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An improved fracture height containment method: artificial gel-barrier technology and its simulation

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Abstract

Overgrowths of hydraulic fracture height occur in reservoirs without stress barriers. It may decrease the efficiency of hydraulic fracturing, pose harm to well production, and increase the possibility of groundwater pollution. Hence, fracture height containment methods are recommended to restrain the overgrowths of fracture height. To enhance the effect of artificial barrier technology, it is improved by replacing the sand or the ceramic used for bridging the fracture tips by gel particles. This innovative technology could be named “artificial gel-barrier technology”. Experiments show that the design of artificial gel-barrier technology is more convenient and controllable, since the dilatability and the gelling performance of the selected gels are mainly controlled by salinity. Experiments also show that the break-through pressure of the gel-barrier is much larger than that of the classical barrier. Numerical simulations reveal that the artificial gel-barrier technology is more helpful and efficient than classical barrier technology. This improved technology has been applied to fracturing operations in Tahe oilfield of China; 73% of these operations were more efficient and the performances of these wells were better than those of adjacent wells.

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Acknowledgements

This study was supported by the Major Program of the National Natural Science Foundation of China (51490653), Sichuan Youth Science and Technology Innovation Research Team Program (2017TD0013), and the China Scholarship Council (201708510130).

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Authors and Affiliations

  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, China

    Yongming Li, Yu Peng, Jinzhou Zhao & Yang Yang

  2. Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, 78712, USA

    Yu Peng & Kamy Sepehrnoori

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  1. Yongming Li
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  2. Yu Peng
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  3. Jinzhou Zhao
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  4. Kamy Sepehrnoori
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  5. Yang Yang
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Corresponding authors

Correspondence to Yu Peng or Jinzhou Zhao.

