There are still many challenges involved with the quantitative interpretation of downhole distributed‐temperature measurements for diagnosing multistage‐fracturing treatments in horizontal wells. These challenges include handling enormous amounts of data measured by the sensors in a continuous time and space domain, a ready‐to‐use fast and robust forward model to simulate temperature behavior, and an efficient algorithm to invert 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 becomes extremely complicated when the measured temperature is inverted to a downhole flow profile. In this study we present an approach for combining forward and inverse models to interpret downhole temperature data. Our goal was to improve computational efficiency. Field data from a gas well in the Marcellus Shale were used to illustrate the feasibility of quantitative interpretation of temperature measurement for fracture diagnosis.

The forward model used the fast‐marching method (FMM). The forward simulation was an order of magnitude faster than the semianalytical model, which is the essential contribution for successfully applying the method in the field case. The improved inversion procedure increased the efficiency of the interpretation. The inversion procedure began with a sensitivity study to select the inversion parameters among various other parameters, such as fracture half‐length and the fracture conductivity, and to determine the impact of their uncertainty on inversion. The inversion model used the initial analysis of the temperature gradient to identify the fracture locations with significant temperature changes for interpretation and eliminated the rest of the fracture locations from interpretation. Thus, we obtained a prior estimation of the selected inversion parameters, which was used as an initial estimate for the inversion process. This prior estimation saved significant computation. The inversion was performed fracture by fracture using either parallel computing or sequential computing on the basis of the sensor locations.

We began with a synthetic example containing multiple fractures to illustrate the approach and test the procedure accuracy and computation speed. The primary inversion parameter was flow rate, though we also interpreted either fracture length or fracture conductivity when assuming all the other parameters as additional constraints. With an adequate initial estimate, the inverted parameters matched the reference “true value” properly. The inversion process converged with reasonable iterations for each fracture (2–3 iterations). The operation time highlights the advantages of the inversion approach presented in this paper. The guided initial estimation ensured that the gradient inversion approach converged and avoided local minimization. Finally, a field application for interpreting the DTS measurement for the flow profile of the multistage‐fractured horizontal well was performed using this inversion method, and it showed encouraging results.

The results of our investigation illustrate the procedure feasibility for using temperature data to diagnose a multistage‐fracturing treatment. Our proposed inversion model was fast and reliable and provided a promising tool that can be used to quantitatively interpret downhole temperature data.

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