Effect of Temperature on Stiffness of Sandstones from the Deep North Sea Basin
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ORIGINAL PAPER
Effect of Temperature on Stiffness of Sandstones from the Deep North Sea Basin Tobias Orlander1 · Katrine Alling Andreassen1,2 · Ida Lykke Fabricius1 Received: 5 December 2019 / Accepted: 10 September 2020 © The Author(s) 2020
Abstract Development of high-pressure, high-temperature (HPHT) petroleum reservoirs situated at depths exceeding 5 km and in situ temperature of 170 °C increases the demand for theories and supporting experimental data capable of describing temperature effects on rock stiffness. With the intention of experimentally investigating temperature effects on stiffness properties, we investigated three sandstones from the deep North Sea Basin. As the North Sea Basin is presently undergoing substantial subsidence, we assumed that studied reservoir sandstones have never experienced higher temperature than in situ. We measured ultrasonic velocities in a low- and high-stress regime, and used mass density and stress–strain curves to derive, respectively, dynamic and static elastic moduli. We found that in both regimes, the dry sandstones stiffens with increasing testing temperature and assign expansion of minerals as a controlling mechanism. In the low-stress regime with only partial microcrack closure, we propose closure of microcracks as the stiffening mechanism. In the high-stress regime, we propose that thermal expansion of constituting minerals increases stress in grain contacts when the applied stress is high enough for conversion of thermal strain to thermal stress, thus leading to higher stiffness at in situ temperature. We then applied an extension of Biot’s effective stress equation including a non-isothermal term from thermoelastic theory and explain test results by adding boundary conditions to the equations. Keyword Sandstones · Rock stiffness · Temperature · Effective stress List of Symbols 𝛼 Biot’s coefficient 𝛽 Volumetric thermal expansion coefficient 𝜂 Linear thermal expansion coefficient 𝜌d Dry density 𝜌m Grain density 𝜙 Porosity k Permeability 𝜎Biot Biot’s effective stress 𝜎dra Total stress 𝜎P Pore pressure reduced by Biot’s coefficient 𝜎eff Non-isothermal effective stress 𝜎H Hydrostatic stress
* Tobias Orlander [email protected] Ida Lykke Fabricius [email protected] 1
Department of Civil Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark
Present Address: Niras A/S, Kgs. Lyngby, Denmark
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𝜎A Axial stress 𝜎R Radial stress P Pore pressure T Temperature 𝜀Biot Strain resulting from Biot’s effective stress 𝜀dra Strain resulting from total stress 𝜀P Strain resulting from pore pressure 𝜀T Strain resulting from temperature 𝜀 Strain resulting from the non-isothermal effective stress 𝛿 Strain resulting in volume expansion 𝜁 Potential strain Δ Change Δ𝛼∕ΔT Γ tP First arrival time of P-wave tS First arrival time of S-wave VP P-wave velocity VS Shear wave velocity Esta Static Young’s modulus Edyn Dynamic Young’s modulus Ks Solid bulk modulus KQ Quartz bulk modulus
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Vol.:(0123456789)
KC Calcite bulk modulus Kdra
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