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Professor HeinemannsDoktorandengruppePHDGVerein zur Förderungvon wissenschaftlichen Arbeitenin Reservoircharakterisierung und -simulationTEXTBOOK SERIESVOLUME 1FLUID FLOW IN POROUS MEDIAbyZoltán E. HEINEMANNProfessor for Reservoir EngineeringLeoben, October 2005actualizedbyDr. Georg MittermeirTehran, February 2013
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Table of Contents3Table of Contents1 Fundamental Properties of Porous Media . 51.11.21.31.41.5Porosity . 61.1.1 General Aspects and Definition . 61.1.2 Determination of Porosity . 71.1.3 Compaction . 91.1.4 Compressibility of Porous Media . 91.1.5 Classification of Porosity . 12Capillary Properties . 141.2.1 Saturation . 141.2.2 Wettability . 141.2.2.1 Classification of Reservoir Rocks based on Wettability . 151.2.2.2 Measurement of Wettability . 161.2.2.2.1 Contact Angle Measurement . 171.2.2.2.2 Amott Method1.19 . 181.2.2.2.3 USBM Wettability Index. 191.2.3 Capillary Pressure . 231.2.3.1 Definition. 231.2.3.2 Measurement of Capillary Pressure in a Porous Medium . 251.2.3.2.1 Method of Centrifuge . 271.2.3.2.2 Mercury Injection (Purcell Method). 311.2.3.3 Conversion of Laboratory Data . 321.2.4 The Leverett Function . 341.2.5 Pore Size Distribution . 351.2.6 Vertical Equilibrium . 36Permeability . 391.3.1 Darcy’s Law . 391.3.2 Definition and Units of Permeability . 401.3.3 Measurements of Permeability . 421.3.4 Klinkenberg Effect . 461.3.5 Analogies between the Laws of Darcy, Ohm and Fourier . 471.3.6 Filtration Velocity . 481.3.7 Quadratic Equation of Filtration . 49Relative Permeabilities . 501.4.1 Definition of Relative Permeability . 511.4.2 Definitions of End-Point Saturations . 511.4.3 Relative Permeability Measurements . 531.4.3.1 The HASSLER method . 531.4.3.2 PENN-STATE-Method . 571.4.3.3 Welge-Method. 581.4.4 Saturation Distribution and Relative Permeability . 58References . 612 Equations of Single-Phase Filtration . 65
Table of Contents2.12.22.32.42.52.6Fundamental Equation of Filtration. . 672.1.1 Differential Form of the Darcy-Law . 672.1.2 Anisotropic Porous Media . 70Equation of State . 732.2.1 Incompressible Fluids . 732.2.2 Low Compressibility Fluids . 732.2.3 Formation Volume Factor . 742.2.4 Ideal and Real Gases . 752.2.5 Equation of continuity . 76Special Forms of the Equation of Filtration . 792.3.1 Incompressible Fluids . 792.3.2 Low Compressibility Fluids . 792.3.2.1 Elastic Porous Media. 80Real and Ideal Gases . 82Boundary and Initial Conditions . 842.5.1 Boundary Conditions . 842.5.2 Initial Conditions . 852.5.3 Discontinuities in Porous Media . 86Schematic of the Filtration Equations . 873 Solutions of the Single-Phase Equation of Filtration . 913.13.23.33.43.53.63.7Steady State Filtration . 923.1.1 Steady State Filtration of Low Compressibility Fluid . 923.1.2 Steady State Filtration in a Radial System . 933.1.3 Steady State Gas Filtration . 96Non-Steady State Filtration in Infinite Acting Systems . 983.2.1 Radial Systems with Constant Production Rate . 983.2.2 Properties of the Ei-Function . 1023.2.3 Pressure Drop in Space and Time . 1033.2.4 The Spatial Distribution of Flow . 107Dimensionless Variables . 108The Infinite Radial System with Constant Pressure at the Interior Boundary . 113Non-Steady State Filtration in a Finite System . 1183.5.1 Constant Production Rate . 1183.5.1.1 Closed Exterior Boundary . 1183.5.1.2 Boundary with Constant Pressure . 1203.5.2 Constant Pressure at the Interior Boundary and Closed Exterior Boundary 121Non-Steady State Filtration in Linear System . 1233.6.1 Linear Flow with Constant Production Rate . 123The Principle of Superposition . 1293.7.1 The First Law of Superposition . 1293.7.2 The Second Law of Superposition . 1323.7.3 Calculation of Multi-Well Problems . 1343.7.4 Single Well with Variable Production Rates . 1343.7.5 Pressure Build-up of Shut-In Well . 1363.7.6 Method of Image . 1373.7.6.1 Pressure Buildup Test Near No Flow Boundary . 1394
Table of Contents3.83.7.6.2 Constant Pressure Boundary . 141References . 1424 Two-Phase Filtration. 1474.14.24.34.44.5The Equation of Two-Phase Filtration . 147Vertical Two-Phase Filtration of Incompressible Fluids . 149The BUCKLEY-LEVERETT Solution . 1524.3.1 The Welge-Method . 155Influence of Gravity and Capillary Force . 1614.4.1 Influence of Gravity . 1614.4.2 Influence of the Capillary Force . 1624.4.3 The Capillary End-Effect . 1644.4.4 Imbibition . 165References . 1695 Piston-Like Displacement . 1735.15.25.3The Mobility Ratio . 173Propagation of a Displacement Front . 1745.2.1 Linear Displacement . 1765.2.2 Displacement in an Inclined Layer . 1785.2.3 Supercritical Displacement . 185References .
FLUID FLOW IN POROUS MEDIA by Zoltán E. HEINEMANN Professor for Reservoir Engineering Leoben, October 2005 actualized by Dr. Georg Mittermeir Tehran, February 2013. Roseggerstr. 11a 8700 Leoben Austria Phone: 43 (0)3842/4331611 E-Mail: phdg@a1.net IBAN: AT78 1200 0100 0531 8976 BIC: BKAUATWW For kind Attention 7KH 7H[WERRN VHULHV RI WKH 3 '* LV DQ DLG IRU Cited by: 20Publish Year: 2013Author: Zoltán E. Heinemann, Georg Mittermeir
