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Fluid Mechanics in Porous Media

02MAZNW

A.A. 2022/23

Course Language

Inglese

Course degree

Master of science-level of the Bologna process in Georesources And Geoenergy Engineering - Torino

Course structure
Teaching Hours
Lezioni 80
Esercitazioni in aula 20
Tutoraggio 20
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Viberti Dario Professore Associato ING-IND/30 77 10 0 20 15
Teaching assistant
Espandi

Context
SSD CFU Activities Area context
ING-IND/30 10 B - Caratterizzanti Ingegneria per l'ambiente e il territorio
2022/23
The aim of the course consists in giving the fundamental concepts necessary to characterize, to understand and to describe analytically and numerically the behavior of fluids in porous media and, in particular the dynamic behavior of hydrocarbon reservoirs. The course is divided in some main chapters such as: reservoir fluids PVT properties; rock properties; rock fluid interaction properties; diffusivity equations for slightly compressible and compressible fluids. The course has to be considered as introductory to most of the other course of the petroleum engineering program.
The course provides the fundamental concepts and competences necessary to characterize, understand and describe through the main reference models the flow behaviour of water, hydrocarbons, CO2 and Hydrogen in underground porous media taking into account the phase behaviour and phase changes under different thermodynamic conditions. The course provides the essential background for the courses of Reservoir Engineering, Well Logging and Well Testing, Underground Fluid Storage.
Understanding the parameters used to characterize the dynamic behavior of fluid and of reservoirs, in terms of physical meaning and order of magnitude. Ability of approaching different technical problems by the selection the most suitable model. Critical approach in review to real data. Communication skills, ability of using and understanding the technical language and terminology adopted worldwide in the industries. Ability in increasing their own knowledge by selecting the appropriate technical and scientific literature.
Understanding the parameters describing the fluids and rock fluids interaction behavior and used in fluid flow problems- Knowledge of physical meaning and order of magnitude is expected. Ability of approaching different technical problems by the selection the most suitable model. Critical approach to review real data. Communication skills, ability of using and understanding the technical language and terminology adopted worldwide in the industries. Ability in increasing their own knowledge by selecting the appropriate technical and scientific literature.
Student should have an average background in physics, mathematics and Geology.
Student should have an average background in physics (in particular mass and force, gravity, vector calculus, velocity, acceleration, Newton’s laws, pressure, static of fluids, Stevino’s law, Pascal’s law, Archimede’s principle, Bernulli Theorem), mathematics (in particular the use of differential and integral calculus, interpolation and linear regression) and basic knowledges in Geology.
Basics definitions and nomenclature Thermodynamic behavior of hydrocarbon mixtures: qualitative phase behaviour (PVT) of single and multi-component systems; hydrocarbon reservoir nomenclature and classification. quantitative phase behaviour of hydrocarbons: PVT parameters of gas, oil, and water. Fluid viscosity. Drive mechanisms and recovery factors. Static pressure profiles: hydrostatic equilibrium of hydrocarbon reservoirs; pressure gradients fluid contacts; interpretation of static pressure profiles for different reservoirs typology. Rock petrophysical properties: Routine core analyses; Porosity: total, effective, primary and secondary; Fluid saturation; Electrical conductivity: Archie's law. Basic concepts of log interpretation, mathematical models and numerical solutions. Darcy's law: hydraulic conductivity, permeability; generalized equation; Darcy's law in different flow geometries: linear, radial flow, vertical free flow, 3D flow. Permeability tensor, homogeneity and isotropy. Darcy's law for gases, slip flow and Klinkenberg effect. Forchheimer equation. Rock-fluids interaction properties: Special core analyses; Extension of Darcy's law to multiphase flow: effective permeability; relative permeability, mobility. Gas Oil Ratio. Superficial and interfacial tension, contact angle, wettability, immiscible fluids flow. Capillary pressure and capillary rise. J function; Imbibition and drainage; residual saturations. Diffusivity equation for monophase flow of slightly compressible fluids (oil and water): definition of the mathematical model; basic assumptions; analytical solutions in transient, steady and pseudo steady conditions, skin effect and productivity index; water encroachment. Diffusivity equation for monophase flow of highly compressible fluids (gas): diffusivity equations for laminar flow; analytical solution for turbulent flow, integration of Forchheimer equation under steady state conditions. Extension to pseudo-steady state and transient conditions. Turbolence skin and non-Darcy coefficient. Multiphase flow models: diffusivity equation in pressure and saturation; numerical models: fundamentals on Finite Difference Methods; treatment of non linearities, transmissibility.