Appendix

Appendix

The expressions of W1, W2, W31, W32 and W33 are

$${W_1}= - \frac{{4\left( {1 - {\upsilon ^2}} \right)}}{E}{\sigma _{{\text{mid}}}}\sqrt {{l^2} - {z^2}} ,$$
$$\begin{aligned} {W_2} & = - \frac{{4{\sigma _{{\text{up}}}}z\left( {1 - {\upsilon ^2}} \right)}}{{E\pi }}\left[ {{\text{ln}}\left( {\sqrt {{l^2} - {{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)}^2}} +\sqrt {{l^2} - {z^2}} } \right) - \ln \sqrt {\left| {{{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)}^2} - {z^2}} \right|} } \right. \\ & \quad - \frac{{{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s}}{{\left| z \right|}}\left. {{\text{ln}}\left( {\left| {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)}^2}} } \right) - \frac{{{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s}}{{\left| z \right|}}\ln \left( {l\sqrt {\left| {{{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)}^2} - {z^2}} \right|} } \right)} \right] \\ & \quad - \frac{{4{\sigma _{{\text{up}}}}\left( {1 - {\upsilon ^2}} \right)}}{{E\pi }}\left[ {\sqrt {{l^2} - {z^2}} \arccos \frac{{{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s}}{l} - \left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)\ln \left( {\sqrt {{l^2} - {{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)}^2}} +\sqrt {{l^2} - {z^2}} } \right)} \right. \\ & \quad +\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)\ln \sqrt {\left| {{{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)}^2} - {z^2}} \right|} +\left. {\left| z \right|{\text{ln}}\left( {\left| {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)}^2}} } \right) - \left| z \right|{\text{ln}}\left( {l\sqrt {\left| {{{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2} - s} \right)}^2} - {z^2}} \right|} } \right)} \right] \\ & \quad +\frac{{4{\sigma _{{\text{low}}}}z\left( {1 - {\upsilon ^2}} \right)}}{{E\pi }}\left[ {{\text{ln}}\left( {\sqrt {{l^2} - {{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right)}^2}} +\sqrt {{l^2} - {z^2}} } \right) - \ln \sqrt {\left| {{{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right)}^2} - {z^2}} \right|} } \right. \\ & \quad - \frac{{{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s}}{{\left| z \right|}}{\text{ln}}\left( {\left| {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right)}^2}} } \right)\left. {+\frac{{{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s}}{{\left| z \right|}}{\text{ln}}\left( {l\sqrt {\left| {{{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right)}^2} - {z^2}} \right|} } \right)} \right] \\ & \quad - \frac{{4{\sigma _{{\text{low}}}}\left( {1 - {\upsilon ^2}} \right)}}{{E\pi }}\left[ {\sqrt {{l^2} - {z^2}} \arccos \frac{{{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s}}{l}{\kern 1pt} - \left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right){\text{ln}}\left( {\sqrt {{l^2} - {{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right)}^2}} +\sqrt {{l^2} - {z^2}} } \right)} \right. \\ & \quad +\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right)\ln \sqrt {\left| {{{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right)}^2} - {z^2}} \right|} +\left. {\left| z \right|\ln \left( {\left| {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right)}^2}} } \right) - \left| z \right|{\text{ln}}\left( {l\sqrt {\left| {{{\left( {{h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0pt} 2}+s} \right)}^2} - {z^2}} \right|} } \right)} \right] \\ \end{aligned}$$
$$\begin{aligned} {W_{31}} & = - \frac{{4z\left( {1 - {\upsilon ^2}} \right)\left( {{p_{{\text{maxup}}}} - {p_{{\text{fmax}}}}} \right)}}{{E\pi \left( {l+s} \right)}}\left( {l\,{\text{ln}}\left| z \right| - l\,{\text{ln}}\left| {l+\sqrt {{l^2} - {z^2}} } \right|+\frac{\pi }{4}\sqrt {{l^2} - {z^2}} } \right)+\frac{{2{p_{{\text{maxup}}}}\left( {1 - {\upsilon ^2}} \right)\,}}{E}\sqrt {{l^2} - {z^2}} \\ & \quad +\frac{{2\left( {1 - {\upsilon ^2}} \right)\,\left( {{p_{{\text{fmax}}}} - {p_{{\text{maxup}}}}} \right)}}{{E\pi \,\left( {l+s} \right)}}\left[ {{z^2}{\text{ln}}\frac{{\left| z \right|}}{{\left| {l+\sqrt {{l^2} - {z^2}} } \right|}}+\left( {\pi l - l} \right)\sqrt {{l^2} - {z^2}} } \right]+\frac{{4{p_{{\text{maxup}}}}z\left( {1 - {\upsilon ^2}} \right)}}{{E\pi }}\,\left( {{\text{ln}}\left| {l+\sqrt {{l^2} - {z^2}} } \right| - {\text{ln}}\left| z \right|} \right) \\ \end{aligned}$$
