Complexity of Two-Phase Flow in Porous Media
|
|
- Osborne Fowler
- 5 years ago
- Views:
Transcription
1 1 Complexity of Two-Phase Flow in Porous Media Rennes September 16, 2009 Eyvind Aker Morten Grøva Henning Arendt Knudsen Thomas Ramstad Bo-Sture Skagerstam Glenn Tørå Alex Hansen
2 2 Declining oil production, increasing energy consumption: Buying time for developing of alternative energy sources. Paul Roberts: Arguably the most serious crisis ever to face industrial society The End of Oil: On the Edge of a Perilous New World (2004) Low-permeability carbonate rock: All fluid transport through fractures -But where are the fractures, and are there enough of them? Recovering stuck oil: EOR Tar sands of Alberta, Canada
3 3 Lecture Plan: 1. Transient vs. Steady-State Flow 2. Numerical Network Model 3. Steady-State Flow in Numerical Model 4. Parallel Flow Instabilies 5. Statistical Mechanics of Steady-State Flow 6. Some Thermodynamics 7. Film Flow in Crevices 8. Summary
4 4 1. Transient vs. Steady-State Flow
5 5 Experimental Background K.J. Måløy s lab. at the Univ. of Oslo Inlet Q P L Defending Fluid: 90% by weight Glycerol - water solution Viscosity: Pa s Invading Fluid: Air Viscosity ratio: M = Interfacial tension: N/m W Outlet Q
6 6 Flooding Experiments Dimensionless numbers: Instabilities: Transients Ca = capillary number = viscous forces/ capillary forces M = Ca = M = viscosity ratio Ca = Ca = 0.22 (Måløy, Univ. Oslo)
7 7 Ca = Ca = Ca = 0.120
8 8 Steady State Flow What enters a RVE is statistically the same as what leaves it. An RVE inside a reservoir will typically experience steady-state conditions, and not the transients in a flooding experiment.
9 9 Steady state signifies that apart from statistical fluctuations, the system remains constant or changes slowly on the scale of the fluctuations. Hence, even if both fluids move and fluid clusters break up and merge, we will be dealing with a steady state as long as the averaged macroscopic parameters describing the flow remain constant (or change slowly on the time scale of the fluctuations). A setup for studying steady-state flow in the laboratory: Region of spatially homogeneous steady-state flow. Tallakstad, Måløy, Univ. Oslo
10 10 Clusters in spatially homogeneous steady-state flow Clusters have been artificially colored. Tallakstad, Måløy
11 11 Steady state Old wisdom: Equilibrium phenomena are easy Non-equilibrium phenomena are difficult Flooding Equilibrium thermodynamics is 150 years old Non-equilibrium thermodynamics is still being developed Porous media: Flooding has been studied for a long time Steady-state flow has been largely neglected
12 12 2. Numerical Network Model
13 13 Numerical Modeling Ca = M = 100 Ca = M = (Aker et al., 1998) Ca = M=1
14 14 Network of connected Pores Sharp corners: Wetting fluid forms films in the crevices. For now: no crevices, no films
15 15 Dynamics at the pore level: How do the interfaces move?
16 16 Coalescence and Instabilities: Snap-off
17 17 Coalescence and Instabilities: Coalescence
18 18
19 19 3. Steady State Flow in Numerical Model
20 20 Steady-state flow implemented on a torus Largest non-wetting cluster. Flow Direction (Ramstad, 2006)
21 21 Starting from a band of red fluid, the interfaces initially develop capillary fingering and stable displacement. Capillary fingering Wetting fluid Flow direction Non-wetting fluid Ca = M=1 Stable displacement
22 22
23 23 Steady-state configuration is independent of initial preparation of system: It is a state. (It is independent of initial conditions given the flow is fast enough for none of the fluids to get stuck due to capillary forces.) Flow direction Drainage and imbibition are now microscopic concepts.
24 24 Reconstructed pore networks Pore Network from Berea Sandstone (3mm)3 Each pore is described by a number of geometric parameters. Reconstruction by e.g. merging thin slices
25 25 Setting up steady-state flow in reconstructed network: Must make the non-periodic structure periodic
26 26 Making the three-dimensional network periodic in the flow direction:
27 27 Evolution towards steady-state flow Steady state Ca = 0.015, M = 1, S = 0.5 non-wetting saturation
28 28
29 29 Largest non-wetting clusters at different saturation levels in steady state S=0.65 Ca=0.015, M=1 S=0.67 S=0.59 S=0.71 Critical saturation
30 30 Cluster size distribution corresponding to the saturations just shown. At criticality N(s) s-2.27±0.08 Cluster size Average over 20 samples
31 31 Relative density of largest cluster P vs. saturation S. Critical saturation vs. capillary number: Sc = A + B log Ca Interesting consequences for radial flow
32 32 4. Parallel Flow Instabilities
33 33
34 34 Instabilities at the boundary of fluids moving in parallel. Wetting fluid Non-wetting fluid Wetting fluid What happens at this boundary when the capillary number is increased? Flow direction Periodic boundary conditions in the flow direction.
35 35 Kelvin-Helmholtz Shear Instability?
36 36 Flow direction. Flow periodic in the flow direction.
37 37
38 38 Mechanism: The non-wetting fluid produces viscous fingers that penetrate into the wetting fluid. The fingers experience side flow. They break off. This produces clusters of non-wetting fluid that diffuse into the wetting fluid and away from the non-wetting layer. There are never any clusters of wetting fluid within the non-wetting layer.
39 39 Non-wetting saturation profile normal to flow direction as function of time.
40 40 The derivative of the non-wetting saturation profile. This defines a mixing length scale λ.
41 41 Profile is stable and moves towards the non-wetting fluid: effectively an imbibition process.
