The desire to have accurate bottom-hole pressure (BHP) data can come during different phases of a well's life, including well design, mini-frac test, well testing, and production analysis. But frequently, it is not practical, feasible, or economic to deploy a pressure gauge to measure the BHP directly. In most cases, however, the unknown flowing BHP is calculated from the known parameters and surface measurements using multiphase correlations or mechanistic modeling. Recently, artificial neural network (ANN) techniques have been adopted to predict BHP and proved to have better prediction performance than other conventional prediction methods. With the design applied in this study, the use of ANN techniques can be more fully utilized to solve complex multiphase flow problems, such as pressure gradient prediction and complex well trajectories.
Back-propagation (BP) neural network models have been modified to fit into the piece-wise calculation procedures of multiphase correlations to achieve higher prediction accuracy and broaden the prediction range. The model training requires well-segment-scale data sets, which contain pressure gradients as the model output and the model inputs, including inclination angle, liquid and gas superficial velocities, gas-liquid surface tension, liquid density, specific gravity of free gas, liquid and gas viscosities, average pressure and temperature. Different BP neural network model structures have been tested to find a suitable neuron number in the hidden-layer of the model. Two pressure gradient prediction models were trained for slug flow and annular mist flow.
Ultimately, a combined BHP calculation procedure was designed combining the multiphase correlations and trained ANN models. The statistical tests using the collected data showed that the combined procedure gave the best prediction performance against the eleven multiphase correlations studied in this work and had the lowest average absolute percent error of 3.1% and standard deviation of 0.034. Independent field data was used to test the extendibility of the combined procedure prediction range. Comparing to the multiphase correlations, the combined procedure gave fairly accurate predictions with an average absolute percent error of 23.0% and a standard deviation of 0.176. To facilitate field application, a multiphase flow BHP calculator with a user interface was developed.