The prediction of wellhead pressure for multiphase flow of vertical wells using artificial neural networks

Abstract

Multiphase flow through both vertical and horizontal tubulars is getting higher interest in the oil and gas industry. Prediction of wellhead pressure through vertical wells is a very critical point that has a great influence on different applications. In this research, an artificial neural network with backpropagation technique (ANN-BP) was used to predict the wellhead pressure (WHP) for multiphase flow for vertical well systems. This permits the calculation of the pressure drop across the vertical well section by knowing the bottom hole flowing pressure (BHP). More than 150 data sets from different wells in the Middle East with different conditions were used to build the model. About 80% of the data were used to train the model while the rest unseen 20% were used to test and validate the model. The network structure, including the training function, the transfer function, the number of hidden layers, and the number of neurons in each layer, was highly optimized by trying different combinations of each parameter. The developed ANN model yielded high accuracy in predicting the WHP with an average absolute percentage error (AAPE) for both training and testing which are 0.61% and 1.13%, respectively. The optimized model comprised a single hidden layer with 20 neurons activated with the transfer function “tansig.” The correlation coefficient between the actual and predicted values for both training and testing was 0.98. A new empirical equation was then developed to mimic the developed ANN model by extracting the network weights and biases. The developed ANN-based correlation outweighs the previously established correlations in the literature upon comparison using unseen dataset.

Appendix

The developed ANN-based model was validated by comparing its results and those obtained from the previously published correlations listed in the following table. Pressure drop was calculated based on these correlations and then subtracted from the bottom hole pressure to produce the final wellhead pressure. These empirical correlations defined the total pressure drop gradients ${\left(\frac{dp}{dl}\right)}_t$ as the summation of three different components as follows, Eq. (6);

$$ {\left(\frac{dp}{dl}\right)}_t={\left(\frac{dp}{dl}\right)}_f+{\left(\frac{dp}{dl}\right)}_h+{\left(\frac{dp}{dl}\right)}_a $$

(6)

where ${\left(\frac{dp}{dl}\right)}_f$ is the pressure drop gradient due to friction, ${\left(\frac{dp}{dl}\right)}_h$ is the pressure drop gradient due to hydrostatic head, and ${\left(\frac{dp}{dl}\right)}_a$ is the pressure drop gradient due acceleration.

Both the hydrostatic pressure drop term and the acceleration term can be defined as general terms for all correlations and can be calculated by the following Eqs. (7) and (8).;

$$ {\left(\frac{dp}{dl}\right)}_h=\rho gcos\theta $$

(7)

$$ {\left(\frac{dp}{dl}\right)}_a=-\rho v\frac{dv}{dl} $$

(8)

where ρ is the fluid density, g is the gravity acceleration, θ is the inclination angle with respect to the vertical direction, v is the fluid velocity, and l is the pipe length.

The pressure drop gradient due to friction varies from one correlation to another. A summary of pressure drop gradient due to friction of each used correlation is shown in Table (3).

Table 3 A summary of the pressure drop gradient due to friction for the used empirical correlations for multiphase flow (Brill and Mukherjee 1999)