42 42 Wetting fluid Constant current of non-wetting bubbles Non-wetting fluid Mixing zone moving with constant speed Steady state in a reference frame moving with constant speed to the right.
43 43 Starting out with the wetting fluid in the middle: an equilibrium is set up. The profile survives!
44 44 This layer is stable! Non-wetting fluid Wetting fluid Non-wetting fluid
45 45 5. Statistical Mechanics of Steady-State Flow
46 46 Returning to the concept of a state. A state is described by a small number of macroscopic parameters When the system is in such a state, it evolves through following a path in the space of all possible microscopic configurations such that the macroscopic averages remain constant. The equations that governs the path are the microscopic flow equations. These equations are very hard to solve (numerically). But, they provide far too much information! This information is needed to understand transients, but not to describe the dynamical steady state. Is there a way to get the needed information to describe macroscopically the steady state without having to resort to complete overkill?
47 47 Sequence of configurations through time integration: t t 4 t t The order of the configurations has been randomized: Does this randomization change the statistics? 2
48 48 If order plays no role: All steady-state properties will be completely described by the configurational probability distribution W{cf} where {cf} signifies the positions of all interfaces between the immiscible fluids in the porous medium. A configuration is fully described by the position of all interfaces. This leads to the possibility to exchange time integration by more efficient methods.
49 49 Metropolis Monte Carlo Sampling Configurational probability W{cf} Old configuration Test configuration {cfold} {cftest} Chosen by random change of old configuration. Draw a random number r [0,1]. If W{cfold}/W{cftest} > r: Reject test configuration. If W{cfold}/W{cftest} r: Accept test configuration.
50 50 We need to know what W{cf} is? Assumption: W{cf}=W(E{cf}) Probability depends on single macroscopic function E=E{cf}. Energy
51 51 Statistical mechanics of steady-state flow Pressure field solves the Kirchhoff equations. Microscopic energy function: E{cf} = (1/2) min Σ <ij> (pi-pj-pcij)2/µ eff ij Pressure field solves the Kirchhoff equations. Temperature 1/T=dΣ /de Effective viscosity Capillary pressure W{cf} = e-e{cf}/t W{cf} = W(E{cf}) (All configurations with same energy are equally probable.) Boltzmann distribution Configurational entropy Σ = log N(E) Basic assumption
52 52 All of thermodynamics now follows. Partition function: Z=Σ {cf} W{cf} Average energy (dissipation): E=Σ {cf} Thermodynamic variables: Pressure P Total flow rate Q Saturation S Fractional flow f Energy E Capillary pressure Pc Entropy Σ Temperature T Viscosity ratio M Free energy G = -T log Z E{cf} W{cf} / Z E=E(Σ,P) ( E/ P)Σ = - Q ( E/ Σ )P = T ( T/ P)Σ = - ( Q/ Σ )P
53 53 Numerical model: Controlling P (or Q) and saturation S. Tallakstad, Måløy, Univ. Oslo: Controlling P (or Q) and fractional flow f. Monte Carlo: S=S(T,P) f=f(t,p)
54 54 6. Some Thermodynamics
55 55 Temperature: Boltzmann weight: W{cf} = exp[-(1/2t) min Σ <ij> (pi-pj-pcij)2/µ eff ij ] Viscous pressures are all proportional to pressure P W{cf}=W(P,pc,T) Rescaling: W(P, pc, T) = W(P/T1/2,pc/T1/2,1) Setting T P2 Equation of state W(P, pc, T) = W(1, 1/Ca,1) Only dynamical parameter is Capillary number (besides M).
56 56 1st Law of Thermodynamics de = δ Q - δ W Reversible work related to change in flow rate Q; P dq. Irreversible work on the microscale related to creating new interfaces in the pores. 2nd Law of Thermodynamics In an isolated system, a process can occur only if it increases the entropy of the system. The steady state is at maximum entropy
57 57 3rd Law of Thermodynamics T 0 Σ 0 The zero-temperature state, i.e., when P = 0, the state with the least number of interfaces is the optimal one. This is when the two fluids are fully separated. This state has zero entropy.
58 58 A thermodynamic equation (Not yet a complete story) Fractional flow as a function of saturation S. Pressure difference as a function of saturation S. Keeping total flow rate Q constant.
59 59 Valid for a wide range of M. P = A (df/ds)q + B At constant Q
60 60 One more observation df/ds has a maximum for some F. P = C F2 + D F + E
61 61 This is the analytical form of the fractional flow vs. saturation curve. This corresponds to having an analytical form for the relative permeability curves. Experimental results from the literature
62 62 More Phase Transitions in the Steady State (2D system) (Single-phase flow of wetting fluid) (Single-phase flow non-wetting fluid) Single vs. multiphase flow.
63 63 Three-dimensional parameter Space: Saturation S Viscosity Ratio M Capillary Number Ca Both fluids move Only one fluid moves
64 64 7. Film Flow in Crevices
65 65 P: Pressure drop in bulk fluid p: Pressure drop in film Q: Bulk flow rate q: Film flow rate A: Bulk area a: film area
66 66 The Wedge Problem in a Closed Geometry Darcy equations for bulk and film flow: Film conservation
67 67 Surface Tension Eliminating P, p and q: Young relation
68 68 A Diffusion-Convection-Reaction Equation:
69 69 Diffusion constant Convection speed Reaction constant Shock fronts Diffusion constant increases with increasing concentration.
70 70 The area along the tube is constant: When Q = 0: No bulk flow. Convection term is zero.
