


Politecnico di Torino  
Academic Year 2016/17  
02MAZNA Fluid Mechanics in Porous Media 

Master of sciencelevel of the Bologna process in Petroleum Engineering  Torino 





Subject fundamentals
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. 
Expected learning outcomes
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. 
Prerequisites / Assumed knowledge
Student should have an average background in physics, mathematics and Geology.

Contents
Origin of hydrocarbons: formation, migration and main types of trap.
Basics concepts of hydrocarbon chemistry. Thermodynamic behavior of hydrocarbon mixtures: qualitative phase behaviour (PVT) of single and multicomponent 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. Rockfluids 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 enchroachment. 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 pseudosteady state and transient conditions. Turbolence skin and nonDarcy coefficient. Multiphase flow models: diffusivity equation in pressure and saturation; numerical models: fundamentals on Finite Difference Methods; treatment of non linearities, transmissibility. 
Delivery modes
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.

Texts, readings, handouts and other learning resources
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 
Assessment and grading criteria
All the students have to give the written test consisting in a variable number of both theoretical questions and exercises. The oral exam is optional and can be given only if the result of the written test is positive.

