A first-order model for temperature rise for uniform and differential compression of sediments in basins

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Abstract

We deduce algebraic expressions for temperature rise for ideal cases of uniform and spatially varying compression of sediments of single mineralogy. According to the results of the present work, the temperature rise is related to the coefficient of volume expansion, isothermal compressibility, dimension, bulk density, and specific heat of the sediment columns. Rise of temperature due to compression of sediment is effectively inversely proportional to the volume coefficient of expansion (or contraction) of sediments. Compression-related temperature rise is expected to augment diagenesis. A more realistic model of temperature rise dealing with the rate of compression of sediments that of the pore fluid(s) and the vacant pore space individually would be required.

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Acknowledgements

Research sabbatical for the year 2017 and the CPDA grant received from IIT Bombay supported SM. Editorial handling by Christian Dullo, Monika Dullo and the Topic Editor. Detail review by an anonymous reviewer.

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Correspondence to Soumyajit Mukherjee.

Appendices

Appendix 1

The compaction coefficient/uniaxial compressibility is (Fjar et al. 2008)

$$\Delta h/h{\text{ }}={\text{ }}{C_{\text{m}}}\alpha \Delta {P_{\text{f}}},$$
(29)

where Δh is the change in height of sedimentary layer due to compaction, h is the initial height of the layer, Cm is the coefficient of uniaxial compression, α is the Biot’s poro-elastic parameter, and ΔPf is the change in pore fluid pressure.

Appendix 2

As per Mukherjee (2017; also see Mukherjee 2018a, b, c for similar equations), kx is the density gradient along X-horizontal direction up to a distance l0 and ky is the density gradient along a perpendicular Y direction up to a distance b0. Vertically down along Z direction, and up to h0 distance porosity falls as per Athy’s exponential law. In this case,

$${\rho _{\text{e}}}={\text{ }}{\rho _{\text{m}}}+{\text{ }}0.5\left( {{k_x}{l_0}+{\text{ }}{k_y}{b_0}} \right){\text{ }}+{\text{ }}\left( {{\rho _{\text{m}}} - {\text{ }}{\rho _{\text{f}}}} \right){\emptyset _0}{z_1}^{{ - 1}}\lambda \left( {{{\exp }^{ - {\text{ho}}}}{\lambda ^{ - 1}} - 1} \right).$$
(30)

Symbols defined in “Conclusions and discussion”. ρe can be substituted in place of ρ in Eqs. (20) and (26) and proceeded for the subsequent derivations.

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Mukherjee, S., Kumar, N. A first-order model for temperature rise for uniform and differential compression of sediments in basins. Int J Earth Sci (Geol Rundsch) 107, 2999–3004 (2018). https://doi.org/10.1007/s00531-018-1634-6

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Keywords

  • Sediment compaction
  • Compression
  • Basin evolution
  • Thermal structure