71 71 No bulk flow: Diffusion only y=x2/t
72 72 Solutions: x/t1/2
73 73 Physical solution x/t1/2 Shock front
74 74 Bulk flow: Non-linear diffusion-convection equation Solitary wave solution Integration constants Z=x-ut Solitary wave speed
75 75 Solitary wave speed u (a+ + a-) a+ a-
76 76 Solitary wave speed u (a+ + a-)
77 77 a Stationary solutions: a1 a2 x
78 78 a x
79 79 Solvable under steady-state conditions for a class of profiles
80 80 Asymptotic solution: There is a divergence for finite AT/Ai for which a diverges. Critical area at which film goes unstable.
81 81 This instability leads to bubble formation in the pores.
82 82 AT = (x + 0.5)2
83 83 8. Summary
84 84 Transient vs. Steady-State Flow Numerical Network Model Steady-State Flow in Numerical Model Parallel Flow Instabilies Statistical Mechanics of Steady-State Flow Some Thermodynamics Film Flow in Crevices
Steady-state Two-phase Flow in Porous Media: Statistics and Transport Properties
Steady-state Two-phase Flow in Porous Media: Statistics and Transport Properties Ken Tore Tallakstad, 1 Henning Arendt Knudsen, 1 Thomas Ramstad, 2,3 Grunde Løvoll, 1 Knut Jørgen Måløy, 1 Renaud Toussaint,
More informationdynamics of f luids in porous media
dynamics of f luids in porous media Jacob Bear Department of Civil Engineering Technion Israel Institute of Technology, Haifa DOVER PUBLICATIONS, INC. New York Contents Preface xvii CHAPTER 1 Introduction
More informationA two-dimensional network simulator for two-phase flow in porous media
A two-dimensional network simulator for two-phase flow in porous media Eyvind Aker, Knut Jørgen Måløy Department of Physics University of Oslo, N-0316 Oslo, Norway Alex Hansen Department of Physics, Norwegian
More informationSteady-state, simultaneous two-phase flow in porous media: experiment and simulation
Steady-state, simultaneous two-phase flow in porous media: experiment and simulation Ken Tore Tallakstad, 1, Grunde Løvoll, 1, Thomas Ramstad, 2, Henning Arendt Knudsen, 1 Knut Jørgen Måløy, 1 and Alex
More informationApplications of Partial Differential Equations in Reservoir Simulation
P-32 Applications of Partial Differential Equations in Reservoir Simulation Deepak Singh Summary The solution to stochastic partial differential equations may be viewed in several manners. One can view
More informationBjørnar Sandnes. Henning Arendt Knudsen. Knut Jørgen Måløy. Eirik Grude Flekkøy. Grunde Løvoll. Yves Meheust. Renaud Toussaint Univ.
Pattern formation: building mazes with grains Bjørnar Sandnes Henning Arendt Knudsen Knut Jørgen Måløy Eirik Grude Flekkøy x (a) z (b) (c) Grunde Løvoll Yves Meheust NTNU Renaud Toussaint Univ. Strasbourg
More informationSeismic stimulation for enhanced oil production
Seismic stimulation for enhanced oil production Eirik G. Flekkøy, University of Oslo Mihailo Jankov, Olav Aursjø, Henning Knutsen, Grunde Løvold and Knut Jørgen Måløy, UiO Renaud Toussaint, University
More informationPORE-SCALE PHASE FIELD MODEL OF TWO-PHASE FLOW IN POROUS MEDIUM
Excerpt from the Proceedings of the COMSOL Conference 2010 Paris PORE-SCALE PHASE FIELD MODEL OF TWO-PHASE FLOW IN POROUS MEDIUM Igor Bogdanov 1*, Sylvain Jardel 1, Anis Turki 1, Arjan Kamp 1 1 Open &
More informationChapter Seven. For ideal gases, the ideal gas law provides a precise relationship between density and pressure:
Chapter Seven Horizontal, steady-state flow of an ideal gas This case is presented for compressible gases, and their properties, especially density, vary appreciably with pressure. The conditions of the
More informationPaper E A pore network model for calculation of interfacial velocities
Paper E A pore network model for calculation of interfacial velocities Submitted to Advances in Water Resources, fall 21. A PORE NETWORK MODEL FOR CALCULATION OF INTERFACIAL VELOCITIES H.F. Nordhaug a,
More informationAbility of Darcy s Law for Extension in Two- Phase Flow for Sedimentary Medium in Capillary Non-equilibrium Situations
Research Article imedpub Journals http://www.imedpub.com Resources, Recycling and Waste Management Ability of Darcy s Law for Extension in Two- Phase Flow for Sedimentary Medium in Capillary Non-equilibrium
More informationA LABORATORY STUDY OF FOAM FOR EOR IN NATURALLY FRACTURED RESERVOIRS. William R. Rossen Bander. I. AlQuaimi
A LABORATORY STUDY OF FOAM FOR EOR IN NATURALLY FRACTURED RESERVOIRS William R. Rossen Bander. I. AlQuaimi Gravity Backround Gas-injection EOR can displace nearly all oil contacted, but sweep efficiency
More informationThe Physical Origin of Interfacial Coupling in Two-Phase Flow through Porous Media
Transport in Porous Media 44: 109 122, 2001. c 2001 Kluwer Academic Publishers. Printed in the Netherls. 109 The Physical Origin of Interfacial Coupling in Two-Phase Flow through Porous Media RAMON G.
More informationA New Method for Calculating Oil-Water Relative Permeabilities with Consideration of Capillary Pressure
A Ne Method for Calculating Oil-Water Relative Permeabilities ith Consideration of Capillary Pressure K. Li, P. Shen, & T. Qing Research Institute of Petroleum Exploration and Development (RIPED), P.O.B.
