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Factors affecting the lower limit of the safe mud weight window for drilling operation in hydrate-bearing sediments in the Northern South China Sea

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Abstract

Maintaining wellbore stability is the basis and prerequisite for efficient methane production from offshore gas hydrates. Nevertheless, owing to the invasion and disturbance by drilling mud, gas hydrates around wellbore gradually dissociate, resulting in the rapid reduction of sediment strength, thereby the borehole collapse. Accurate design of mud density based on appropriate strength criterion is a feasible measure to avoid this case, but the traditional Mohr–Coulomb (MC) criterion was commonly used now. Herein, the self-designed low temperature triaxial experimental equipment was set up to explore the strength of sediment with different saturation of hydrate, and a new strength criterion was developed. Moreover, impact law and mechanism of several critical factors on the lower limit of the safe mud weight window (abbreviated as MDlow value) was then investigated. The investigation results showed that the MDlow value calculated by the new criterion is higher (or more conservative), which is more conducive for prevention of borehole collapse. Further analysis reveals that the increase of cohesion or hydrate saturation enhances the reservoir strength, resulting in the smaller MDlow value. In this way, the wider window is more conducive to reasonable mud density design. Furthermore, the safe mud weight window for hydrate reservoir is temperature sensitive, and it varies obviously when the drilling fluid temperature is between 288.14 K and 288.45 K. Finally, the investigation in this study also shows that the MDlow value was still affected by stress difference. The preferred design strategy is to orient the azimuth of wellbore axis at 90° if horizontal wellbore is drilled for hydrate development.

Article highlights

  • The Modified Mohr–Coulomb (MMC) strength criterion suitable for hydrate deposits is established.

  • Determination method for MDlow value required for drilling in the hydrate reservoir is obtained.

  • Factors affecting the MDlow value are also investigated to provide reference for the engineering application of hydrate development.

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Acknowledgements

This work is supported by Program for the National Key Research and Development Program (Grant No. 2016YFC0304005) and the Postdoctoral Program of Henan Polytechnic University (Grant No. 712108/210).

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Authors and Affiliations

  1. School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo, 454000, China

    Qingchao Li

  2. School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo, 454000, China

    Jingjuan Wu

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  1. Qingchao Li
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  2. Jingjuan Wu
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LQ: simulation, programing and data analysis. WJ: original draft preparation and manuscript revision.

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Correspondence to Qingchao Li or Jingjuan Wu.

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Appendix A: Derivation method for determining function of f(P m )

Relationship between σj, σi and σr mentioned in Eqs. (11) may exhibits three possibilities: σj > σi > σr, σj > σr > σi or σr > σi > σj. Accordingly, derivation method for determining function of f(Pm) was discussed in the following three cases.

(1) When the case of σj > σi > σr occurs, σ1 and σ3 can be expressed as:

$$ \begin{gathered} \sigma_{1} { = 0}{\text{.5}}\left( {\sigma_{\theta } { + }\sigma_{z} } \right){ + }0.5\sqrt {\left( {\sigma_{\theta } { - }\sigma_{z} } \right)^{2} { + }4\sigma_{\theta z}^{2} } \hfill \\ \sigma_{3} \,=\,P_{m} { - }P_{p} \hfill \\ \end{gathered} $$
(A-1)

The final form of f(Pm) was obtained in this case by substituting Eqs. (A-1) into Eqs. (13):

$$ f\left( {P_{m} } \right)\,=\,E - F \cdot P_{p} { + }\left( {F{ + }1} \right) \cdot P_{m} - 0.74\left( {P_{m} - P_{p} } \right)^{2} - A - \sqrt {\left( {B - P_{m} } \right)^{2} { + }D} $$
(A-2)

Taking the first derivative of f(Pm) function, we can get:

$$ f^{^{\prime}} \left( {P_{m} } \right)\,=\,\left( {F{ + }1} \right) - 1.48\left( {P_{m} - P_{p} } \right) + \frac{{B - P_{m} }}{{\sqrt {\left( {B - P_{m} } \right)^{2} { + }D} }} $$
(A-3)

In Eqs. (A-3), the six variables A, B, C, D, E and F were written as

$$ \begin{gathered} A\,=\,\sigma_{B}^{xx} + \sigma_{B}^{yy} - 2\left( {\sigma_{B}^{xx} - \sigma_{B}^{yy} } \right)cos2\theta - 4\sigma_{B}^{xy} sin2\theta - P_{p} + \sigma_{z} \hfill \\ B\,=\,\sigma_{B}^{xx} + \sigma_{B}^{yy} - 2\left( {\sigma_{B}^{xx} - \sigma_{B}^{yy} } \right)cos2\theta - 4\sigma_{B}^{xy} sin2\theta - P_{p} - \sigma_{z} \hfill \\ D = 4\sigma_{\theta z}^{2} \hfill \\ E = \frac{4cos\varphi }{{1 - sin\varphi }}C_{0} + 24.04S_{h}^{1.27} - 4.72 \hfill \\ F = \frac{{2\left( {1 + sin\varphi } \right)}}{1 - sin\varphi } + 4.44 \hfill \\ \end{gathered} $$
(A-4)

