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Response of Upper Jurassic (Malm) Limestone to Temperature Change: Experimental Results on Rock Deformation and Permeability

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Abstract

The present study aimed to quantify the thermally induced deformation and the associated evolution of permeability in Blaubeuren limestone, an outcrop analogue of the Upper Jurassic (Malm) carbonate formation, providing references for hydro-thermo-mechanical responses of the reservoir rock to temperature changes within future enhanced geothermal systems as located in the Southern German Molasse Basin. Experiments deriving the changes in the primary (water-accessible) pore volume and the bulk volume of three water-saturated rock samples were conducted via loading the samples to defined stress states (\({\sigma}_{3}\) of 15 MPa; \({\sigma}_{1}\) of up to 75 MPa ), respectively, and then cycling sample temperature between 30 °C and defined levels up to 120 °C at a sustained pore pressure of 0.5 MPa. Permeability was measured under isothermal conditions at each attained temperature. The primary voids dilated upon heating and partly contracted via cooling in each applied temperature cycle yielding thereby residual dilation. However, the concomitant bulk sample deformation manifested residual compaction. The permeability increased with increasing temperature and showed residual decreases by the end of the temperature cycling tests. Flow of pore fluid from the primary voids into the secondary voids at increased temperatures due to the decreased fluid viscosity mimicked irreversible dilation in the primary voids. The interplay between pressure solution-driven compaction and thermal expansion in rock solids was considered to account for the sample deformation and the development of permeability. It is presumable that the pressure solution-driven compaction and the contraction in rock solids would influence the long-term hydro-thermo-mechanical behavior of the Upper Jurassic carbonate reservoir rocks in the cooling process related to fluid injection at the geothermal systems located therein.

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Abbreviations

THMC:

Thermo-hydro-mechanical- and chemical-coupled process

EGS:

Enhanced geothermal systems

SEM:

Scanning electron microscopy

MTS:

Mechanical testing system

\({V}_{b}\) :

Bulk volume of rock samples

\({V}_{s}\) :

Volume of rock solids

\({V}_{pb}\) :

Overall pore volume

\({V}_{p}\) :

Primary pore volume

\({V}_{ps}\) :

Secondary pore volume

\(m\) :

Volume fraction of primary voids in the overall void space

\({\Phi}_{b}\) :

Overall porosity

\({\Phi}_{p}\) :

Porosity related to primary voids

\({\Phi}_{p}^{^{\prime}}\) :

Approximated porosity of primary voids accounting for the effects of thermal expansion (contraction) in rock solids and pressure solution only

\({\Phi}_{s}\) :

Porosity related to secondary voids

\({\alpha}_{s}\) :

Volumetric thermal expansion coefficient of rock solids composed of calcite

\({V}_{s0}\) :

Initial volume of rock solids at the onset of temperature cycles

\({V}_{p0}\) :

Primary pore volume at the onset of temperature cycles

\({V}_{b0}\) :

Bulk sample volume at the onset of temperature cycles

\(d{V}_{out}\) :

Volume of outflow from the downstream side of the rock samples during the permeability measurements

\({\sigma}_{1}\) :

Axial stress

\({\sigma}_{3}\) :

Confining pressure

\({p}_{P}\) :

Pore pressure

\({dp}_{p}\) :

Differential pore pressure applied over the length of the rock samples during permeability measurements

\({\sigma}_{V}\) :

Vertical stress due to overburden

\({p}_{f}\) :

Formation fluid pressure

\({\sigma}_{H}\) :

Maximum horizontal stress

\({\sigma}_{h}\) :

Minimum horizontal stress

\(\tilde{\sigma}\) :

Mean stress

\({\varepsilon}_{vb}\) :

Bulk volumetric strain

\({\varepsilon}_{vb}^{exp.}\) :

Thermal expansion (contraction) in rock solids approximating reversible deformation in the overall void space upon temperature cycling

\({\varepsilon}_{vb}^{irr.}\) :

Irreversible (time-dependent) bulk volumetric strain as developed in the isothermal stage at each attained temperature

\({\dot{\varepsilon}}_{vb}^{irr.}\) :

Rate of irreversible bulk volumetric strain at each attained temperature

\({\varepsilon}_{vp}\) :

Pore volumetric strain in the primary voids

\({\varepsilon}_{vp}^{irr.}\) :

Irreversible (time-dependent) pore volumetric strain in the primary voids as developed in the isothermal stage at each attained temperature

\({\dot{\varepsilon}}_{vp}^{irr.}\) :

Rate of irreversible pore volumetric strain in the primary voids at each attained temperature

\({\tilde{\sigma}}_{d}\) :

Mean effective stress

\(M\) :

A constant in an empirical power-law relation of the irreversible compaction rates to the applied mean effective stress

\(i\) :

An index depicting the power-law dependence of the irreversible compaction rates on the applied mean effective stress

\({\varepsilon}_{vc}\) :

Pressure solution-driven compaction strain

\({\dot{\varepsilon}}_{vc}\) :

Pressure solution-driven compaction rate

\(k\) :

Sample permeability

\(l\) :

Length of the rock samples

\(A\) :

Cross-sectional area of the rock samples

\(\mu\) :

Temperature-dependent viscosity of deionized water

\({C}^{*}\) :

A point in the strain–stress curves indicating the onset of inelastic compaction upon deviatoric loading

\({C}^{*{^{\prime}}}\) :

A point in the strain–stress curves indicating the onset of shear dilation upon deviatoric loading

\(t\) :

Time (instants)

\({T}_{a}\left(t\right)\) :

Ambient temperature in the laboratory varying with time

\({T}_{a0}\) :

Average ambient temperature

\({T}_{c}\left(t\right)\) :

Cell temperature as a function of time

\({T}_{c0}\) :

Initial value of cell temperature in a studied heating (cooling) ramp

\({T}_{i}(L, t)\) :

Induced temperature as a function of the position along the length of the external capillary tubes and time

\(L\) :

Positions along the length of the external capillary tubes

\({\text{D}}\) :

Diffusivity of calcite within the grain boundary fluid phase

\({\text{C}}\) :

Solubility of calcite within the grain boundary fluid phase

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Acknowledgements

The authors thank Liane Liebeskind for assistance and operation of the MTS rock deformation apparatus and Fiorenza Deon for the acquisition of the SEM-micrographs. Inspiring discussions with Christopher J. Spiers and constructive comments by the editors and two reviewers helped to improve the manuscript and are greatly acknowledged. The present study was funded by the IMAGE-Project within the 7th Framework Program of the EU (Grant No.: 608553).

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Authors and Affiliations

  1. Helmholtz-Zentrum Potsdam - Deutsches GeoForschungsZentrum GFZ, Telegrafenberg, 14473, Potsdam, Germany

    Liang Pei, Guido Blöcher, Harald Milsch, Günter Zimmermann & Ernst Huenges

  2. Wuhan Institute of Rock and Soil Mechanics, Chinese Academy of Science, Xiaohongshan, 430071, Wuhan, People’s Republic of China

    Liang Pei & Xiaochun Li

  3. Institute for Applied Geosciences, Technical University Darmstadt, 64287, Darmstadt, Germany

    Ingo Sass

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  1. Liang Pei
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Pei, L., Blöcher, G., Milsch, H. et al. Response of Upper Jurassic (Malm) Limestone to Temperature Change: Experimental Results on Rock Deformation and Permeability. Rock Mech Rock Eng 54, 337–358 (2021). https://doi.org/10.1007/s00603-020-02270-5

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