More informationFracture relative permeability revisited
Fracture relative permeability revisited NOROLLAH KASIRI and GHASEM BASHIRI, Iran University of Science and Technology Relative permeability is one of the most uncertain terms in multiphase flow through
More informationHyemin Park, Jinju Han, Wonmo Sung*
Experimental Investigation of Polymer Adsorption-Induced Permeability Reduction in Low Permeability Reservoirs 2014.10.28 Hyemin Park, Jinju Han, Wonmo Sung* Hanyang Univ., Seoul, Rep. of Korea 1 Research
More informationSimulation of Imbibition Phenomena in Fluid Flow through Fractured Heterogeneous Porous Media with Different Porous Materials
Journal of Applied Fluid Mechanics, Vol. 10, No. 5, pp. 1451-1460, 2017. Available online at.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645. DOI: 10.169/acadpub.jafm.73.242.2721 Simulation of Imbibition
More informationThe role of capillary pressure curves in reservoir simulation studies.
The role of capillary pressure curves in reservoir simulation studies. M. salarieh, A. Doroudi, G.A. Sobhi and G.R. Bashiri Research Inistitute of petroleum Industry. Key words: Capillary pressure curve,
More informationCoupled free-flow and porous media flow: a numerical and experimental investigation
Coupled free-flow and porous media flow: a numerical and experimental investigation Master s Thesis Pavan Cornelissen 3863514 Supervisors: Kilian Weishaupt, MSc prof. dr. ir. Rainer Helmig prof. dr. ir.
More informationarxiv: v1 [physics.flu-dyn] 19 Dec 2017
Rheology of High-Capillary Number Flow in Porous Media Santanu Sinha Beijing Computational Science Research Center, East Xibeiwang Road, Haidian District, Beijing 93, China. Magnus Aa. Gjennestad,, Morten
More informationPore-Level Bénard Marangoni Convection in Microgravity
Pore-Level Bénard Marangoni Convection in Microgravity Peyman Mohammadmoradi, and Apostolos Kantzas * Chemical and Petroleum Engineering Department, University of Calgary *Corresponding author: 2500 University
More informationPore-scale modeling extension of constitutive relationships in the range of residual saturations
WATER RESOURCES RESEARCH, VOL. 37, NO. 1, PAGES 165 170, JANUARY 2001 Pore-scale modeling extension of constitutive relationships in the range of residual saturations Rudolf J. Held and Michael A. Celia
More informationAN EXPERIMENTAL INVESTIGATION OF BOILING HEAT CONVECTION WITH RADIAL FLOW IN A FRACTURE
PROCEEDINGS, Twenty-Fourth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, January 25-27, 1999 SGP-TR-162 AN EXPERIMENTAL INVESTIGATION OF BOILING HEAT CONVECTION
More informationPore-Scale Analysis of Interfacial Instabilities and Impact of Heterogeneity on Relative Permeability by Lattice Boltzmann Method
Louisiana State University LSU Digital Commons LSU Master's Theses Graduate School 3-31-2018 Pore-Scale Analysis of Interfacial Instabilities and Impact of Heterogeneity on Relative Permeability by Lattice
More informationMEASUREMENT OF CAPILLARY PRESSURE BY DIRECT VISUALIZATION OF A CENTRIFUGE EXPERIMENT
MEASUREMENT OF CAPILLARY PRESSURE BY DIRECT VISUALIZATION OF A CENTRIFUGE EXPERIMENT Osamah A. Al-Omair and Richard L. Christiansen Petroleum Engineering Department, Colorado School of Mines ABSTRACT A
More informationMODELING ASPHALTENE DEPOSITION RELATED DAMAGES THROUGH CORE FLOODING TESTS
SCA2010-33 1/6 MODELING ASPHALTENE DEPOSITION RELATED DAMAGES THROUGH CORE FLOODING TESTS Ali Rezaian ; Morteza Haghighat Sefat; Mohammad Alipanah; Amin Kordestany, Mohammad Yousefi Khoshdaregi and Erfan
More informationSimulating Fluid-Fluid Interfacial Area
Simulating Fluid-Fluid Interfacial Area revealed by a pore-network model V. Joekar-Niasar S. M. Hassanizadeh Utrecht University, The Netherlands July 22, 2009 Outline 1 What s a Porous medium 2 Intro to
More informationJuan E. Santos a,b,c, Gabriela B. Savioli a and Robiel Martínez Corredor c a
Juan E. Santos a,b,c, Gabriela B. Savioli a and Robiel Martínez Corredor c a Universidad de Buenos Aires, Fac. Ing., IGPUBA, ARGENTINA b Department of Mathematics, Purdue University, USA c Universidad
More informationGrowth activity during fingering in a porous Hele-Shaw cell
PHYSICAL REVIEW E 70, 026301 (2004) Growth activity during fingering in a porous Hele-Shaw cell Grunde Løvoll, 1,2 Yves Méheust, 3,2,1 Renaud Toussaint, 1,3 Jean Schmittbuhl, 2 and Knut Jørgen Måløy 1
More informationNumerical Simulation of Viscous Fingering Phenomenon in Immiscible Displacement of Two Fluids in Porous Media Using Lattice Boltzmann Method
nd Micro and Nano Flows Conference West London, UK, 1- September 009 Numerical Simulation of Viscous Fingering Phenomenon in Immiscible Displacement of Two Fluids in Porous Media Using Lattice Boltzmann
More informationGeneralised Separable Solution of Double Phase Flow through Homogeneous Porous Medium in Vertical Downward Direction Due to Difference in Viscosity
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 932-9466 Vol. 8, Issue (June 203), pp. 305-37 Applications and Applied Mathematics: An International Journal (AAM) Generalised Separable Solution
More informationPore Scale Analysis of Oil Shale/Sands Pyrolysis
