Quantitative Methods in Reservoir Engineering

by Chin, PhD

• ISBN13: 9780750675680
• ISBN10: 0750675683
• Format: Paperback
• Copyright: 2002-06-18
• Publisher: Elsevier Science

Summary

For the practitioner, this volume is a valuable tool for predicting reservoir flow in the most efficient and profitable manner possible, using quantitative methods rather than anecdotal and outdated methods. For the student, this volume offers insight not covered in other textbooks. too many approaches in traditional petroleum engineering are based on "ad hoc" and "common sense" methods that have no rigorous mathematical basis. Most textbooks dealing with reservoir engineering do not go into the necessary mathematical detail and depth. This new book by Wilson Chin, a revision of two earlier books published by Gulf Publishing, Modern Reservoir Flow and Well Transient Analysis and Formation Invasion, integrates rigorous mathematical methods for simulating and predicting reservoir flow both near and away from the well.

Table of Contents

Preface	xi
Motivating Ideas and Governing Equations	1	(18)
Examples of incorrect formulations	3	(4)
Darcy's equations for flow in porous media	7	(4)
Logarithmic solutions and beyond	11	(1)
Fundamental aerodynamic analogies	12	(6)
Problems and exercises	18	(1)
Fracture Flow Analysis	19	(24)
Single straight-line fracture in an isotropic circular reservoir containing incompressible fluid	19	(8)
Line fracture in an anisotropic reservoir with incompressible liquids and compressible gases	27	(5)
Effect of nonzero fracture thickness	32	(2)
Flow rate boundary conditions	34	(1)
Uniform vertical velocity along the fracture	35	(2)
Uniform pressure along the fracture	37	(1)
More general fracture pressure distributions	38	(1)
Velocity conditions for gas flows	39	(1)
Determining velocity fields	40	(1)
Problems and exercises	41	(2)
Flows Past Shaly Bodies	43	(9)
Straight-line shale segment in uniform flow	43	(6)
Curved shale segment in uniform flow	49	(1)
Mineralized faults, anisotropy, and gas flow	49	(1)
Problems and exercises	50	(2)
Streamline Tracing and Complex Variables	52	(27)
The classical streamfunction	52	(3)
Streamfunction for general fluids in heterogeneous and anisotropic formations	55	(2)
Subtle differences between pressure and streamfunction formulations	57	(3)
Streamline tracing in the presence of multiple wells	60	(3)
Streamfunction expressions for distributed line sources and vortexes	63	(2)
Streamfunction solution using complex variables techniques	65	(1)
Circle Theorem: Exact solutions to Laplace's equation	66	(2)
Generalized streamline tracing and volume flow rate computations	68	(2)
Streamline tracing in 3D flows	70	(3)
Tracer movement in 3D reservoirs	73	(3)
Fluid flow instabilities	76	(2)
Problems and exercises	78	(1)
Flows in Complicated Geometries	79	(29)
What is conformal mapping?	80	(2)
Using ``simple'' complex variables	82	(2)
The classic radial flow solution	84	(2)
Circular borehole with two symmetric radial fractures	86	(2)
Circular borehole with two uneven, opposite, radial fractures; or a single radial fracture	88	(1)
Circular borehole with multiple radial fractures	89	(2)
Straight shale segment at arbitrary angle	91	(3)
Infinite array of straight-line shales	94	(1)
Pattern wells under aquifer drive	95	(1)
Three-dimensional flows	96	(1)
Point spherical flow	97	(1)
Finite line source with prescribed pressure	97	(2)
Finite line source with prescribed flow rate	99	(1)
Finite conductivity producing fracture having limited areal extent	100	(1)
Finite conductivity nonproducing fracture having limited areal extent	101	(1)
Borehole interactions	101	(1)
Producing fracture near multiple wells under aquifer drive	102	(1)
Producing fractures near multiple wells in solid wall reservoirs	103	(1)
Straight-line shale segment near multiple wells in uniform flow	104	(1)
Examples 5-16 and 5-17. Nonproducing faults in solid wall and aquifer-driven reservoirs	105	(1)
Highly curved fractures and shales	106	(1)
Problems and exercises	107	(1)
Radial Flow Analysis	108	(14)
Steady liquids in homogeneous media	108	(1)
Simple front tracking for liquids in homogeneous isotropic media	109	(2)
Steady-state gas flows in homogeneous, isotropic media	111	(2)
Transient compressible flows	113	(1)
Numerical solution for steady flow	114	(2)
Explicit and implicit schemes for transient compressible liquids	116	(2)
Transient compressible gas flows	118	(3)
Problems and exercises	121	(1)
Finite Difference Methods for Planar Flows	122	(38)
Finite differences: basic concepts	122	(4)
Formulating steady flow problems	126	(2)
Steady flow problems: seven case studies	128	(25)
Isotropy and anisotropy: fluid invasion in cross-bedded sands	153	(5)
