Inversing Fracture Parameters Using Early-Time Production Data For Fractured Wells

The authors studied models of inversing fracture parameters using early-time production data from fractured wells. Inverse results help evaluate the performance of fracturing, improve fracturing design, and predict the long-term production dynamics of fractured wells. First, polynomials were used to match variable flows. A new analytical model describing the transient-pressure behaviour of variable flow production was developed. This model is significantly superior to existing superposition analysis models in terms of calculation speed, accuracy, and stability. Then, in order to establish the best match between the calculated bottomhole pressure and the actual measured bottomhole pressure, the wellbore storage coefficient, fracture conductivity, fracture half-length, and fracture skin factor were selected as inverse fracture parameters. An automatic matching model was established, and a Levenberg-Marquardt algorithm based on a stochastic initial value and maximum probability was developed. This algorithm (1) is easy to implement, (2) can search local optimal solutions as much as possible, and (3) to improves the multisolution of inverse problems. Finally, the sensitivity of fracture parameters was analysed. Some existing automatic matching methods were compared and validated. A set of accurate, high-precision data acquisition and calculation devices was identified to promote application of the results.