Pore Scale Analysis of Oil Shale/Sands Pyrolysis C.L. Lin, J.D. Miller, and C.H. Hsieh Department of Metallurgical Engineering College of Mines and Earth Sciences University of Utah Outlines Introduction
More informationBOILING IN A VERTICAL FRACTURE
PROCEEDINGS, Twenty-Third Workshop on Geothermal Reservoir Engineering Stanford University, Stanford. California. January 26-28. 1998 SGP-TR-158 BOILING IN A VERTICAL FRACTURE Robert J. DuTeaux Stanford
More informationA Model for Non-Newtonian Flow in Porous Media at Different Flow Regimes
A Model for Non-Newtonian Flow in Porous Media at Different Flow Regimes Quick introduction to polymer flooding Outline of talk Polymer behaviour in bulk versus porous medium Mathematical modeling of polymer
More informationMulti-rate mass transfer modeling of two-phase flow in highly heterogeneous fractured and porous media
Multi-rate mass transfer modeling of two-phase flow in highly heterogeneous fractured and porous media Jan Tecklenburg a,, Insa Neuweiler a, Jesus Carrera b, Marco Dentz b a Institute of Fluid Mechanics
More informationThe effect of heterogeneity on unsteady-state displacements
The effect of heterogeneity on unsteady-state displacements Abstract Darryl Fenwick, Nicole Doerler, and Roland Lenormand, Institut Français du Pétrole In this paper, we discuss the effect of heterogeneity
More informationCompetition ofgravity, capillary and viscous forces during drainage in a two-dimensional porous medium, a pore scale study
Energy 30 (2005) 861 872 www.elsevier.com/locate/energy Competition ofgravity, capillary and viscous forces during drainage in a two-dimensional porous medium, a pore scale study Grunde Løvoll a,b,, Yves
More informationRelative Permeability Measurement and Numerical Modeling of Two-Phase Flow Through Variable Aperture Fracture in Granite Under Confining Pressure
GRC Transactions, Vol. 36, 2012 Relative Permeability Measurement and Numerical Modeling of Two-Phase Flow Through Variable Aperture Fracture in Granite Under Confining Pressure Noriaki Watanabe, Keisuke
More informationCENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer
CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer You are assigned to design a fallingcylinder viscometer to measure the viscosity of Newtonian liquids. A schematic
More informationWETTABILITY CHANGE TO GAS-WETNESS IN POROUS MEDIA
WETTABILITY CHANGE TO GAS-WETNESS IN POROUS MEDIA Kewen Li and Abbas Firoozabadi Reservoir Engineering Research Institute (RERI) Abstract In the petroleum literature, gas is assumed to be the non-wetting
More informationInternational Journal of Multiphase Flow
International Journal of Multiphase Flow 52 (2013) 22 34 Contents lists available at SciVerse ScienceDirect International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow
More informationModern Chemical Enhanced Oil Recovery
Modern Chemical Enhanced Oil Recovery Theory and Practice James J. Sheng, Ph. D. AMSTERDAM BOSTON «HEIDELBERG LONDON ELSEVIER NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Gulf Professional
More informationTwo-phase Flow Calculations in Pore Unit-cells Implementing Mixed FEM/Lattice-Boltzmann Simulators
Two-phase Flow Calculations in Pore Unit-cells Implementing Mixed FEM/Lattice-Boltzmann Simulators E. D. Skouras,*, A. N. Kalarakis, M. S. Valavanides 3, and V. N. Burganos Foundation for Research and
More informationEvaluation of Petrophysical Properties of an Oil Field and their effects on production after gas injection
Evaluation of Petrophysical Properties of an Oil Field and their effects on production after gas injection Abdolla Esmaeili, National Iranian South Oil Company (NISOC), Iran E- mail: esmaily_ab@yahoo.com
More informationscaling parameters of laboratory modelling of
Influence of low and high IFT fluid systems on scaling parameters of laboratory modelling of CO 2 injection into saline aquifers The 6 th Trondheim Conference on CO 2 Capture, Transport, and Storage 14-16
More informationInflow Performance 1
1 Contents 1. Introduction 2. The Radial Flow Equation 3. Straight Line Inflow Performance Relationship 4. Vogel Inflow Performance Relationship 5. Other Inflow Performance Relationship 6. Establishing
More informationSTEADY-STATE, SIMULTANEOUS TWO-PHASE FLOW IN POROUS MEDIA
STEADY-STATE, SIMULTANEOUS TWO-PHASE FLOW IN POROUS MEDIA Ken Tore Tallakstad Thesis submitted for the degree of Master of Science Department of Physics University of Oslo July 2007 2 Acknowledgements
More informationSolution for counter-current imbibition of 1D immiscible twophase flow in tight oil reservoir
J Petrol Explor Prod Technol (27) 7:727 733 DOI.7/s322-6-273-3 ORIGINAL PAPER - PRODUCTION ENGINEERING Solution for counter-current imbibition of D immiscible twophase flow in tight oil reservoir Shuai
More information2. Modeling of shrinkage during first drying period
2. Modeling of shrinkage during first drying period In this chapter we propose and develop a mathematical model of to describe nonuniform shrinkage of porous medium during drying starting with several
More informationINJECTION, CONDUCTION AND PRODUCTION
Chapter III Injection, Conduction and Production Chapter III From a physical point of view strictly steady-state conditions of heterogeneous-fluid flow in oil-producing systems are virtually never encountered.
