Downhole temperature data obtained by either temperature logging or fiber-optic cables have been used to evaluate stimulation treatments and post-stimulation performance of horizontal wells with multiple fractures. Field cases qualitatively show capabilities of detecting creation of transverse fractures, poor zonal isolation, and inflow locations, although downhole temperature behavior in those wells are not fully understood from the theoretical modeling perspective.

In this study, we present comprehensive numerical flow and thermal models for a horizontal well with multiple fractures. The well experiences single-phase water flow during injection and shut-in, and gas-water two-phase flow during production. These models are formulated for reservoir and wellbore domains with consideration of their coupling. The reservoir models are formulated in three-dimensional space on the basis of mass conservation of each component and thermal energy conservation with Darcy's law in transient conditions. The wellbore models are also transient, and formulated for one-dimensional space on the basis of mass conservation of each component, conservation of combined-phase momentum, and total energy conservation. The wellbore and sandface temperature profiles are obtained as solutions of these models. These models enable us to simulate field operations in multi-stage fracturing treatment; injection and shut-in occur alternately for each stage from toe to heel with zonal isolation. Following the stimulation treatments, these models are used to simulate temperature behavior during production in gas-water two-phase flow.

We show an example of a single fracture in which the developed model simulates temperature behavior during injection, shut-in and production to show capabilities of the developed model. This study shows injected fluid makes the fluid temperature in the fracture lower than the geothermal temperature even after one month of shut-in. This affects the temperature interpretation during production because the initial temperature is different from the geothermal temperature assumed as initial temperature by most studies published before. A synthetic case with five fractures demonstrates capabilities of detection of created fracture locations from the shut-in temperature profile. In addition, we apply the model to a field case. The case studies justify qualitative interpretations in situations occurring in fields such as warm-up behavior with multiple clusters during shut-in period.

This paper provides insights from the theoretical modeling perspective for the downhole temperature interpretation qualitatively performed at current time. It also discusses validity and precautions of the assumptions made in previous studies.

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