$$\begin{aligned} {W_{32}} & =\frac{{4z\left( {1 - {\upsilon ^2}} \right)}}{{E\pi }}\left[ {\frac{{l{p_{{\text{fmax}}}}+s{p_{{\text{maxup}}}}}}{{l+s}}} \right]\left( {\ln \frac{{\left| z \right|\left( {\sqrt {{l^2} - {s^2}} +\sqrt {{l^2} - {z^2}} } \right)}}{{\left| {l+\sqrt {{l^2} - {z^2}} } \right|\sqrt {\left| {{s^2} - {z^2}} \right|} }} - \frac{s}{{\left| z \right|}}\ln \frac{{\left| s \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {s^2}} }}{{l\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right) \\ & \quad +\frac{{4\left( {1 - {\upsilon ^2}} \right)}}{{E\pi }}\left[ {\frac{{l{p_{{\text{fmax}}}}+s{p_{{\text{maxup}}}}}}{{l+s}}} \right]\left( {\sqrt {{l^2} - {z^2}} \arcsin \frac{s}{l}+s\ln \frac{{\sqrt {{l^2} - {s^2}} +\sqrt {{l^2} - {z^2}} }}{{\sqrt {\left| {{s^2} - {z^2}} \right|} }} - } \right.\left. {\left| z \right|\ln \frac{{\left| s \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {s^2}} }}{{l\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right) \\ & \quad +\frac{{2\left( {1 - {\upsilon ^2}} \right)\left( {{p_{{\text{fmax}}}} - p{}_{{{\text{maxup}}}}} \right)}}{{E\pi \left( {l+s} \right)}}\left[ {\left( {{s^2} - {z^2}} \right)\ln \left( {\frac{{\sqrt {{l^2} - {s^2}} +\sqrt {{l^2} - {z^2}} }}{{\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right)} \right.+\left. {\sqrt {{l^2} - {z^2}} \left( {l - \sqrt {{l^2} - {s^2}} } \right)+{z^2}\ln \frac{{\left| {l+\sqrt {{l^2} - {z^2}} } \right|}}{{|z|}}} \right] \\ & \quad - \frac{{2z\left( {1 - {\upsilon ^2}} \right)\left( {{p_{{\text{fmax}}}} - {p_{{\text{maxup}}}}} \right)}}{{E\pi \left( {l+s} \right)}}\left[ {\sqrt {{l^2} - {z^2}} \arcsin \frac{s}{l}+\left( {\frac{{{s^2}}}{{\left| z \right|}} - \left| z \right|} \right)\ln \frac{{\left| s \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {s^2}} }}{{l\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right] \\ \end{aligned}$$
$$\begin{aligned} {W_{33}} & = - \frac{{4\left( {1 - {\upsilon ^2}} \right){p_{{\text{maxlow}}}}z}}{{E\pi }}\left( {\ln \frac{{\sqrt {{l^2} - {s^2}} +\sqrt {{l^2} - {z^2}} }}{{\sqrt {\left| {{s^2} - {z^2}} \right|} }} - \frac{s}{{\left| z \right|}}\ln \frac{{\left| s \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {s^2}} }}{{l\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right) \\ & \quad +\frac{{4{p_{{\text{maxlow}}}}\left( {1 - {\upsilon ^2}} \right)}}{{E\pi }}\left[ {\arccos \frac{s}{l}\sqrt {{l^2} - {z^2}} +\left| z \right|\ln \frac{{\left| s \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {s^2}} }}{{l\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right. - \left. {s\ln \frac{{\sqrt {{l^2} - {s^2}} +\sqrt {{l^2} - {z^2}} }}{{\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right] \\ & \quad +\frac{{4z\left( {1 - {\upsilon ^2}} \right)\left( {{p_{{\text{fmax}}}} - {p_{{\text{maxlow}}}}} \right)}}{{E\pi \left( {l - s} \right)}}\left[ {\frac{{\left| z \right|}}{2}\ln \frac{{\left| s \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {s^2}} }}{{l\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right.+\frac{\pi }{4}\sqrt {{l^2} - {z^2}} - \frac{1}{2}\arcsin \frac{s}{l}\sqrt {{l^2} - {z^2}} \\ & \quad - \left( {l - \frac{s}{2}} \right)\left( {\ln \frac{{\sqrt {{l^2} - {s^2}} +\sqrt {{l^2} - {z^2}} }}{{\sqrt {\left| {{s^2} - {z^2}} \right|} }} - \frac{s}{{\left| z \right|}}\ln \frac{{\left| s \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {s^2}} }}{{l\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right) - \left. {\frac{s}{2}\ln \frac{{\sqrt {{l^2} - {s^2}} +\sqrt {{l^2} - {z^2}} }}{{\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right] \\ & \quad +\frac{{4\left( {1 - {\upsilon ^2}} \right)\left( {{p_{{\text{fmax}}}} - {p_{{\text{maxlow}}}}} \right)}}{{E\pi \left( {l - s} \right)}}\left[ {\frac{{\pi l\sqrt {{l^2} - {z^2}} }}{2}} \right. - l\left( {s\ln \frac{{\sqrt {{l^2} - {s^2}} +\sqrt {{l^2} - {z^2}} }}{{\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right. - \left| z \right|\ln \frac{{\left| s \right|\sqrt {{l^2} - {z^2}} +\left| z \right|\sqrt {{l^2} - {s^2}} }}{{l\sqrt {\left| {{s^2} - {z^2}} \right|} }} \\ & \quad +\left. {\sqrt {{l^2} - {z^2}} \arcsin \frac{s}{l}} \right) - \frac{1}{2}\sqrt {\left( {{l^2} - {s^2}} \right)\left( {{l^2} - {z^2}} \right)} +\left. {\left( {{s^2} - {z^2}} \right)\frac{l}{2}\ln \frac{{\sqrt {{l^2} - {s^2}} +\sqrt {{l^2} - {z^2}} }}{{\sqrt {\left| {{s^2} - {z^2}} \right|} }}} \right] \\ \end{aligned}$$

where h is the thickness of pay layer, m; s is the distance between the centers of perforation/pay layer and fracture, m; σmid is the minimum horizontal principal stress at pay layer center, MPa; σup and σlow are the stress differences between the pay layer center and upper/lower layer center, MPa; pfmax, pmaxup and pmaxlow are the fluid pressure at appropriate positions in Fig. 6.

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Li, Y., Peng, Y., Zhao, J. et al. An improved fracture height containment method: artificial gel-barrier technology and its simulation. Environ Earth Sci 77, 324 (2018). https://doi.org/10.1007/s12665-018-7506-3

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