Abstract
During hydraulic fracturing, thousands of barrels of fluid are injected into the rock surrounding the created fractures. Observations show that later during flowback, only a small fraction of the injected fluid volume is produced back. In tight naturally fractured formations, this can be explained by the leading role of preexisting rock discontinuities in the transport of fluids in such rocks. In this work, we investigate the mechanics of injected fluid flow in and out of preexisting rock discontinuities during a typical operational sequence of fracturing treatment, well shut-in and flowback. The mechanics of fluid flow in compliant discontinuities, where conductivity is sensitive to stress changes, is different from that in a stiff rock matrix. To understand and quantify rock pressurization, fluid leakoff and flowback rates, we develop a numerical model of fluid flow in a system of arbitrarily oriented discontinuities. Using this model, we predict spatial distribution of the injected fluid in a naturally fractured rock at any time after the beginning of the fracturing treatment as well as after the well shut-in and during flowback. The model explains the trapping of injected fluid in the discontinuities during production. We validate the model by comparison with field data and provide rough estimates of the volumetric fracturing fluid accumulation in the rock discontinuities after the treatment. The spatial extent of rock “flooding” around hydraulic fractures is found to depend on the density and orientation of rock discontinuities.
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Abbreviations
- \(B_{\text{f}}\) :
-
Fluid compressibility (Pa−1)
- \(H_{\text{f}}\) :
-
Fracture height (m)
- \({\text{JRC}}\) :
-
Joint roughness coefficient (–)
- \(L_{\text{f}}\) :
-
Fracture half-length (m)
- \(L_{\text{front}}\) :
-
Depth of fluid penetration into discontinuity (m)
- \(L_{*}\) :
-
Length scale (m)
- \(N_{\text{d}}\) :
-
Number of discontinuities (–)
- \(T_{1}\) :
-
Fracture closure time (s)
- \(T_{2}\) :
-
Time where flowback begins (s)
- \(T_{*}\) :
-
Time scale (s)
- \(V\) :
-
Volume returning from discontinuities (m3)
- \(V_{{1{\text{d}}}}\) :
-
Volume returning from one discontinuity (m3)
- \(V_{\text{f}}\) :
-
Volume of fluid stored in a hydraulic fracture (m3)
- \(V_{{{\text{inj}}/{\text{HF}}}}\) :
-
Volume injected per fracture (m3)
- \(V_{{{\text{LO}}/{\text{HF}}}}\) :
-
Total leakoff volume per fracture (m3)
- \(V_{*}\) :
-
Volume scaling factor (m3)
- \(a\) :
-
Aperture of a discontinuity (mm)
- \(\tilde{a}\) :
-
Nondimensional aperture (–)
- \(a_{0}\) :
-
Zero-stress aperture of discontinuity (mm)
- \(a_{{0,{\text{s}}}}\) :
-
Shear-induced aperture of a discontinuity at zero effective stress (mm)
- \(a_{*}\) :
-
Aperture scale (mm)
- \(c\) :
-
Conductivity of a discontinuity (mD-ft)
- \(\tilde{c}\) :
-
Nondimensional conductivity (–)
- \(c_{*}\) :
-
Conductivity scale (mD-ft)
- \(g\) :
-
Gravity acceleration (m/s2)
- \(k\) :
-
Ratio of vertical stress to true vertical depth (MPa/m)
- \(k_{1}\) :
-
Minimum ratio of relative average horizontal stress to true vertical depth (MPa/m)
- \(k_{2}\) :
-
Maximum ratio of relative average horizontal stress to true vertical depth (MPa/m)
- \(l\) :
-
Length of intersection between a hydraulic fracture and discontinuity (m)
- \(l_{\text{front}}\) :
-
Nondimensional depth of fluid penetration into discontinuity (–)
- \(l_{\text{m}}\) :
-
Scale transformation factor from microns to the units of choice (meter) (–)
- \(p\) :
-
Fluid pressure (MPa)
- \(p_{\text{fb}}\) :
-
Flowback pressure (MPa)
- \(p_{\text{tr}}\) :
-
Treatment pressure (MPa)
