Mathematics of Surface Facility Models – A Supplementary Description

The focus of this study is on the mathematical description of surface facility models that employ hydraulic relationships. Hydraulic equations are mathematical formulas that directly convert pressure loss into rates. They do this by considering pipes as a network of nodes and connection. To do so, first a single producing well under constant tubing head pressure, and later a single manifold combining two production streams are considered here. For each model, the mathematical description, method of assembling Jacobian matrices, and number of iterations required to satisfy the Newton-Raphson method are explained. Additionally, it was demonstrated how to investigate the dynamic behavior of surface facility models in relation to hydraulic relationships, including pipeline characteristics, the manifold s equilibrium pressure, the maximum amount of the system s deliverability, and the appropriate separator pressure selection. This work presents a supplementary description to the mathematics of the surface facility model to facilitate the implementation of hydraulic relationship in the modeling and development of surface facility simulators.