Transport in Porous Media

, Volume 116, Issue 2, pp 727–752 | Cite as

Numerical Simulation of Hydraulic Fracturing Water Effects on Shale Gas Permeability Alteration

  • Vena. F. EvelineEmail author
  • I. Yucel Akkutlu
  • George J. Moridis


Hydraulic fracturing has been recognized as the necessary well completion technique to achieve economic production from shale gas formation. However, following the fracturing, fluid–wall interactions can form a damaged zone nearby the fracture characterized by strong capillarity and osmosis effects. Here, we present a new reservoir multi-phase flow model which includes these mechanisms to predict formation damage in the aftermath of the fracturing during shut-in and production periods. In the model, the shale matrix is treated as a multi-scale porosity medium including interconnected organic, inorganic slit-shaped, and clay porosity fields. Prior to the fracturing, the matrix holds gas in the organic and the inorganic slit-shaped pores, water with dissolved salt in the inorganic slit-shaped pores and the clay pores. During and after fracturing, imbibition causes water invasion into the matrix, and then, the injected water–clay interaction may lead to clay-swelling pressure development due to osmosis. The swelling pressure gives additional stress to slit-shaped pores and cause permeability reduction in the inorganic matrix. We develop a simulator describing a system of three pores, two phases (aqueous and gaseous phases), and three components (\(\hbox {H}_{2}\hbox {O}, \hbox {CH}_{4}\), and salt), including osmosis and clay-swelling effect on the permeability. The simulation of aqueous-phase transport through clay shows that high swelling pressure can occur in clays as function of salt type, salt concentration difference, and clay-membrane efficiency. The new model is used to demonstrate the damage zone characteristics. The simulation of two-phase flow through the shale formation shows that, although fracturing is a rapid process, fluid–wall interactions continue to occur after the fracturing due to imbibition mechanism, which allows water to penetrate into the inorganic pore network and displace the gas in-place near the fracture. This water invasion leads to osmosis effect in the formation, which cause clay swelling and the subsequent permeability reduction. Continuing shale–water interactions during the production period can expand the damage zone further.


Numerical simulation Osmosis Formation damage Clay swelling Hydraulic fracturing 

List of Symbols


Surface are between element n and m (\(\hbox {m}^{2}\))

\(C_\mu \)

Sorbed-gas concentration in kerogen grain volume (\(\hbox {mol}/\hbox {m}^{3}\))

\(D_\mathrm{o,A}^{\mathrm{H}_2 \mathrm{O}} ; D_\mathrm{o,A}^{\mathrm{CH}_4 } ; D_\mathrm{o,A}^\mathrm{Salt} \)

Free-diffusion coefficient of \(\hbox {H}_{2}\hbox {O}\), \(\hbox {CH}_{4}\) and salt in the aqueous phase (\(\hbox {m}^{2}/\hbox {s}\))

\(\mathbf{F}_\mathrm{A}^{\mathrm{H}_2 \mathrm{O}} ; \mathbf{F}_\mathrm{A}^{\mathrm{Salt}} \)

Total mass flux of \(\hbox {H}_{2}\hbox {O}\) and salt in aqueous-phase flow (\(\hbox {kg}/\hbox {s}\,\hbox {m}^{2}\))

\({\mathbf{F}_\mathrm{A}^{\mathrm{H}_2 \mathrm{O}} } \Big |_{\mathrm{adv}} ; {\mathbf{F}_\mathrm{G}^{\mathrm{H}_2 \mathrm{O}} } \Big |_{\mathrm{adv}} \)

Advective mass flux of \(\hbox {H}_{2}\hbox {O}\) in aqueous- and gas-phase flow (\(\hbox {kg}/\hbox {s}\,\hbox {m}^{2}\))

\({\mathbf{F}_\mathrm{A}^{\mathrm{CH}_4 } } \Big |_{\mathrm{adv}} ; {\mathbf{F}_\mathrm{G}^{\mathrm{CH}_4 } } \Big |_{\mathrm{adv}} \)