Problems and exercises	158	(2)
Curvilinear Coordinates and Numerical Grid Generation	160	(14)
General coordinate transformations	162	(1)
Thompson's mapping	163	(1)
Some reciprocity relations	164	(1)
Conformal mapping revisited	165	(2)
Solution of mesh generation equations	167	(5)
Problems and exercises	172	(2)
Steady-State Reservoir Applications	174	(28)
Governing equations	176	(1)
Steady areal flow: generalized log r solution	177	(4)
Streamline tracing in curvilinear coordinates	181	(2)
Calculated steady flow examples	183	(1)
Well in Houston	184	(5)
Well in Dallas	189	(1)
Well in center of Texas	190	(2)
Fracture across Texas	192	(2)
Isothermal and adiabatic gas flows	194	(3)
Mesh generation: several remarks	197	(4)
Problems and exercises	201	(1)
Transient Compressible Flows: Numerical Well Test Simulation	202	(10)
Transient pressure drawdown	203	(4)
Transient pressure buildup	207	(4)
Problems and exercises	211	(1)
Effective Properties in Single and Multiphase Flows	212	(10)
Constant density liquid in steady linear flow	212	(3)
Lineal multiphase flow in two serial cores	215	(4)
Effective properties in steady cylindrical flows	219	(1)
Steady, single-phase, heterogeneous flows	219	(1)
Time scale for compressible transients	219	(2)
Problems and exercises	221	(1)
Modeling Stochastic Heterogeneities	222	(7)
Observations on existing models	222	(2)
A mathematical strategy	224	(2)
Contractional fractures	226	(2)
Problems and exercises	228	(1)
Real and Artificial Viscosity	229	(6)
Real viscosity and shockwaves	229	(3)
Artificial viscosity and fictitious jumps	232	(2)
Problems and exercises	234	(1)
Borehole Flow Invasion, Lost Circulation, and Time Lapse Logging	235	(10)
Borehole invasion modeling	235	(1)
Thin Iossy muds (that is, water)	236	(1)
Time-dependent pressure differentials	237	(1)
Invasion with mudcake effects	237	(1)
Time lapse logging	238	(5)
Lost circulation	243	(1)
Problems and exercises	244	(1)
Horizontal, Deviated, and Modern Multilateral Well Analysis	245	(43)
Fundamental issues and problems	246	(6)
Governing equations and numerical formulation	252	(14)
Example calculations	266	(1)
Convergence acceleration, two deviated horizontal gas wells in a channel sand	267	(3)
Dual-lateral horizontal completion in a fractured, dipping, heterogeneous, layered formation	270	(3)
Stratigraphic grids, drilling dome-shaped structures	273	(2)
Simulating-while-drilling horizontal gas wells through a dome-shaped reservoir	275	(6)
Modeling wellbore storage effects and compressible borehole flow transients	281	(6)
Problems and exercises	287	(1)
Fluid Mechanics of Invasion	288	(18)
Qualitative ideas on formation invasion	290	(4)
Background literature	294	(3)
Darcy reservoir flow equations	297	(6)
Moving fronts and interfaces	303	(2)
Problems and exercises	305	(1)
Static and Dynamic Filtration	306	(35)
Simple flows without mudcake	306	(6)
Flows with moving boundaries	312	(4)
Coupled dynamical problems: mudcake and formation interaction	316	(9)
Dynamic filtration and borehole flow rheology	325	(9)
Concentric power law flows without pipe rotation	334	(2)
Concentric power law flows with pipe rotation	336	(1)
Formation invasion at equilibrium mudcake thickness	337	(1)
Dynamic filtration in eccentric boreholes	338	(2)
Problems and exercises	340	(1)
Formation Tester Applications	341	(11)
Problems and exercises	351	(1)
Analytical Methods for Time Lapse Well Logging Analysis	352	(21)
Experimental model validation	352	(4)
Characterizing mudcake properties	356	(4)
Porosity, permeability, oil viscosity, and pore pressure determination	360	(7)
Examples of time lapse analysis	367	(5)
Problems and exercises	372	(1)
Complex Invasion Problems: Numerical Modeling	373	(35)
Finite difference modeling	373	(8)
Lineal liquid displacement without mudcake	381	(5)
Cylindrical radial liquid displacement without cake	386	(3)
Spherical radial liquid displacement without cake	389	(2)
Lineal liquid displacement without mudcake including compressible flow transients	391	(2)
Von Neumann stability of implicit time schemes	393	(2)
Gas displacement by liquid in lineal core without mudcake, including compressible flow transients	395	(4)
Simultaneous mudcake buildup and displacement front motion for incompressible liquid flows	399	(8)
Problems and exercises	407	(1)
Forward and Inverse Multiphase Flow Modeling	408	(45)
Immiscible Buckley-Leverett lineal flows without capillary pressure	409	(7)
Molecular diffusion in fluid flows	416	(8)
Immiscible radial flows with capillary pressure and prescribed mudcake growth	424	(14)
Immiscible flows with capillary pressure and dynamically coupled mudcake growth	438	(14)
Problems and exercises	452	(1)
Cumulative References	453	(9)
Index	462	(10)
About the Author	472