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NUMERICAL MODELING OF TURBULENT GAS FLOW IN POROUS MEDIA: A FRACTIONAL DIFFUSION APPROACH

l NUMERICAL MODELING OF TURBULENT GAS FLOW IN POROUS MEDIA: A FRACTIONAL DIFFUSION APPROACH. Masters thesis, King Fahd University of Petroleum and Minerals.

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Arabic Abstract

إن فهم الفيزياء وراء سير الموائع في الأوساط المسامية لذو أهمية بالغة في عدة مجالات، بدءاً من استخراج المياه من جوف الأرض وحتى علوم ميكانيا التربة. وبالطبع فإن صناعة الزيت والغاز ليست بمنأى عن ذلك، فالفهم الجيد لهذا الموضوع يزداد أهمية يوماً بعد يوم، خصوصاً مع الأرتفاع المتزايد للطلب على الطاقة. إن فهمنا الحالي لسير الموائع في الأوساط المسامية يعتمد على سنوات طويلة من البحث والدراسة، والمزيد من الدراسات الحديثة يفترض أن تساعدنا على الوصول إلى فهم أعمق وبالتالي القدرة على اتخاذ قرارات أصحّ. إن الهدف الرئيسي من هذه الدراسة هو محاولة الوصول إلى فهم أعمق لقوانين الفيزياء اللتي تحكم سير الموائع في الأوساط المسامية (كما في حالة خزانات الزيت والغاز)، وذلك بالنظر إليها في ضوء حالات التدفق المضطرب؛ حيث تكون القوانين التقليديه (كقانون لعالم هنري دارسي) ومثيله الخاص بالغازات (معادلة فورتشايمر) غير صالحين لوصف فيزياء تلك الموائع بالدقة الملطوبة. في هذه الدراسة، تم تعديل معادلة فورتشايمر لتكون صالحة لوصف السير المضطرب للغاز في الأوساط المسامية، وتم اختبار المعادلة بعد التعديل على أكثر من نموذج محاكاة للتأكد من أهمية التعديل وقدرته على حساب نتائج أفضل.

English Abstract

Understanding the physics of fluid flow in a porous media is of high interest in many fields, such as water extraction from aquifers and the geo-mechanics related to soil mechanics. The oil and gas industry is no exception to this, and the topic is getting more and more attention with the increasing energy demand. Our current understanding of fluid flow in the porous media is based on years of research on this topic in the said fields, and the outcomes of the future work should provide the basis for better predictions and decisions. We aim in this research to explore the physics of fluid flow in porous media (such as in Oil and Gas Reservoirs) based upon the concept of anomalous diffusion cases; where classical Darcy’s law and its modification for gas (Forchheimer’s Equation) do not fully describe the fluid physics. Henry Darcy was the first to develop an equation describing fluid flow through porous media. His equation was developed to calculate flow rate of water through sand beds. What we know now as permeability, was first used to estimate the conductivity of sand beds in his experiment. Darcy’s Law has good analogy to Fick’s Law in the diffusion theory, which describes the usual diffusion in porous media. However, the usual diffusion is not always the case, as there are several cases where the paths of the fluid flow are complex, or the velocity of the fluid is very high, hence, the anomalous diffusion takes place. Fractional derivatives has been used as a mean to describe the anomalous diffusion process, this requires the modification of the conventional laws (Darcy’s law for liquid and Forchheimer’s for gas). In this work, we implement the application of the memory formalisms on the pressure flux term for gas flow, by modifying the Forchheimer’s Equation. We use fractional order derivatives to represent the memory formalisms and its effect on the pressure distribution. The modified Forchheimer’s Equation is used to derive a diffusivity equation for the gas flow, and its solution is obtained numerically. The pressure behavior of the gas reservoir is modeled after incorporating the memory parameter (α), and the effect on the pressure distribution over time is analyzed. The results of this study show that the bottom hole pressure is affected by the memory parameter and that the α affects the calculation of permeability values from graphical analysis. And from that, we can see that the pressure data obtained from normal diffusion models will be erroneous if the actual fluid was an anomalous flow. As a validation strategy, the permeability (k) and (α) are estimated using non-linear regression (Levenberg-Marquardt algorithm) considering both normal and fractional diffusion to show the importance of the model modification on the parameters estimation process, and how ignoring the anomalous effect would result in less accurate results.



Item Type:Thesis (Masters)
Subjects:Petroleum > Reservoir Engineering and Management
Petroleum > Reservoir Characterization
Petroleum > Reservoir Modelling and Simulation
Divisions:College Of Engineering Sciences > Petroleum Engineering Dept
Committee Advisor:Awotunde, Abeeb
Committee Members:Al-Hashim, Hasan and Mahmoud, Mohamed and Malik, Nadeem and Tatar, Nasser-Eddine
ID Code:139677
Deposited By:RAMI MOHAMED ALLOUSH (g201202400)
Deposited On:23 Jun 2015 10:57
Last Modified:23 Jun 2015 10:57

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