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1. 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

…*Texas* *Tech* *University*, Lidia Bloshanskaya, August 2013
the impact of nonlinearity on its… …t)
5
*Texas* *Tech* *University*, Lidia Bloshanskaya, August 2013
pressure distribution… …law
au + cn
(Bu, u)n−1 u = − ∇p,
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(2.4)
*Texas* *Tech* *University*… …ρ∇ · u − u · ∇p,
dp dt
dp
7
(2.9)
*Texas* *Tech* *University*, Lidia Bloshanskaya… …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 08, 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. 08 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 08]. 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

2. Aavani, Pooya. Ordinary and delay differential equation models of viral infection with application to HIV and Hepatitis C virus.

Degree: 2012, Texas Tech University

URL: http://hdl.handle.net/2346/46950

Human adaptive immune response consists of three major types of cells, namely, CD4 T cells, CTL (Cytotoxic T Lymphocytes), and antibodies. CTL attack and kill
cells that are infected by viruses. Antibodies are capable of identifying and neutralizing viruses. In the presence of virus infection, CD4 T Cells stimulate the proliferation of CTL. Also the proliferation of antibodies becomes stimulated by viruses. These ideas are used to introduce a new ordinary differential equation model for exploring the dynamics of infection. Production of viruses by infectious CD4 T cells are not instantaneous and they require time to occur. Thus, explaining the dynamics of infections more accurately
in the model, it is important to consider a time gap, which is known as delay. The new delay differential equation model, which considers a delay in the production of
viruses, is also analyzed in this thesis.
Both models are useful to be applied for HIV and hepatitis C infections, because
in these models target cells are CD4 T cells, infectious agents are viruses, and the
biological implications of the mathematical results are similar to the stages of the
infections.
*Advisors/Committee Members: Allen, Linda J. S. (Committee Chair), Allen, Edward J. (committee member), Hoang, Luan (committee member).*

Subjects/Keywords: Mathematical immunology; Virus dynamics; Reproduction number; Asymptotic stability; Global stability

…*Texas* *Tech* *University*, Pooya Aavani, August 2012
4.5
4.6
2
)/a > 1. The density… …2.8402). . . . . . . . . . .
vii
42
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*Texas* *Tech* *University*, Pooya Aavani, August… …The immune system is active. This
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*Texas* *Tech* *University*, Pooya Aavani, August 2012… …cells become infected, and the parameter λ is the growth rate of the
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*Texas* *Tech* *University*… …µf is the rate of decay of anti-
4
*Texas* *Tech* *University*, Pooya Aavani, August 2012…

Record Details Similar Records

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

APA (6^{th} Edition):

Aavani, P. (2012). Ordinary and delay differential equation models of viral infection with application to HIV and Hepatitis C virus. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/46950

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):

Aavani, Pooya. “Ordinary and delay differential equation models of viral infection with application to HIV and Hepatitis C virus.” 2012. Thesis, Texas Tech University. Accessed August 08, 2020. http://hdl.handle.net/2346/46950.

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

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Aavani, Pooya. “Ordinary and delay differential equation models of viral infection with application to HIV and Hepatitis C virus.” 2012. Web. 08 Aug 2020.

Vancouver:

Aavani P. Ordinary and delay differential equation models of viral infection with application to HIV and Hepatitis C virus. [Internet] [Thesis]. Texas Tech University; 2012. [cited 2020 Aug 08]. Available from: http://hdl.handle.net/2346/46950.

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

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Aavani P. Ordinary and delay differential equation models of viral infection with application to HIV and Hepatitis C virus. [Thesis]. Texas Tech University; 2012. Available from: http://hdl.handle.net/2346/46950

Not specified: Masters Thesis or Doctoral Dissertation

3. Gohlke, Jedidiah W. A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations.

Degree: Mathematics and Statistics, 2011, Texas Tech University

URL: http://hdl.handle.net/2346/ETD-TTU-2011-08-1809

The incompressible Navier-Stokes equations model the relationship between the velocity and pressure of a ﬂuid and can be used to describe the motion of a ﬂuid. Because they are nonlinear, they are in most cases diﬃcult or impossible to solve
analytically. They must, therefore, be approximated numerically. One approach
developed by Alexandre Chorin is to use a projection method to approximate the pressure and velocity. We will look at Chorin’s approach and then consider a
modiﬁed approach called the gauge method, which mitigates some of the boundary condition diﬃculties in Chorin’s approach. We will then consider an improvement to the gauge method that gives us second order convergence in the velocity in both time and space and slightly better than order 3/2 convergence in the pressure in time. We will then present a code to automate the gauge method and consider some test cases to verify that the code converges at the appropriate rate.
*Advisors/Committee Members: Long, Kevin (Committee Chair), Howle, Victoria E. (committee member), Kirby, Robert C. (committee member), Hoang, Luan (committee member).*

Subjects/Keywords: Navier-Stokes equations; Projection method; Gauge method; Code validation

…*Texas* *Tech* *University*, Jedidiah Wayne Gohlke, August 2011
8.8
8.9
8.10
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8.12… …40
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*Texas* *Tech* *University*, Jedidiah Wayne Gohlke, August 2011
8.14… …viii
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*Texas* *Tech* *University*, Jedidiah Wayne Gohlke, August 2011… …case.
1
*Texas* *Tech* *University*, Jedidiah Wayne Gohlke, August 2011
CHAPTER 2
THE… …same number of equations as unknowns, the
2
*Texas* *Tech* *University*, Jedidiah Wayne Gohlke…

Record Details Similar Records

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

APA (6^{th} Edition):

Gohlke, J. W. (2011). A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/ETD-TTU-2011-08-1809

Not specified: Masters Thesis or Doctoral Dissertation

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

Gohlke, Jedidiah W. “A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations.” 2011. Thesis, Texas Tech University. Accessed August 08, 2020. http://hdl.handle.net/2346/ETD-TTU-2011-08-1809.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Gohlke, Jedidiah W. “A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations.” 2011. Web. 08 Aug 2020.

Vancouver:

Gohlke JW. A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations. [Internet] [Thesis]. Texas Tech University; 2011. [cited 2020 Aug 08]. Available from: http://hdl.handle.net/2346/ETD-TTU-2011-08-1809.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gohlke JW. A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations. [Thesis]. Texas Tech University; 2011. Available from: http://hdl.handle.net/2346/ETD-TTU-2011-08-1809

Not specified: Masters Thesis or Doctoral Dissertation