A Semi-Empirical Transient Thermal Model for Multiple Flowline Bundle Cool-Down Process
Authors: Chin Y. Doreen , Zhou X. , Perera R. , Wang X. 
Published: October 2008

Abstract
In this paper, a semi-empirical transient thermal model is proposed for cased, insulated, multiple flowline bundle. The model is developed by solving an inhomogeneous ordinary differential equation with related initial condition. A nonuniformity factor is used in the model. The model provides a theoretical principle for bundle cool-down temperature data reduction and overall heat transfer coefficient calculation.
The cool down temperature responses obtained from four cool down tests performed on a three-flowline bundle, and the correlations from the proposed model and from the conventional thermal model are presented in this paper. The resultant overall heat transfer coefficients are also presented. Compared to the conventional exponential temperature correlation, the current model provides an improved correlation to the experimentally determined cool-down temperature responses and overall heat transfer coefficients. Comparison of the correlated temperature responses and the resultant overall heat transfer coefficients from two models shows that a small deviation in temperature response correlation (±5.00%) can result in a high under-estimation in overall heat transfer coefficient (46%).

Introduction
Thermal performance of subsea pipeline systems is important to the development and reliable operation of deepwater oil and gas system due to the potential hydrate formation and wax deposition problem. Good thermal performance is required not only to ensure that hydrate formation does not occur during steady state operation, but also to provide sufficient cool down time before hydrates form during an emergency shutdown situation. Premature hydrate blockage may occur if the cooling rate of the pipeline system is too high.
The information available in the open literature for thermal analysis of bundled multiple flowline system is limited. Jee[1] analyzed the thermal behaviors of bundles and set out a general method for determining temperature profiles of multiple flowline bundles. Brown, et al. [2] proposed a transient heat transfer model for predicting the transient thermal behavior of a bundled pipeline system composed of an arbitrary number of internal pipes within a single casing piper, and illustrated its application to the design and operation of the Britannia flowline bundles. Zabaras and Zhang [3,4] conducted numerical and theoretical analyses for steady state and cool down performance of multiple flowline bundles and subsea hardware. Danielson and Brown [5] developed a steady state analytic model for a three line flowing bundle. Chin, et al [6,7] conducted numerical analyses on multiphase heat transfer of three-flowline bundles, and investigated the thermal interaction among the flowlines.
The thermal cool down test is a common method used in offshore industry for determining the overall heat transfer coefficient and shut-in response of a flowline bundle and to assure the thermal performance of the designed bundle system. Understanding the validation of the thermal model and the principle used for test data reduction is very important for correct interpretation of the test results.
In this paper, a new transient thermal model is developed for the cool down temperature response of cased multiple flowline bundles. The model is derived from the energy conservation equation.