Acid fracture operations in carbonate formations are used to create highly conductive channels from the reservoir to the wellbore. Conductivity in calcite formations is expected to be highest near the wellbore, where most of the etching occurs. The near wellbore fracture etched-width profile can be estimated from the measured temperature distribution. Temperature data can be obtained from fiber optic distributed temperature sensing (DTS) installed behind casings to monitor fracturing operations.

Heat transfer is commonly coupled in acid fracture models to account for temperature's effects on acid reactivity with carbonate minerals. Temperature profiles are usually evaluated during simulations of fracture fluid injection, but seldom during fracture closure. Since most of the acid is spent during injection, many models have assumed that the remaining acid reacts proportionally along the fracture length. Because of this assumption, neither acid spending nor temperature is usually simulated during fracture closure.

In this study, a fully integrated temperature model was developed wherein both the acid reaction and heat transfer were simulated while the fracture was closing. At each time step, transient heat convection, conduction, and generation were calculated along the wellbore, reservoir, and fracture dimensions. Modeling temperature during this transient period provides a significant understanding of the fracture etched-width distribution. During shut-in, cold fracture fluids are heated, mainly because of heat flow from the formation to the fracture. The amount of fluid stored in the fracture determines how fast the fluid is heated. Wider fracture segments contain larger amounts of cold fracture fluids, resulting in it taking longer to reach the reservoir temperature. Because of this phenomenon, near a wellbore, the vertical fracture etched-width profile can be determined from the temperature distribution. Also, minerals' spatial distributions along the wellbore's lateral can be estimated in multistage acid fracturing. This is done by minimizing the difference between the observed and modeled temperatures.

This evaluation of etched width profiles at the fracture entrance provides an estimation of fracture-conductive channel locations. Moreover, it has significantly improved the understanding of mineralogy distribution in multi-layer formations. This information will be particularly useful when designing acid fracturing jobs in nearby wells or revisiting the same wellbore for further stimulation.

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