Inversion of Downhole Temperature Measurements in Multistage Fracture Stimulation in Horizontal Wells
Authors: Zhang Shuang , Zhu Ding 
Published: October 2017

Abstract
Today there are still many challenges in the quantitative interpretation of downhole distributed temperature measurements to diagnose multistage fracture treatments in horizontal wells. These challenges include handling enormous amount of data measured by the sensors continuously in time and space domain, a readily-to-be-used fast but robust forward model to simulate temperature behavior, and an efficient algorithm to inverse the parameters that are of interest. Because multistage fracturing involves many uncertain parameters; ranging from reservoir properties to treatment design, to fracture geometries and conductivity; the problem is extremely complex when inverse the measured temperature to a downhole flow profile. This study presents an approach to combine forward and inversion models to interpret downhole temperature data. The goal is to improve computational efficiency. Examples use the field data from a gas well in Marcellus shale formation to illustrate the feasibility of quantitative interpretation of temperature measurement for fracture diagnosis.
The forward model uses the fast marching method. The forward simulation is order-of-magnitude faster than even the semi-analytical model, which is the essential contribution to apply the method in the field case successfully. The inversion procedure starts with a sensitivity study to select the inversion parameters among various parameters such as fracture half-length, fracture conductivity, and determine the impact of their uncertainty on inversion. The inversion model uses the initial analysis on temperature gradient to identify the zones with significant temperature changes for interpretation and eliminates the rest of the data from interpretation. Thus, we obtain a prior estimation of the selected inversion parameters, which will be used as an initial guess of the inversion process. This prior estimation saves significant computation. The inversion is performed fracture by fracture either using parallel computing or sequential computing based on the sensor locations.
We first show a synthetic example with multiple fractures to illustrate the approach, test the procedure accuracy and computation speed. The primary inversion parameter is flow rate, and either fracture length or fracture conductivity, with all other parameters as an additional constraint. With an adequate initial guess, the inverted parameters match the reference "true value" properly. The inversion process converges with limited iterations for each fracture. The operation time highlights the advantages of the inversion model. The guided initial guess ensures the gradient inversion method converge and avoid local minimization. Finally, a field application is performed using this inversion model and shows encouraging results.
The results of the paper illustrate the feasibility and procedure of using temperature date to diagnose multistage fracture treatment. The proposed inversion model is fast and reliable which provides a promising tool that can be used to interpret downhole temperature data quantitatively.