTb for various values of αTe (b) for ke = 7.5 kJ/hm K and kf = 1.5957 kJ/hm K

Grahic Jump Location
Fig. 5

Variation of NHA2 with (NPr)fs for different kf at a given M=2228.4 kJ/m3 K and υ=0.0159 m2/s; different M at a given kf=1.5957 kJ/hm K and υ=0.0159 m2/s; and different υ at a given kf=1.5957 kJ/hm K and M=2228.4 kJ/m3 K, respectively

Grahic Jump Location
Fig. 6

Variation of NHA2 with (NNuL)f for different M at a given αTe=0.0037 m2/s, hc=255.87 kJ/hm2 K, and Lc=0.0004 m; different αTe at a given M=2228.4 kJ/m3 K, hc=255.87 kJ/hm2 K, and Lc=0.0004 m; different hc at a given M=2228.4 kJ/m3 K, αTe=0.0037 m2/s, and Lc=0.0004 m; and different Lc at a given αTe=0.0037 m2/s, and hc=255.87 kJ/hm2 K, respectively

Grahic Jump Location
Fig. 7

Variation of NHA2 with αTf for various αTs (a), and with αTs for various αTf values at a given ϕ=0.25, ks=9.346 kJ/hm K, and kf=1.5957 kJ/hm K

Grahic Jump Location
Fig. 8

Variation of NHA3 with NNuL for different values of (a) (NNuL)T and ks, and (b) (NNuL)T,kf

Grahic Jump Location
Fig. 9

Variation of NHA3 with (NNuL)T for various values of NNuL, ks, and kf

Grahic Jump Location
Fig. 10

Variation of NHA4 with αH for different αTb and NHA2, and with αTb for different αH and a given NHA2=5.128 value, respectively

Grahic Jump Location
Fig. 11

Variation of NHA4 with NHA2 for different αH values

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