Mathematical modelling of transient flow and heat transfer in a producing gas well

Abstract

This thesis focuses on the mathematical modeling of transient flow in a producing gas well. A producing gas well is a well that has enough pressure to push the gas from the reservoir to the wellhead. Most previous models considered steady state conditions with simplified governing equations that neglect some important parameters such as gas compressibility and gas flow propagations. This situation led to partial prediction or poor perception of the behavior of the flow characteristics, making it difficult to predict the productive capability of the producing well and could also lead to its early or premature closure. The present work incorporates a source term in the governing equations which take into account the inflow, well geometry, temperature difference and sound wave propagation. Other parameters considered include the thermal conductivity of the flow environment, the formation permeability, the inclination angles of well, and the diameter of the tubing, casing and wellbore. The governing equations comprising non-linear partial differential equations are solved numerically using the finite difference implicit Steger-Warming flux vector splitting method (FSM). Validation with an existing work has been carried out with a well-depth of 3000 m, wellhead and bottomhole pressure 9.5 of Mpa, well temperature 273 K, and mass flow rate of 9 kg/s. In determining the productive capability of the gas well, the inflow characteristics from reservoir to the bottom of the wellbore at different mass flow rates and inclinations of the well are considered. At reservoir pressure of 6000 Mpa, wellbore pressure 5800 Mpa, inlet velocity 40 m/s and productivity index of 20 Mpa, with the mass flow rate varying from 2 kg/s to 9 kg/s, and inclination angles taken to vary at 15o intervals, the inflow characteristics from the reservoir to the bottom of the wellbore are observed to be increasing with depth, which indicate that the gas well under consideration is capable of production. However, when the mass flow rate is less than 2 kg/s, the inflow pressure, temperature and velocity decrease indicating the inability of the well to produce. Temperature changes between the flowing fluid and formation interface are observed to influence the inflow characteristics which also depend on the outer diameter of tubing, casing and their thermal conductivities.