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Texas Tech University

1. Chang, Dahwei. Peaceman's numerical productivity index for non-linear flows in porous media.

Degree: Mathematics, 2009, Texas Tech University

URL: http://hdl.handle.net/2346/14592

From Darcyâ€™s law to Darcy-Forchheimer equation, there have being a lot efforts finding solutions for flows in porous media. Peaceman used a system of well blocks to replace the well bore in finding numerical solutions for linear flows. Our work uses a single well block to find the pressure distribution throughout the well for non-linear flows. In the process we found a block invariant which can be used to build the pressure distribution formula. From it, we can find the productivity index, one of the important factors in petroleum engineering.
Theoretical derivation and numerical data are also presented in this report.
*Advisors/Committee Members: Aulisa, Eugenio (Committee Chair), Toda, Magdalena D. (committee member), Howle, Victoria E. (committee member).*

Subjects/Keywords: Peaceman; Porous media; Darcy's law; Darcy-forchheimer equation; Flow

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Chang, D. (2009). Peaceman's numerical productivity index for non-linear flows in porous media. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/14592

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Chang, Dahwei. “Peaceman's numerical productivity index for non-linear flows in porous media.” 2009. Thesis, Texas Tech University. Accessed August 05, 2020. http://hdl.handle.net/2346/14592.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Chang, Dahwei. “Peaceman's numerical productivity index for non-linear flows in porous media.” 2009. Web. 05 Aug 2020.

Vancouver:

Chang D. Peaceman's numerical productivity index for non-linear flows in porous media. [Internet] [Thesis]. Texas Tech University; 2009. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2346/14592.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chang D. Peaceman's numerical productivity index for non-linear flows in porous media. [Thesis]. Texas Tech University; 2009. Available from: http://hdl.handle.net/2346/14592

Not specified: Masters Thesis or Doctoral Dissertation

2.
Bloshanskaya, Lidia.
Mathematical model of well productivity index for *Forchheimer* flows in fractured reservoirs.

Degree: PhD, Mathematics, 2013, Texas Tech University

URL: http://hdl.handle.net/2346/58420

Porous media (rocks, soils, aquifers, oil and gas reservoirs) plays an essential role in our modern environment. The pores of such material are usually filled with fluid, liquid or gas, and the flow of the fluids through the media is a subject of common interest of many different fields of study.
In the middle of 19th century, Henry Darcy experimented on water filtration through sand and he eventually formulated the famous Darcy's law which relates the pressure gradient to the velocity of the fluid linearly. This empirical law laid the foundations for the quantitative theory of fluid dynamics. However, linear law has limited range of validity. In 20th century, Forchheimer proposed his equations to account for the nonlinearity of the flow.
In this thesis we generalize the Forchheimer equations and examine the properties of the corresponding parabolic partial differential equations. The developed framework is used to
study the well productivity index (PI) as a functional defined on the solutions of differential equations modeling non-linear flows. Petroleum engineers use the PI to characterize the well performance to manage the well reserves. We study the long term dynamics of the PI and its dependence on the nonlinearity and geometric parameters. The obtained results can be effectively used in reservoir engineering and can be applied to other problems modeled by the nonlinear diffusive equations.
*Advisors/Committee Members: Aulisa, Eugenio (committee member), Hoang, Luan (committee member), Ibragimov, Akif (Committee Chair).*

Subjects/Keywords: Porous media; Fractures; Nonlinear flow; Non-darcy; Forchheimer equation

…computation of PSS PI. In §5.1 we generalize the famous Peaceman approach to g-*Forchheimer* *equation*… …hydrodynamical point of view,
the *Darcy* *equation* is interpreted as the momentum *equation*. The *Darcy*… …two-term, power,
and three-term) are widely used. *Darcy* and *Forchheimer* laws can be… …*equation*:
dp
= −κ∇ · u .
dt
2.2
(2.11)
Generalized *Forchheimer* equations
In order… …form
of the g-*Forchheimer* momentum *equation* (2.6):
8
Texas Tech University…

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Bloshanskaya, L. (2013). Mathematical model of well productivity index for Forchheimer flows in fractured reservoirs. (Doctoral Dissertation). Texas Tech University. Retrieved from http://hdl.handle.net/2346/58420

Chicago Manual of Style (16^{th} Edition):

Bloshanskaya, Lidia. “Mathematical model of well productivity index for Forchheimer flows in fractured reservoirs.” 2013. Doctoral Dissertation, Texas Tech University. Accessed August 05, 2020. http://hdl.handle.net/2346/58420.

MLA Handbook (7^{th} Edition):

Bloshanskaya, Lidia. “Mathematical model of well productivity index for Forchheimer flows in fractured reservoirs.” 2013. Web. 05 Aug 2020.

Vancouver:

Bloshanskaya L. Mathematical model of well productivity index for Forchheimer flows in fractured reservoirs. [Internet] [Doctoral dissertation]. Texas Tech University; 2013. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2346/58420.

Council of Science Editors:

Bloshanskaya L. Mathematical model of well productivity index for Forchheimer flows in fractured reservoirs. [Doctoral Dissertation]. Texas Tech University; 2013. Available from: http://hdl.handle.net/2346/58420