Advective mass flux of \(\hbox {CH}_{4}\) in aqueous- and gas-phase flow (\(\hbox {kg}/\hbox {s}\,\hbox {m}^{2}\))

\({\mathbf{F}_\mathrm{A}^\mathrm{Salt} } \Big |_{\mathrm{adv}} \)

Advective mass flux of salt in aqueous-phase flow (\(\hbox {kg}/\hbox {s}\,\hbox {m}^{2}\))

\({\mathbf{F}_\mathrm{A}^{\mathrm{H}_2 \mathrm{O}} } \Big |_{\mathrm{dif}}; {\mathbf{F}_\mathrm{G}^{\mathrm{H}_2 \mathrm{O}} } \Big |_{\mathrm{dif}} \)

Diffusion mass flux of \(\hbox {H}_{2}\hbox {O}\) in aqueous- and gas-phase flow (\(\hbox {kg}/\hbox {s}\,\hbox {m}^{2}\))

\({\mathbf{F}_\mathrm{A}^{\mathrm{CH}_4 }} \Big |_{\mathrm{dif}}; {\mathbf{F}_\mathrm{G}^{\mathrm{CH}_4 } } \Big |_{\mathrm{dif}} \)

Diffusion mass flux of \(\hbox {CH}_{4}\) in aqueous- and gas-phase flow (\(\hbox {kg}/\hbox {s}\,\hbox {m}^{2}\))

\({\mathbf{F}_\mathrm{A}^\mathrm{Salt} } \Big |_{\mathrm{dif}} \)

Diffusion mass flux of salt in aqueous-phase flow (\(\hbox {kg}/\hbox {s}\,\hbox {m}^{2}\))

\(k_\mathrm{I} \)

Slit-shaped pore permeability (\(\hbox {m}^{2}\))

\(k_\mathrm{m} \)

Permeability of porous medium acting as semi-permeable membrane (\(\hbox {m}^{2}\))

\(k_0 \)

Slit-shaped pore permeability at zero effective stress (\(\hbox {m}^{2}\))

\(\ell _\mathrm{IC} \)

Shape factor (\(1/\hbox {m}^{2}\))


Coefficient in Gangi’s permeability model (-)

\(M^{\kappa } \)

Mass accumulation of component \(\kappa \)

\(M_\mathrm{s} \)

Salt molar mass (kg/mol)

\(M_{\mathrm{CH}_4 } \)

Molecular weight of \(\hbox {CH}_{4}\) (kg/mol)


Slit-shaped pore pressure (Psi; Pa)

\(P_\mathrm{A} ; P_\mathrm{G} \)

Aqueous- and gas-phase pressure (Psi; Pa)

\(P_\mathrm{A,I} \)

Inorganic slit-shaped pore pressure (Psi; Pa)

\(P_\mathrm{A,C} \)

Clay-pore pressure (Psi; Pa)

\(P_\mathrm{conf} \)

Confining pressure (Psi; Pa)

\(P_1 \)

Effective stress when the slit-shaped pores are close completely (Psi; Pa)

\(P_\mathrm{L} \)

Langmuir pressure (Psi; Pa)

\(q^{\kappa } \)

Source/sink of component \(\kappa \) (\(\hbox {kg}/\hbox {s}\,\hbox {m}^{3}\))

\(q^{\mathrm{H}_2 \mathrm{O}}; q^\mathrm{Salt}; q^{\mathrm{CH}_4 } \)

Source/sink of component \(\hbox {H}_{2}\hbox {O}\), salt and \(\hbox {CH}_{4}\) (\(\hbox {kg}/\hbox {s}\,\hbox {m}^{3}\))


Gas constant, equal to 8.3145 (J/mol K) or 0.082 (atm l/mol K)

\(R_\mathrm{n}^{\kappa ,k+1} \)

Residuals of component K at time k+1, in element n

\(S_\mathrm{A} ; S_\mathrm{G} \)

Aqueous- and gas-phase saturation




Temperature (\(^{\circ }\hbox {C}; \hbox { K}\))


