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S. OLADYSHKIN, M. PANFILOVS. OLADYSHKIN, M. PANFILOV

Laboratoire d'Énergétique et de Mécanique Théorique et Appliquée Ecole Nationale Supérieure de GéologieInstitut National Polytechnique de Lorraine

STREAMLINE SPLITTING THE STREAMLINE SPLITTING THE THERMO- AND HYDRODYNAMICS THERMO- AND HYDRODYNAMICS

IN COMPOSITIONAL FLOW THROUGH POROUS IN COMPOSITIONAL FLOW THROUGH POROUS MEDIAMEDIA

APPLICATION TO HAPPLICATION TO H22-WATER IN RADIOACTIVE WASTE -WATER IN RADIOACTIVE WASTE DEPOSITSDEPOSITS

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SommaireP

r e s

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t a t

I o n

Flow Model

Limit compositional model

Streamline HT-splitting

Introduction

Validation to the limit thermodynamic modelValidation to the limit thermodynamic model

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IntroductionIntroductionPhysical descriptionPhysical description

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Hydrogen generation in a radioactive waste deposit

Gas generation:

Waste storage

Storage pressure growth : - Initial : 100 bar - Increased by H2 : 300 bar

Monitoring problem :H2 transport through porous media

accompanied with radionuclides

H2 + CO2 + N2 + O2 + …

Corrosion in storage tank

underground: 900 - 1100m

Water

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Fluid structure

Phases :

Components :

Gas Liquid

H2CO2N2O2H20…

Gas

Liquid

2 phases

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Similar phenomena in an underground H2 storage

Well Well

GAS and LIQUID

H20 + H2 + CO2 + CH4 + …

Hydrogen storage

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Initial stateL

L + G

G

Phase behaviour

Critical point

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Flow ModelFlow Model

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2 phases (gas & liquid)N chemical components

Compositional model

Mass balance for each chemical component k :

Momentum balance for each phase (the Darcy law)

Phase equilibrium :

Phase state :

( = the chemical potential)

or

Closure relationships:or

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Limit contrast Limit contrast compositional modelcompositional model

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Canonical dimensionless form of the compositional

modelgas flow

liquid flow

transport of basicchemical components

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Mathematical type of the system

Parabolic equation

Hyperbolic equation

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gas flow

liquid flow

transport of basicchemical components

Characteristic parameters of a gas-liquid

system

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Perturbation parameter:

Parameter of relative phase mobility:

Perturbation propagation timeReservoir depletion time

Characteristic parameters of the system

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Limit behaviour

Semi-stationarity : p and C(k) are steady-state, while s is non stationary

gas flow

liquid flow

transport of basicchemical components

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Streamline HT-splittingStreamline HT-splitting

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Integration of the transport subsystem

gas flow

liquid flow

transport of basicchemical components

This subsystem can be integrated along streamlines :

Asymptotic contrast compositional model :

A differential thermodynamic system

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Hydrodynamic subsystem (limit hydrodynamic model):

Thermodynamic subsystem (limit thermodynamic model):

HT-splitting

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variation of the total composition in an open system

The thermodynamic independent system is monovariant: all the thermodynamic variables depend on

pressure only The new thermodynamic model is valid along streamlines

Split Thermodynamic Model

Properties

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Due to the monovariance, the thermodynalmic differential equations may be simplified to a “Delta-law”:

Thermodynamic “Delta-law”

“Delta-law”

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Individual gas volume

Individual condensate volume

Interpretation of the delta-law

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gas flow

liquid flow

Split Hydrodynamic Model

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Validation to the limit Validation to the limit thermodynamic modelthermodynamic model

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These functions have been calculated using Eclipse simulation data for a

dynamic system

F1 F2

Validation of the Delta-law

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Phase plot

Fluid compositionCH4

H2

C10H22

Initial conditions:P0 = 315 barT = 363 K

T

P

Flow simulation: Fluid properties

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Well

Flow simulation: Flow problem

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Validation of the Delta-law

F1

F2

These functions have been calculated using the Eclipse simulation data

“Delta-law”

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Liquid mole fractions

Gas mole fractions

Validation of the total limit thermodynamic model

Composition variation in an open thermodynamic system

Compositional Model (Eclipse) - points; Limit thermodynamic model - solid Compositional Model (Eclipse) - points; Limit thermodynamic model - solid curvescurves

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FinitaFinita