(2) When the case of σj > σr > σi occurs, σ1 and σ3 can be expressed as:

$$ \begin{gathered} \sigma_{1} { = 0}{\text{.5}}\left( {\sigma_{\theta } { + }\sigma_{z} } \right){ + }0.5\sqrt {\left( {\sigma_{\theta } { - }\sigma_{z} } \right)^{2} { + }4\sigma_{\theta z}^{2} } \hfill \\ \sigma_{3} { = 0}{\text{.5}}\left( {\sigma_{\theta } { + }\sigma_{z} } \right) - 0.5\sqrt {\left( {\sigma_{\theta } { - }\sigma_{z} } \right)^{2} { + }4\sigma_{\theta z}^{2} } \hfill \\ \end{gathered} $$
(A-5)

Function f(Pm) and its first derivative can be written as Eqs. (A-6) and Eqs. (7) respectively.

$$ \begin{gathered} f\left( {P_{m} } \right) = E + \left( {0.5F - 1} \right)\left( {A - P_{m} } \right) - \left( {0.5F + 1} \right)\sqrt {\left( {B - P_{m} } \right)^{2} + D} \hfill \\ \begin{array}{*{20}c} {} & {} & {} \\ \end{array} - 0.185\left[ {\left( {A - P_{m} } \right) - \sqrt {\left( {B - P_{m} } \right)^{2} + D} } \right] \hfill \\ \end{gathered} $$
(A-6)
$$ \begin{gathered} f^{^{\prime}} \left( {P_{m} } \right) = \left( {1 - 0.5F} \right){ + }\left( {0.5F + 1} \right)\frac{{\left( {B - P_{m} } \right)}}{{\sqrt {\left( {B - P_{m} } \right)^{2} + D} }} \hfill \\ \begin{array}{*{20}c} {} & {} & {} \\ \end{array} - 0.185\left[ {\frac{{\left( {B - P_{m} } \right)}}{{\sqrt {\left( {B - P_{m} } \right)^{2} + D} }} - 1} \right] \hfill \\ \end{gathered} $$
(A-7)

(3) When the case of σr > σi > σj occurs, σ1 and σ3 can be expressed as:

$$ \begin{gathered} \sigma_{1} \,=\,P_{m} { - }P_{p} \hfill \\ \sigma_{3} { = 0}{\text{.5}}\left( {\sigma_{\theta } { + }\sigma_{z} } \right) - 0.5\sqrt {\left( {\sigma_{\theta } { - }\sigma_{z} } \right)^{2} { + }4\sigma_{\theta z}^{2} } \hfill \\ \end{gathered} $$
(A-8)

Similarly, function f(Pm) and its first derivative can be written as Eqs. (A-9) and Eqs. (10) respectively.

$$ f\left( {P_{m} } \right) = A - 3P_{m} + 2P_{p} - \sqrt {\left( {B - P_{m} } \right)^{2} + D} $$
(A-9)
$$ f^{^{\prime}} \left( {P_{m} } \right) = - 3 + \frac{{\left( {B - P_{m} } \right)}}{{\sqrt {\left( {B - P_{m} } \right)^{2} + D} }} $$
(A-10)

Based on the function f(Pm) and its first derivative derived above, the Newton–Raphson iteration was obtained.

$$ P_{m1} \,=\,P_{m0} - \frac{{f\left( {P_{m} } \right)}}{{f^{^{\prime}} \left( {P_{m} } \right)}} $$
(A-11)

where, Pm0 is the pre-assumed fluid pressure in MPa. Pm1 is the calculated result in MPa. Moreover, in order to facilitate readers to understand the role of each function in these Matlab codes submitted as “Supplementary Material”, Fig. A-1 gives the corresponding structure diagram.

Acknowledgements

This work is supported by Program for the National Key Research and Development Program (Grant No. 2016YFC0304005) and the Postdoctoral Program of Henan Polytechnic University (Grant No. 712108/210).

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Li, Q., Wu, J. Factors affecting the lower limit of the safe mud weight window for drilling operation in hydrate-bearing sediments in the Northern South China Sea. Geomech. Geophys. Geo-energ. Geo-resour. 8, 82 (2022). https://doi.org/10.1007/s40948-022-00396-0

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