Temperature Transient Modeling and Analysis for Hydraulically Fractured Wells

Abstract

In this work, new analytical sandface temperature solutions are developed for linear flow towards an infinite-conductivity hydraulically fractured well producing under specified constant-rate or constant- bottomhole pressure (BHP) production. The solutions apply for slightly compressible, single-phase undersaturated oil reservoirs with irreducible water saturation or liquid-dominated geothermal reservoirs. They include the effects of conduction, convection, the Joule-Thomson expansion of fluids and adiabatic expansion of the total rock and fluid system, and fluid loss fracture damage. They neglect the variation of rock and fluid properties with pressure and temperature so that pressure diffusivity and thermal energy balance equations are decoupled to obtain the analytical linear-flow temperature solutions using Laplace (for constant-rate) and Boltzmann (for constant-BHP) transformations. To validate the analytical solutions, a numerical solution is developed to solve the mass and thermal energy balance equations simultaneously and account for the variation of rock and fluid properties with pressure and temperature. We proposed a correction to fluid viscosity variation as input for the analytic solutions. The numerical and analytical solutions have been compared and verified with a commercial thermal reservoir simulator. Results indicate that the fracture surface temperature is decreasing with a square of time for constant-rate production but is constant for constant BHP 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 for both production modes as the matrix permeability decreases. The fracture damage has different signatures on temperature transients at early and late times for both modes 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 thermal and mechanical properties of the rock and fluids. The numerical solution can be used for a more general analysis procedure based on automated history matching for constant as well as variable rate and pressure production test sequences.