More informationModeling of 1D Anomalous Diffusion In Fractured Nanoporous Media
LowPerm2015 Colorado School of Mines Low Permeability Media and Nanoporous Materials from Characterisation to Modelling: Can We Do It Better? IFPEN / Rueil-Malmaison - 9-11 June 2015 CSM Modeling of 1D
More informationMechanical Engineering. Postal Correspondence Course HEAT TRANSFER. GATE, IES & PSUs
Heat Transfer-ME GATE, IES, PSU 1 SAMPLE STUDY MATERIAL Mechanical Engineering ME Postal Correspondence Course HEAT TRANSFER GATE, IES & PSUs Heat Transfer-ME GATE, IES, PSU 2 C O N T E N T 1. INTRODUCTION
More informationFOAM DRAINAGE part 3
FOAM DRAINAGE part 3 gas effect : coupling coarsening and drainage () C 2 F 6 :almost «insoluble», so no coarsening N 2 : much more soluble, significantly faster coarsening Free-drainage, liquid fraction
More informationFaculty of Science and Technology MASTER S THESIS. Writer: Thomas Melvin Danielsen
Faculty of Science and Technology MASTER S THESIS Study program/ Specialization: Petroleum Engineering/Reservoir Technology Spring semester, 24 Open Writer: Thomas Melvin Danielsen Faculty supervisor:
More informationTHEORETICAL AND EXPERIMENTAL STUDY OF THE POSITIVE IMBIBITION CAPILLARY PRESSURE CURVES OBTAINED FROM CENTRIFUGE DATA.
THEORETICAL AND EXPERIMENTAL STUDY OF THE POSITIVE IMBIBITION CAPILLARY PRESSURE CURVES OBTAINED FROM CENTRIFUGE DATA. Abstract Trond BolHs and Ole Torsaeter, The Norwegian Institute of Technology This
More informationInfluence of the Flow Direction on the Mass Transport of Vapors Through Membranes Consisting of Several Layers
Influence of the Flow Direction on the Mass Transport of Vapors Through Membranes Consisting of Several Layers Thomas Loimer 1,a and Petr Uchytil 2,b 1 Institute of Fluid Mechanics and Heat Transfer, Vienna
More informationNUMERICAL INVESTIGATION OF THE DEPENDENCE OF RESIDUAL OIL SATURATION ON GEOMETRY, WETTABILITY, INITIAL OIL SATURATION AND POROSITY
SCA2014-042 1/6 NUMERICAL INVESTIGATION OF THE DEPENDENCE OF RESIDUAL OIL SATURATION ON GEOMETRY, WETTABILITY, INITIAL OIL SATURATION AND POROSITY Xiaobo Nie, Y. Mu, R. Sungkorn, V. Gundepalli and J. Toelke
More informationPHYSICAL REALITIES FOR IN DEPTH PROFILE MODIFICATION. RANDY SERIGHT, New Mexico Tech
PHYSICAL REALITIES FOR IN DEPTH PROFILE MODIFICATION RANDY SERIGHT, New Mexico Tech 1. Gel treatments (of any kind) are not polymer floods. 2. Crossflow makes gel placement challenging. 3. Adsorbed polymers,
More informationSimulation of T-junction using LBM and VOF ENERGY 224 Final Project Yifan Wang,
Simulation of T-junction using LBM and VOF ENERGY 224 Final Project Yifan Wang, yfwang09@stanford.edu 1. Problem setting In this project, we present a benchmark simulation for segmented flows, which contain
More informationAnalysis of a drainage efficiency in stratified porous media
Analysis of a drainage efficiency in stratified porous media CHAKIB SELADJI Département de Génie Mécanique Université Abou Bekr BELKAID BP 119 Chétouane Tlemcen 13000 ALGERIA seladji@yahoo.fr Abstract:
More informationDiffusion and Adsorption in porous media. Ali Ahmadpour Chemical Eng. Dept. Ferdowsi University of Mashhad
Diffusion and Adsorption in porous media Ali Ahmadpour Chemical Eng. Dept. Ferdowsi University of Mashhad Contents Introduction Devices used to Measure Diffusion in Porous Solids Modes of transport in
More informationCHAPTER V. Brownian motion. V.1 Langevin dynamics
CHAPTER V Brownian motion In this chapter, we study the very general paradigm provided by Brownian motion. Originally, this motion is that a heavy particle, called Brownian particle, immersed in a fluid
More informationAN EXPERIMENTAL STUDY OF THE RELATIONSHIP BETWEEN ROCK SURFACE PROPERTIES, WETTABILITY AND OIL PRODUCTION CHARACTERISTICS
AN EXPERIMENTAL STUDY OF THE RELATIONSHIP BETWEEN ROCK SURFACE PROPERTIES, WETTABILITY AND OIL PRODUCTION CHARACTERISTICS by Ole Torsæter, Norwegian University of Science and Technology, Trondheim Reidar
More informationOn the displacement of two immiscible Stokes fluids in a 3D Hele-Shaw cell
On the displacement of two immiscible Stokes fluids in a 3D Hele-Shaw cell Gelu Paşa Abstract. In this paper we study the linear stability of the displacement of two incompressible Stokes fluids in a 3D
More informationFundamentals of Basin and Petroleum Systems Modeling
Thomas Hantschel Armin I. Kauerauf Fundamentals of Basin and Petroleum Systems Modeling 4ü Springer Contents Introduction to Basin Modeling 1 1.1 History 1 1.2 Geologien! Processes 3 1.3 Structure of a
More informationPhenomenological Modeling of Critical Condensate Saturation and Relative Permeabilities in Gas/ Condensate Systems
Phenomenological Modeling of Critical Condensate Saturation and Relative Permeabilities in Gas/ Condensate Systems Kewen Li, SPE, and Abbas Firoozabadi, SPE, Reservoir Engineering Research Inst. Summary
More informationFour Verification Cases for PORODRY
Four Verification Cases for PORODRY We designed four different verification cases to validate different aspects of our numerical solution and its code implementation, and these are summarized in Table
More informationCritical capillary number: Desaturation studied with fast X-ray computed microtomography
GEOPHYSICAL RESEARCH LETTERS, VOL. 41, 55 60, doi:10.1002/2013gl058075, 2014 Critical capillary number: Desaturation studied with fast X-ray computed microtomography Ryan T. Armstrong, 1 Apostolos Georgiadis,