- \(p_{*}\) :
-
Pressure scale (MPa)
- \(p_{\text{HF}}\) :
-
Fluid pressure in fracture (MPa)
- \(p_{\text{p}}\) :
-
Pore pressure (MPa)
- \(q\) :
-
Flow rate per unit length (m2/s)
- \(\tilde{q}\) :
-
Nondimensional flow rate per unit length (–)
- \(q_{*}\) :
-
Flow rate per unit length scale (m2/s)
- \(t\) :
-
Time (s)
- \(u_{\text{s}}\) :
-
Relative shear displacement of fracture wall faces (mm)
- \(v\) :
-
Volume of fluid stored in a discontinuity (m3)
- \(\tilde{v}\) :
-
Nondimensional volume of fluid stored in a discontinuity (–)
- \(\tilde{v}_{{1{\text{d}}}}\) :
-
Nondimensional volume returning from one discontinuity (–)
- \(v_{*}\) :
-
Volume scale (m3)
- \(w_{\text{f}}\) :
-
Fracture width (mm)
- \(x\) :
-
Coordinate along a discontinuity (m)
- \(z\) :
-
True vertical depth (m)
- \(\gamma_{\text{HF}}\) :
-
Nondimensional pressure in fracture (–)
- \(\gamma_{\text{fb}}\) :
-
Nondimensional flowback pressure (–)
- \(\gamma_{\text{tr}}\) :
-
Nondimensional treatment pressure (–)
- \(\Delta\) :
-
Spacing between two neighboring discontinuities (m)
- \(\vartheta\) :
-
Dip angle (–)
- \(\mu\) :
-
Fluid viscosity (cP)
- \(\tilde{\mu }\) :
-
Nondimensional fluid viscosity (–)
- \(\mu_{*}\) :
-
Fluid viscosity scale (cP)
- \(\xi\) :
-
Nondimensional coordinate (–)
- \(\varPi\) :
-
Nondimensional pressure (–)
- \(\rho\) :
-
Fluid density (kg/m3)
- \(\tilde{\rho }\) :
-
Nondimensional fluid density (–)
- \(\rho_{0}\) :
-
Fluid density at standard condition (kg/m3)
- \(\sigma_{\text{h}}\) :
-
Minimum horizontal stress (MPa)
- \(\sigma_{{{\text{h}}, {\text{av}}}}\) :
-
Average horizontal stress (MPa)
- \(\sigma_{{{\text{h}}, {\text{av}},0,{ \hbox{max} }}}\) :
-
Maximum average horizontal stress at zero depth (MPa)
- \(\sigma_{{{\text{h}}, {\text{av}},0,{ \hbox{min} }}}\) :
-
Minimum average horizontal stress at zero depth (MPa)
- \(\sigma_{\text{H}}\) :
-
Maximum horizontal stress (MPa)
- \(\sigma_{\text{n}}\) :
-
Normal stress applied to a discontinuity (MPa)
- \(\sigma_{\text{n}}^{{\prime }}\) :
-
Effective normal stress applied to a discontinuity (MPa)
- \(\sigma_{{{\text{n}},{\text{BP}}}}\) :
-
Normal stress applied to bedding planes (MPa)
- \(\sigma_{{{\text{n}},{\text{NF}}}}\) :
-
Normal stress applied to natural fractures (MPa)
- \(\sigma_{{{\text{n}}, {\text{ref}}}}^{'}\) :
-
Reference stress (MPa)
- \(\sigma_{\text{v}}\) :
-
Vertical stress (MPa)
- \(\tau\) :
-
Nondimensional time (–)
- \(\tau_{1}\) :
-
Fracture closure nondimensional time (–)
- \(\tau_{2}\) :
-
Nondimensional time where flowback begins (–)
- \(\phi_{\text{dil}}^{\text{eff}}\) :
-
Effective shear dilation angle (–)
- \(\varphi\) :
-
Azimuth angle (–)
- \(\varphi_{\text{p}}\) :
-
Proppant pack porosity (–)
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Acknowledgements
The authors wish to thank Dr. Dean Willberg for the idea of this study, Dr. Maxim Chertov, Dr. Xiaowei Weng, and Dr. Pavel Spesivtsev for deep technical review of this work. We are also thankful to Dr. Konstantin Sinkov, Dr. Denis Syresin and Dr. Boris Krasnopolsky for constructive discussions; Dr. Sergey Stanchits, Dr. Ella Maria Llanos, Dr. Julia Gale, and Dr. Nick Barton for permission to use their materials in this paper. We appreciate Schlumberger company for permission to publish this work.
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Ipatova, A., Chuprakov, D. Role of Preexisting Rock Discontinuities in Fracturing Fluid Leakoff and Flowback. Transp Porous Med 135, 137–180 (2020). https://doi.org/10.1007/s11242-020-01472-3
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DOI: https://doi.org/10.1007/s11242-020-01472-3