This paper investigates the impact of modeling assumptions on the fidelity of thermal transient simulations. Numerical diffusion and the impact of ignoring the heat capacity of the pipe and ground are examined. An RC time constant formulation for the ground around the pipe is presented. Simulations examine temperature front propagation and pressure induced thermal transients.
Thermal effects can significantly influence both steady state conditions and the propagation of transients through the pipeline. Often neglected is the impact of the transient response of the pipeline surroundings on the propagation of transients through the pipeline. It is tempting to focus is on the transient modeling of the pipeline fluid without considering the transient modeling of the pipeline surroundings. Using buried natural gas pipelines as an example, this paper will demonstrate how the pipeline surroundings influence the in-pipe transients. Because of ground effects, the time required for a buried pipeline to move from one steady temperature profile to another is often measured in weeks or even months. The most common approximation to representing the ground around a buried pipeline is as a resistive heat loss to an ambient "ground" temperature. In this approach, the heat flux to the ground is represented by a heat transfer coefficient (HTC). We will examine the validity of this approximation both through analysis and simulation. We will demonstrate that the time response of the pipe wall and the ground can be represented by a characteristic time constant. We will show how this time constant can be computed from the density, specific heat, and thermal conductivity of the pipe and ground. This paper also examines the numerical diffusion that results from modeling the pipeline using an Eulerian formulation. The Eulerian formulation represents the pipeline state at fixed points along the pipeline. The alternative, a Lagrangian formulation, represents the pipeline state using points that move at the velocity of the fluid. We examine numerical diffusion by simulating the pipeline adiabatically (i.e. no heat flow from the pipeline fluid to the pipe wall or the pipe surroundings). Using this approach, we can observe how numerical diffusion affects the modeling of a temperature front moving through the pipeline independently from other real smoothing affects such as the absorption of the fluid heat by the pipe wall and ground. After demonstrating the very real effects of numerical diffusion, we move on to demonstrate how the pipe wall and pipe surroundings modify the transient thermal effects. We demonstrate that, at least for buried pipelines, the thermal mass of the pipe and ground have such great affect that numerical diffusion can in fact be dealt with by appropriate selection of the modeling distance step. Three pipeline conditions are examined:
An 8 inch buried gas pipeline with 8 feet of soil between the pipeline and "ambient" temperature.
A 24 inch buried gas pipeline with 8 feet of soil between the pipeline and "ambient" temperature.
A 24 inch buried gas pipeline with 4 feet of soil between the pipeline and "ambient" temperature.