More informationUNDERSTANDING IMBIBITION DATA IN COMPLEX CARBONATE ROCK TYPES
SCA2014-059 1/6 UNDERSTANDING IMBIBITION DATA IN COMPLEX CARBONATE ROCK TYPES Moustafa Dernaika 1, Zubair Kalam 2, Svein Skjaeveland 3 1 Ingrain Inc.-Abu Dhabi, 2 ADCO, 3 University of Stavanger This paper
More informationDRAINAGE AND IMBIBITION CAPILLARY PRESSURE CURVES OF CARBONATE RESERVOIR ROCKS BY DIGITAL ROCK PHYSICS
SCA2012-56 1/6 DRAINAGE AND IMBIBITION CAPILLARY PRESSURE CURVES OF CARBONATE RESERVOIR ROCKS BY DIGITAL ROCK PHYSICS Y. Mu 1, Q. Fang 1, C. Baldwin 1, J. Töelke 1, A. Grader 1, M. Dernaika 2, and Z. Kalam
More informationUNIVERSITY OF CALGARY. Two-Phase Flow at the Pore-Scale Using the Volume of Fluid Method. Carla Jordana Sena Santiago A THESIS
UNIVERSITY OF CALGARY Two-Phase Flow at the Pore-Scale Using the Volume of Fluid Method by Carla Jordana Sena Santiago A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE
More informationCapillarity. ESS5855 Lecture Fall 2010
Capillarity ESS5855 Lecture Fall 2010 Capillarity: the tendency of a liquid in a narrow tube or pore to rise or fall as a result of surface tension (The concise Oxford Dictionary) Surface tension: the
More informationA PSEUDO FUNCTION APPROACH IN RESERVOIR SIMULATION
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING Volume 2, Supp, Pages 58 67 c 2005 Institute for Scientific Computing and Information A PSEUDO FUNCTION APPROACH IN RESERVOIR SIMULATION ZHANGXIN
More informationI. Borsi. EMS SCHOOL ON INDUSTRIAL MATHEMATICS Bedlewo, October 11 18, 2010
: an : an (Joint work with A. Fasano) Dipartimento di Matematica U. Dini, Università di Firenze (Italy) borsi@math.unifi.it http://web.math.unifi.it/users/borsi porous EMS SCHOOL ON INDUSTRIAL MATHEMATICS
More informationAmélie Neuville. Advanced Materials and Complex Systems group (AMCS) University of Oslo Norway
Amélie Neuville Advanced Materials and Complex Systems group (AMCS) University of Oslo Norway The Research Council of Norway Postdoc within a PETROMAKS project Mobility grant for young researchers YGGDRASIL,
More informationPrinciples of Convective Heat Transfer
Massoud Kaviany Principles of Convective Heat Transfer Second Edition With 378 Figures Springer Contents Series Preface Preface to the Second Edition Preface to the First Edition Acknowledgments vii ix
More information: Dr. P. H. Bhathawala
Title :SIMILARITY ANALYSIS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS OF FLUID FLOW OF POROUS MEDIA Research Student : KANAN. D. VASHI Registration No. : 2281 Registration Date : 6-01-2010 For The Degree
More informationGame Physics. Game and Media Technology Master Program - Utrecht University. Dr. Nicolas Pronost
Game and Media Technology Master Program - Utrecht University Dr. Nicolas Pronost Soft body physics Soft bodies In reality, objects are not purely rigid for some it is a good approximation but if you hit
More informationMass Transfer and Interfacial Phenomena in Oil Recovery
IMPERIAL COLLEGE OF SCIENCE AND TECHNOLOGY Petroleum Engineering Section, Department of Mineral Resources Engineering. Mass Transfer and Interfacial Phenomena in Oil Recovery by ERIC GORDON MAHERS A thesis
More informationTHE EFFECT OF WATER SATURATION ON GAS SLIP FACTOR BY PORE SCALE NETWORK MODELING
SCA00-53 1/6 THE EFFECT OF WATER SATURATION ON GAS SLIP FACTOR BY PORE SCALE NETWORK MODELING Liu Qingjie, Liu Baohua, Li Xianbing, Yan Shouguo Research Institute of Petroleum Exploration and Development,
More informationPUBLICATIONS. Water Resources Research. Challenges in modeling unstable two-phase flow experiments in porous micromodels
PUBLICATIONS RESEARCH ARTICLE Key Points: We validate our numerical approach by comparison with drainage experiments We demonstrate the impact of three main sources of error We compare the results in a
More informationPhysics 172H Modern Mechanics
Physics 172H Modern Mechanics Instructor: Dr. Mark Haugan Office: PHYS 282 haugan@purdue.edu TAs: Alex Kryzwda John Lorenz akryzwda@purdue.edu jdlorenz@purdue.edu Lecture 22: Matter & Interactions, Ch.
More informationThe Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase Flow in Geothermal Reservoirs
PROCEEDINGS 43rd Workshop on Geothermal Reservoir Engineering Stanford University Stanford California February 12-14 2018 SGP-TR-213 The Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase
More informationMicrofluidics 2 Surface tension, contact angle, capillary flow
MT-0.6081 Microfluidics and BioMEMS Microfluidics 2 Surface tension, contact angle, capillary flow 28.1.2017 Ville Jokinen Surface tension & Surface energy Work required to create new surface = surface
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 11 Dec 2002
arxiv:cond-mat/0212257v1 [cond-mat.stat-mech] 11 Dec 2002 International Journal of Modern Physics B c World Scientific Publishing Company VISCOUS FINGERING IN MISCIBLE, IMMISCIBLE AND REACTIVE FLUIDS PATRICK
More informationCHARACTERIZATION OF HETEROGENEITIES AT THE CORE-SCALE USING THE EQUIVALENT STRATIFIED POROUS MEDIUM APPROACH
SCA006-49 /6 CHARACTERIZATION OF HETEROGENEITIES AT THE CORE-SCALE USING THE EQUIVALENT STRATIFIED POROUS MEDIUM APPROACH Mostafa FOURAR LEMTA Ecole des Mines de Nancy, Parc de Saurupt, 54 04 Nancy, France
More informationTHE PHYSICS OF FOAM. Boulder School for Condensed Matter and Materials Physics. July 1-26, 2002: Physics of Soft Condensed Matter. 1.