Basics definitions and nomenclature Thermodynamic behavior of hydrocarbon mixtures, CO2 and Hydrogen: qualitative phase behaviour (PVT) of single and multi-component systems; hydrocarbon reservoir nomenclature and classification. quantitative phase behaviour: PVT parameters of gas, oil, and water. Fluid viscosity. Drive mechanisms and recovery factors. Static pressure profiles: hydrostatic equilibrium of hydrocarbon reservoirs; pressure gradients fluid contacts; interpretation of static pressure profiles for different reservoirs typology. Rock petrophysical properties: Routine core analyses; Porosity: total, effective, primary and secondary; Fluid saturation; Electrical conductivity: Archie's law. Darcy's law: hydraulic conductivity, permeability; generalized equation; Darcy's law in different flow geometries: linear, radial flow, vertical free flow, 3D flow. Permeability tensor, homogeneity and isotropy. Darcy's law for gases, slip flow and Klinkenberg effect. Forchheimer equation. Rock-fluids interaction properties: Special core analyses; Extension of Darcy's law to multiphase flow: effective permeability; relative permeability, mobility. Gas Oil Ratio. Superficial and interfacial tension, contact angle, wettability, immiscible fluids flow. Capillary pressure and capillary rise. J function; Imbibition and drainage; residual saturations. Diffusivity equation for monophase flow of slightly compressible fluids (oil and water): definition of the mathematical model; basic assumptions; analytical solutions in transient, steady and pseudo steady conditions, skin effect and productivity index; water encroachment. Diffusivity equation for monophase flow of highly compressible fluids (gas): diffusivity equations for laminar flow; analytical solution for turbulent flow, integration of Forchheimer equation under steady state conditions. Extension to pseudo-steady state and transient conditions. Turbolence skin and non-Darcy coefficient. Multiphase flow models: diffusivity equation in pressure and saturation; numerical models: fundamentals on Finite Difference Methods; treatment of non linearities, transmissibility.
The course is divided in 55-60% of theoretical background and 40-45% of exercises in the computer laib. During the exercises the students have to approach practical problems by applying the theory discussed during the lessons.
The course is divided in 55-60% of theoretical background and 40-45% of exercises in the computer laib. During the exercises the students have to approach practical problems by applying the theory discussed during the lessons.
Slides of the course available on line at the course web page for both theory and exercises. Additional material: E.J. Burcik. 1957. Properties of petroleum reservoirs fluids. John Wiley & sons, inc. London C.H. Whitson. M. R. Brule. 2000. Phase behavior. SPE Monograph Series. Richardson, Texas. C.R. Fitts. 2002. Groundwater science. Academic Press. London, UK A.T. Corey. 1977. Mechanics of heterogenous fluids in porous media. Water Resources Pubblications. Fort Collins, Colorado, USA D.W. Green, G.P. Willhite. 1998. Enhanced Oil Recovery. SPE Textbook Series vol.6
Slides of the course available on line at the course web page for both theory and exercises. Additional material: E.J. Burcik. 1957. Properties of petroleum reservoirs fluids. John Wiley & sons, inc. London C.H. Whitson. M. R. Brule. 2000. Phase behavior. SPE Monograph Series. Richardson, Texas. C.R. Fitts. 2002. Groundwater science. Academic Press. London, UK A.T. Corey. 1977. Mechanics of heterogenous fluids in porous media. Water Resources Pubblications. Fort Collins, Colorado, USA D.W. Green, G.P. Willhite. 1998. Enhanced Oil Recovery. SPE Textbook Series vol.6
Modalità di esame: Prova scritta (in aula); Prova orale obbligatoria;
Exam: Written test; Compulsory oral exam;
Final examination is divided into two parts: written test (duration 50 - 75 minutes) and oral examination. The written test is made up of three/four questions (or problems). Results of the written test will be either "Pass" (P) or "No Pass" (NP). Only students with a "Pass" mark on the written test will be able to take the oral examination. The oral examination can only be taken once for each “Pass”, either during the “appello” of the written test or the immediately following “appello”. If a student doesn’t pass the written, doesn’t pass the oral, doesn’t accept the mark of the oral, doesn’t show up for the oral, they must retake the written.
Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.
Exam: Written test; Compulsory oral exam;
Final examination is divided into two parts: written test (duration 50 - 75 minutes) and oral examination. The written test is made up of three/four questions (or problems). Results of the written test will be either "Pass" (P) or "No Pass" (NP). Only students with a "Pass" mark on the written test will be able to take the oral examination. The oral examination can only be taken once for each “Pass”, either during the “appello” of the written test or the immediately following “appello”. If a student doesn’t pass the written, doesn’t pass the oral, doesn’t accept the mark of the oral, doesn’t show up for the oral, they must retake the written.
In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.
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