Heat flow and frictional heating often have a major impact on the hydraulics of a pipeline. An accurate pipeline simulation frequently needs some form of thermal model. Many different approaches are in common use for these models, ranging from a simple assumption of isothermality to detailed transient models of heat flow in the fluid, pipe wall, and surrounding material. Elaborate thermal models can be difficult to create and time-consuming to execute, so it is important to understand the level of detail needed for a given application. This paper investigates the impact of the thermal model on the overall pipeline model accuracy, especially on the linepack (for gas pipelines) and throughput. The isothermal assumption, various types of transient and steady-state fluid thermal models, and coupled transient fluid and ground thermal models are compared for pipelines gas and liquid pipelines.

1. Introduction

Every pipeline simulation must include some sort of thermal model. This can be as simple as an assumption that the fluid in the pipe is always at a fixed temperature, or as complex as a fullblown transient model that calculates heating and energy flow in both the fluid and the ground. For some applications, the results of a pipeline model depend heavily on the accuracy of the associated thermal model; in other cases, an "isothermal" (constant temperature) model is perfectly sufficient. This article evaluates several techniques for fluid and ground thermal modeling with an eye to applicability to common calculations on gas and liquid pipelines. The goal is to determine the level of error that can be expected with different thermal modeling approaches for capacity calculations, linepack calculations, survival-time analysis, and leak detection. First, the physics of thermal behavior of fluid flowing (or sitting) in pipes will be briefly covered. Then, the components of a complete thermal model will be described and compared with common approximations. The equations used for calculating heat flow into and inside the ground also are important parts of the thermal model; two ways of modeling the heat flow into and within the ground will be discussed. The accuracies of the different fluid and ground thermal models will be compared. Next, there will be a discussion of the effects of poor knowledge of difficult-to-predict quantities such as ground temperature and ground thermal conductivity on the models' accuracies. The fanciest thermal model is only as good as the data used to drive it, which often is not very good.

2. Thermal Behavior of Fluids in Pipes

Thermal models based on different approximations have varying degrees of success at handling different thermal phenomena. Before going into the details of the different types of commonly used thermal models, those effects that will be examined in this article are described. An important channel of thermal energy loss from the fluid is conduction into the ground through the pipe wall.

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