THE PHYSICS OF FOAM Boulder School for Condensed Matter and Materials Physics July 1-26, 2002: Physics of Soft Condensed Matter 1. Introduction Formation Microscopics 2. Structure Experiment Simulation
More informationPore-Scale Analysis of Dynamics of Two-Phase Flow. in Porous Media
Pore-Scale Analysis of Dynamics of Two-Phase Flow Multi-Process Pore-scale Modelling in Porous Media Vahid J. Niasar Collaborators: S. Majid Hassanizadeh (Utrecht University) Nikos Karadimitriou (University
More informationPressure Drop Separation during Aqueous Polymer Flow in Porous Media
Pressure Drop Separation during Aqueous Polymer Flow in Porous Media D.C. Raharja 1*, R.E. Hincapie 1, M. Be 1, C.L. Gaol 1, L. Ganzer 1 1 Department of Reservoir Engineering, Clausthal University of Technology
More informationIHTC DRAFT MEASUREMENT OF LIQUID FILM THICKNESS IN MICRO TUBE ANNULAR FLOW
DRAFT Proceedings of the 14 th International Heat Transfer Conference IHTC14 August 8-13, 2010, Washington D.C., USA IHTC14-23176 MEASUREMENT OF LIQUID FILM THICKNESS IN MICRO TUBE ANNULAR FLOW Hiroshi
More informationCYDAR User Manual Two-phase flow module with chemical EOR
CYDAR User Manual Two-phase flow module with chemical EOR 1 CYDAR - Two-phase flow module with chemical EOR CYDAR USER MANUAL TWO-PHASE FLOW MODULE WITH CHEMICAL EOR... 1 CYDAR - TWO-PHASE FLOW MODULE
More informationQuarterly Report for January March 1998 Stanford Geothermal Program DE-FG07-95ID13370
Quarterly Report for January 1998 - March 1998 Stanford Geothermal Program DE-FG7-95ID1337 Table of Contents 1. MEASUREMENTS OF STEAM-WATER RELATIVE PERMEABILITY 1 1.1 SUMMARY 1 1.2 INTRODUCTION 1 1.3
More informationThe Pennsylvania State University. The Graduate School. Department of Energy and Geo-Environmental Engineering THE INFLUENCE OF A FRACTURE TIP ON
The Pennsylvania State University The Graduate School Department of Energy and Geo-Environmental Engineering THE INFLUENCE OF A FRACTURE TIP ON TWO-PHASE FLOW DISPLACEMENT PROCESSES A Thesis in Petroleum
More informationSCA : A STRUCTURAL MODEL TO PREDICT TRANSPORT PROPERTIES OF GRANULAR POROUS MEDIA Guy Chauveteau, IFP, Yuchun Kuang IFP and Marc Fleury, IFP
SCA2003-53: A STRUCTURAL MODEL TO PREDICT TRANSPORT PROPERTIES OF GRANULAR POROUS MEDIA Guy Chauveteau, IFP, Yuchun Kuang IFP and Marc Fleury, IFP This paper was prepared for presentation at the International
More informationSoft Bodies. Good approximation for hard ones. approximation breaks when objects break, or deform. Generalization: soft (deformable) bodies
Soft-Body Physics Soft Bodies Realistic objects are not purely rigid. Good approximation for hard ones. approximation breaks when objects break, or deform. Generalization: soft (deformable) bodies Deformed
More informationOptimization of DPF Structures with a 3D-Unit Cell Model
Optimization of DPF Structures with a 3D-Unit Cell Model Wieland Beckert, Marcel Dannowski, Lisabeth Wagner, Jörg Adler, Lars Mammitzsch Fraunhofer IKTS, Dresden, Germany *Corresponding author: FhG IKTS,
More informationPhysical Models for Shale Gas Reservoir Considering Dissolved Gas in Kerogens
Physical Models for Shale Gas Reservoir Considering Dissolved Gas in Kerogens Cai Wang, Gang Lei, Weirong Li, Lei Wang, Zunyi Xia, and Huijie Wang, Peking University Abstract To figure out the complexity
More informationDNAPL migration through interbedded clay-sand sequences
Groundwater Quality: Natural and Enhanced Restoration of Groundwater Pollution (Proceedings ofthe Groundwater Quality 2001 Conference held al Sheffield. UK. June 2001). IAHS Publ. no. 275. 2002. 455 DNAPL
More informationTHE EFFECTS OF DISPLACEMENT RATE AND WETTABILITY ON IMBIBITION RELATIVE PERMEABILITIES
SCA2005-39 1/12 THE EFFECTS OF DISPLACEMENT RATE AND WETTABILITY ON IMBIBITION RELATIVE PERMEABILITIES V.H. Nguyen 1, A.P. Sheppard 2, M.A. Knackstedt 2 and W.V. Pinczewski 1 1 School of Petroleum Engineering,
More informationSemi-Annual Report September 1, March 1,1997
Surfactant - Polymer Interaction for Improved Oil Recovery Semi-Annual Report September 1,1996 - March 1,1997 Work Performed Under Contract No.: DE-FG22-96PC96223 For U.S. Department of Energy Office of
More information