Analytical Solution of Buckley-Leverett Equation For Oil-Water Flow Using Artificial Neural Network Based Relative Permeability Model A. Wahyudi (a), T. Marhaendrajana (a), Z. Syihab (a), K.A. Sidarto (b)
a) Petroleum Engineering, Bandung Institute of Technology
Jalan Ganesha 10, Bandung 40132, Indonesia
a) Mathematics, Bandung Institute of Technology
Jalan Ganesha 10, Bandung 40132, Indonesia
Abstract
This paper presents an approximation of the oil-water relative permeability equation using Deep Learning to solve the Buckley-Leverett equation analytically. An artificial neural network-based approximation was developed to obtain two network models, namely for relative water permeability and oil relative permeability. Initially, an approximation of the oil-water relative permeability equation is prepared based on empirical data on relative permeability. Next, this approximation is used in the fractional flow equation to solve the equation analytically. To verify the model, the resulting solution is compared with an analytical adjustment based on the Corey relative permeability model. The comparison shows that the analytical solution based on the artificial neural network model has reasonable agreement with the solution based on the Corey model. The artificial neural network model was developed using the Tensorflow Python library. The advantage of using this library is the automatic gradient capability so that derivatives of fractional flow equations can be obtained and used in analytical solutions. Mathematically, approximation using artificial neural network has the advantage of a relative permeability value that is continuous along the saturation value.
