Solution of a One-Dimensional Three-Phase Flow in Horizontal Wells Using a Drift-Flux Model

Abstract

To design wells and its equipments along the oil fields, one has to solve the flow that occurs inside the oil reservoirs and its injecting and producing wells. This work presents a multiphase isothermal flow model to the solution for horizontal wells using a drift-flux model (water, oil and gas) along a one-dimensional domain. The problem is discretized with a Finite Volume Method and solved using Newton’s Method. As a drift-flux model is a homogeneous model, it uses the mixture momentum and continuity equations and it is also necessary to solve the gas and oil phase continuity equations in order to solve the three-phase flow. Lateral mass inflow, due to the flow from reservoir to well, is considered as a source/sink term in the one-dimensional continuity equations. Spatial and temporal interpolation schemes are of first order, mostly upwind schemes. Results are compared with a CMG-IMEX blackoil reservoir simulator. The algorithm is implemented using a C++ OOP programming language and all the derivatives of the Jacobian Matrix are calculated numerically, making the code more generic, allowing user to change property models and drift parameters according to the problem. The study of the coupling between well and reservoirs is a state-of-art research activity. Most of the important petroleum companies are developing proprietary softwares for modeling as much as possible the several phases of the oil production chain.