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Analytical Solution Incorporating History-Dependent Processes for Quick Assessment of Capillary Trapping During CO2 Geological Storage

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Abstract

Carbon storage in saline formations is considered as a promising option to ensure the necessary decrease of CO2 anthropogenic emissions. Its industrial development in those formations is above all conditioned by its safety demonstration. Assessing the evolution of trapped and mobile CO2 across time is essential in the perspective of reducing leakage risks. In this work, we focus on residual trapping phenomenon occurring during the wetting of the injected CO2 plume. History dependent effects are of first importance when dealing with capillary trapping. We then apply the classical fractional flow theory (Buckley–Leverett type model) and include trapping and hysteresis models; we derive an analytical solution for the temporal evolution of saturation profile and of CO2 trapped quantity when injecting water after the gas injection (“artificial imbibition”). The comparison to numerical simulations for different configurations shows satisfactory match and justifies, in the case of industrial CO2 storage, the assumptions of incompressible flow with no consideration of capillary pressure. The obtained analytical solution allows the quick assessment of both the quantity and the location of mobile gas left during imbibition.

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Abbreviations

q :

Volumetric flow rate, m3 s−1

A :

Area, m2

S :

Saturation

f :

Volumetric fractional flow

h :

Aquifer height, m

T :

Injection time, s

V :

Volume, m3

fr :

Mass fraction

k :

Permeability

Q :

Injection volumetric flow, m3 s−1

μ :

Viscosity, Pa s

λ :

Mobility

\({\varphi}\) :

Porosity

r :

Radius, m

\({\xi}\) :

Dimensionless radius

ζ :

Similarity variable

t :

Time, s

τ :

Dimensionless time

P :

Pressure, Pa

ρ :

Density, kg m−3

g:

Gas phase

l:

Liquid phase

Δ:

Flow reversal

r:

Residual

max:

Maximum

rel:

Relative

+:

Upstream

−:

Downstream

shocki:

Shock no.i

*:

Chosen (given)

collision:

Collision

freeg:

Mobile gas

c:

Capillary

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  1. Risks Division, BRGM, 3 Avenue C. Guillemin, 45060, Orleans Cedex 2, France

    Jean-Charles Manceau & Jérémy Rohmer

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  1. Jean-Charles Manceau
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  2. Jérémy Rohmer
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Correspondence to Jean-Charles Manceau.

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Manceau, JC., Rohmer, J. Analytical Solution Incorporating History-Dependent Processes for Quick Assessment of Capillary Trapping During CO2 Geological Storage. Transp Porous Med 90, 721–740 (2011). https://doi.org/10.1007/s11242-011-9812-z

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