## Abstract

This work presents novel analytical temperature-Transient solutions for matrix linear flow toward an infinite-conductivity hydraulically fractured well producing under specified constant rate (CR) or constant bottomhole pressure (CBHP) production. The solutions apply to the single-phase flow of a slightly compressible fluid with constant viscosity (e.g., undersaturated oil reservoirs with irreducible water saturation or liquid-dominated geothermal reservoirs). They include the effects of conduction, convection, the Joule-Thomson (J-T) expansion of fluids and adiabatic expansion of the total rock and fluid system, and fluid loss fracture damage and assume constant rock and fluid physical and thermophysical properties with pressure and temperature. They are obtained by using Laplace (for CR) and Boltzmann (for CBHP) transformations. To validate the analytical solutions, an in-house numerical solution is also developed. It solves the mass and thermal energy balance equations coupled simultaneously and accounts for the variation of rock and fluid properties with pressure and temperature. The in-house simulator was validated by using a commercial reservoir simulator. Results indicate that the fracture surface temperature is decreasing with a square root of time for CR production but is constant for CBHP production. The temperature responses for both modes of production are controlled by the adiabatic expansion of the rock and fluid properties and the thermal diffusivity of the rock. The effect of thermal conductivity plays a significant role in both production modes as the matrix permeability decreases. The fracture damage has different signatures on temperature transients depending on the mode of production. The approximate analytical solutions show the information content of temperature-Transient data acquired from an infinitely conductive hydraulically fractured well under matrix linear flow. They are simple and can be used to perform matrix linear-flow analysis jointly with pressure and rate transient data to estimate the physical and thermophysical properties of the rock and fluids. We also propose a simple correction to fluid viscosity variation as input for the analytic solutions to accurately estimate the physical and thermophysical parameters in case drawdowns are significant.

Original language | English |
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Pages (from-to) | 1793-1817 |

Number of pages | 25 |

Journal | SPE Journal |

Volume | 28 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2023 |

### Bibliographical note

Publisher Copyright:© 2023 Society of Petroleum Engineers. All rights reserved.

### Funding

The support of the member companies of the University of Tulsa Petroleum Reservoir Exploitation Projects (TUPREP) is gratefully acknowledged. The authors acknowledge the Computer Modeling Group for making available multiple STARS licenses.

Funders | Funder number |
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TUPREP | |

University of Tulsa Petroleum Reservoir Exploitation Projects |