5 What's the point

8/11/2019 5 What's the point

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Vermelding onderdeel organisatie

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Whats the point of fractionalflow modeling?

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All models are false but

some models are

us ul

.

- George E P Box


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Whats usefulin fractional-flow

modeling? Exact solutions for benchmarking accuracy and

numerical artifacts of simulators

Identify key parameters in complex models

Identify key aspects of complex processes

Viscous instability in sequence of banks

Most important conditions for conductingexperiments

Can lead to improved designs, to be tested and

refined with simulation Solutions that can be extended to resolution not

feasible with finite-difference simulation

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Identify key elements of process

In this example, surfactant preflush precedes foaminjection; only one fractional-flow curve applies

Authors claimed model with 11 foam parameters essential

Fitting single coreflood with uniform mobility in foam bankis easy with fractional-flow method; only one foamparameter is needed Sw in foam bank

Identify key parameters in complex models


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Foam for Miscible Flood: Solution

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Foam for Miscible Flood: Solution

High-mobility gas banks ahead offoam likely to finger through oil in2D or 3D; actual velocity of oil banklikely to be slower velocity of foam bank


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Example of Insights: Gas Injection inSAG Foam Process

Inject gas (fw = 0); initial condition Sw = 1

Surfactant Preflush has placed AGENT (surfactant) inregion of interest; only one fractional-flow curve

Most important conditions for conducting experiments

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Example of Insights: Gas Injection inSAG Foam Process

For foam model in this study, fractional-flowanalysis predicts shock to foam collapse no mobility control anywhere

Benchmark accuracy of simulators

Yet 2D simulations(incorrectly) showcontrol of gravityoverride, even asgrid refined

Tip-off wasinjectivity


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Example of Insights: Gas Injection in

SAG Foam Process Fractional-flow analysis predicts extremely high

mobility near well, where foam dries out and collapses

Therefore, get good injectivity and low mobility awayfrom well: perfect for overcoming gravity override

Verify with simulation

Insights improved designs

Example of Insights: UnderestimatedFoam Injectivity in Simulators In gas injection in SAG process, foam dries out and

collapses near injection well; this greatly increasesinjectivity

Simulators do not resolve near-well region well

Fractional-flow simulation allows resolution to arbitrary

accuracy (e.g., cm) Show huge errors in simulator injectivity

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Extensions to Two-Phase Fractional-

Flow Methods Consider local variation in Sw within shock

Three phases, many components (gets complicated!)

Non-uniform initial conditions, changing injection

Fingering (Koval theory)

Gravity (capillary-gravity equilibrium)

Layers differing in k, in capillary equilibrium

Compressible phases; phase changes (steam flooding)

Phase changes (steam flooding)

Non-uniform porous media, non-Newtonian fluids

Gravity segregation at steady state

Dynamic, non-s.s. processes Complex geochemical reactions with rock

Non-monotonic fw(Sw) functions and multiple steady states;capillary hysteresis

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Extensions: Local variations withinshock Shock is not really a dis-

continuity, but a sharp,continuous transition:

traveling wave.

Traveling wave isgoverned by balance be-tween convective forcessharpening the front anddispersive forces spreading it out

Entropy condition (rule that shock cant cut throughfw(Sw) curve) derives from analysis of traveling wave

Traveling wave sometimes changes behavior oflarge-scale displacement


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Extension: Three-phase flow

Muchmore complicatedthat two-phase fractional-flow theory; see Lake, etal. Enhanced OilRecovery, 1989 for intro.

Mathematicians are stillworking out basic proofsof solution validity

One key insight: Inmulticontact miscibility,

key is to have eithercrude oil or solventbeyond extended tie lineat plait point.

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Extension: Non-Newtonian two-phase flow

Characteristics are curved, but Sw still constant oneach characteristic

Construction of shocks complicated, but behind shocksone can solve forboth changing

saturation and non-Newtonian

rheologysimultaneously

Used to solve forinjectivity of non-Newtonian foam


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Extensions: Gravity segregation at

steady state A different two-variable problem: solve for Sw(x,z) at

steady state instead of Sw(x,t) in 1D

Need change of variable from z to stream function;lose some information about vertical position of fronts

Can solve for distance to complete segregation for co-injected gas and liquid at steady state

Insights led to focus on waysto improve injectivity of foam

Method can be extended to

nonuniform injection: e.g.,injection of gas above water

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Extensions: Dynamic, non local-steady-state processes; multiplesteady state Assume process is at local steady-state everywhere

but where conditions change rapidly in shocks

Analysis of traveling wave at shock must account fordynamics, non-steady-state processes within traveling

wave Can describe geochemical reactions, mass transfer

processes, foam dynamics


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Extensions to Two-Phase Fractional-

Flow Methods Consider local variation in Sw within shock

Three phases, many components (gets complicated!)

Non-uniform initial conditions, changing injection

Fingering (Koval theory)

Gravity (capillary-gravity equilibrium)

Layers differing in k, in capillary equilibrium

Compressible phases; phase changes (steam flooding)

Phase changes (steam flooding)

Non-uniform porous media, non-Newtonian fluids

Gravity segregation at steady state

Dynamic, non-s.s. processes Complex geochemical reactions with rock

Non-monotonic fw(Sw) functions and multiple steady states;capillary hysteresis

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5 What's the point