Theoretical Basis for Interpretation of Temperature Data During Acidizing Treatment of Horizontal Wells

Optimum fluid placement is crucial for successful acid-stimulation treatments of long horizontal wells where there is a broad variation of reservoir properties along the wellbore. Various methods have been developed and applied in the field to determine the fluid placement and effectiveness of the diversion process, but determining the injection profile during the course of matrix acidizing still remains a challenge. Recently, distributed temperature-sensing (DTS) technology has enabled us to observe the dynamic temperature profile along the wellbore during acid treatments. Quantitative interpretation of dynamic temperature data can provide an invaluable tool to assess the effectiveness of the treatment as well as optimize the treatment through on-the-fly modification of the treatment parameters such as volume, injection rate, and diversion method. In this paper, we discuss how fluid placement can be quantified using dynamic temperature data. A mathematical model has been developed to simulate the temperature behavior along the wellbore during and shortly after acid treatments. This model couples a wellbore and a near-wellbore flow and thermal model considering the effect of both mass and heat transfer between the wellbore and the formation. The model accounts for all significant thermal processes involved during a treatment, including heat of reaction, conduction, and convection. Then, an inversion procedure is applied to interpret the acid-distribution profile from the measured temperature profiles. To illustrate how to apply the model and analyze the DTS data, examples of matrix acidizing are presented. The temperature, flow, and pressure data were generated by a horizontal well-acidizing simulator. The inverse model is verified, and the effect of the distribution of stimulation fluid along the lateral and the effectiveness of the diversion processes on the transient temperature response is also discussed. We address some issues regarding solving the inverse problem and discuss the alternative methods of using warm-back information for cases in which inversion is difficult.