Optimum fluid placement is crucial for a successful acid-stimulation treatment, both for horizontal wells where there is a broad variation of reservoir properties along the wellbore and for vertical wells with multiple zones and/or extensive productive intervals. Recently, distributed-temperature-sensing technology has enabled us to observe dynamic temperature profiles along a well-bore during and after an acid treatment. This technology allows us to monitor and evaluate treatments in real time by capturing a sequence of temperature profiles at different times and inverting temperature response to acid-injection profiles. We have developed mathematical models to simulate the temperature behavior along a wellbore, horizontal or vertical, during and just after an acid treatment. This approach couples a wellbore model and a near-wellbore formation thermal model considering the effects of both mass and heat transfer between the wellbore and the formation. The models account for all significant thermal processes involved during a treatment, including heat of reaction, conduction, and convection. An inversion procedure is applied to interpret the acid-distribution profiles from the measured temperature profiles. For horizontal wells, the results indicate that the distribution of stimulation fluid along a lateral and the effectiveness of diversion processes during an acid treatment can be quantified in real time using distributed-temperature measurements. The model shows that the relative injectivities into different zones can be interpreted from the temperature response measured during injection. For vertical wells, we have focused on diagnosing the volume of acid placed in each zone from the flowback temperature history. During the flowback period, the zones that have taken more acid volume will show more heating because of reaction and will have higher temperature when hotter fluid enters the wellbore. This provides a mechanism to quantitatively determine the acid distribution. The methods developed from this study can help to diagnose and optimize acidizing design, and improve the efficiency of acid stimulation.
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