Partial molar volume of solvent (liters per mol)

\(x^{s} \)

Salt mass fraction

\(x_\mathrm{A}^{\mathrm{H}_2 \mathrm{O}} ; x_\mathrm{A}^\mathrm{Salt} ; x_\mathrm{A}^{\mathrm{CH}_4} \)

Mass fraction of component \(\hbox {H}_{2}\hbox {O}\), salt and \(\hbox {CH}_{4}\) in aqueous-phase flow

\(x_\mathrm{G}^{\mathrm{H}_2 \mathrm{O}} ; x_\mathrm{G}^\mathrm{Salt} ; x_\mathrm{G}^{\mathrm{CH}_4} \)

Mass fraction of component \(\hbox {H}_{2}\hbox {O}\), salt and \(\hbox {CH}_{4}\) in gas-phase flow

\(x_\mathrm{A,I}^\mathrm{Salt} ; x_\mathrm{A,I}^{\mathrm{H}_2 O} \)

Salt and \(\hbox {H}_{2}\hbox {O}\) mass fraction in inorganic pore

\(x_\mathrm{A,C}^\mathrm{Salt} ; x_\mathrm{A,C}^{\mathrm{H}_2 \mathrm{O}} \)

Salt and \(\hbox {H}_{2}\hbox {O}\) mass fraction in clay pore

\(V_\mathrm{n} \)

Volume of element n (\(\hbox {m}^{2}\))

\(V_\mathrm{sL} \)

Langmuir volume, sorbed-gas volume per total grain mass (\(\hbox {m}^{3}/\hbox {kg}\))

\(w_\mathrm{A,IC}^{\mathrm{H}_2 \mathrm{O}} ; w_\mathrm{A,IC}^{\mathrm{CH}_4 } ; w_\mathrm{A,IC}^\mathrm{Salt} \)

Mass-exchange of \(\hbox {H}_{2}\hbox {O}\), \(\hbox {CH}_{4}\) and salt between slit-shaped and clay-pore mass (\(\hbox {kg}\,\hbox {m}^{-3}\,\hbox {s}^{-1}\))

Greek Letters

\(\alpha \)

Effective stress coefficient (-)

\(\varepsilon _\mathrm{ks} \)

Total organic content, organic grain volume per total grain volume (-)

\(\kappa \)


\(\mu _\mathrm{A} \hbox { and } \mu _\mathrm{G} \)

Viscosity of aqueous- and gas-phase (Pa s)

\(\pi \)

Osmotic pressure (Pa)

\(\rho _\mathrm{A} ; \rho _\mathrm{G} \)

Aqueous- and gas-phase density (\(\hbox {kg}/\hbox {m}^{3}\))

\(\rho _\mathrm{f} \)

Fluid density (\(\hbox {kg}/\hbox {m}^{3}\))

\(\rho _\mathrm{grain} \)

Grain density (\(\hbox {kg}/\hbox {m}^{3}\))

\(\rho _\mathrm{sc,gas} \)

Gas density in standard condition (\(\hbox {kg}/\hbox {m}^{3}\))

\(\sigma \)

Clay-membrane efficiency (-)

\(\tau _\mathrm{A} ;\tau _\mathrm{G} \)

Tortuosity of the aqueous- and gas-phase (-)


Dissociation coefficient (-)

\(\phi \)

Porosity of porous medium (fraction)

\(\phi _\mathrm{C} \)

Clay porosity (fraction)

\(\phi _\mathrm{I} \)

Inorganic slit-shaped pore porosity (fraction)

\(\phi _\mathrm{k} \)

Organic (kerogen) porosity (fraction)



The authors thank to the Indonesian State Oil Company, PERTAMINA, for their support of this work.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Vena. F. Eveline
    • 1
    Email author
  • I. Yucel Akkutlu
    • 1
  • George J. Moridis
    • 2
  1. 1.Texas A&M UniversityCollege StationUSA
  2. 2.Lawrence Berkeley National LaboratoryBerkeleyUSA

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