Cooldown of Subsea Deadleg With a Cold Spot: Experimental and Numerical Heat-Transfer Analysis

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1 Cooldown of Subsea Deadleg With a Cold Spot: and Heat-Transfer Analysis Ola Hagemann and Atle Jensen, University of Oslo, and Stig Grafsrønningen, Future Technology A/S Summary and numerical heat-transfer analysis was conducted on a T-shaped acrylic-glass pipe, representing a production header in a subsea production system with a vertical deadleg. The header was insulated, while the deadleg was not insulated and carried a cold spot on the top. The experimental conditions were set to mimic those of steady-state production, followed by a 3-hour shutdown (cooldown). The internal fluid temperature and the wall temperature were measured by use of resistance temperature detectors (RTDs) and thermocouples, respectively, while particle image velocimetry (PIV) was used to measure the velocities in the deadleg. It was shown that the mean velocity field during both steady state and cooldown was periodic, with a clockwise and counterclockwise rotation along the deadleg wall. By use of a k ω shear-stress transport (SST) Reynolds-averaged Navier-Stokes (RANS) model in ANSYS CFX (13a, b), the thermal field was correctly predicted for 3 hours of cooldown by modeling the cold spot as an isothermal wall. The RANS model was unable to recreate the periodic velocity field observed in the experiment. Introduction In a subsea facility, the pipelines will be surrounded by cold seawater, which will actively cool the production fluid inside. If the temperatures drop below a critical value, hydrate formation can occur. Deadlegs are inactive parts of production pipelines occupied by stagnant hydrocarbons. These areas often pose a major hydrateformation risk, and, in some cases, they need to be insulated. However, if a valve or similar equipment is situated on the deadleg, it will only be partially insulated and will act as a cold spot where steel is in direct contact with the surrounding water. These cold spots act as strong thermal bridges and will lower the temperatures throughout the system. Accurate prediction of this thermal effect is important for the insulation design and the operational philosophy of the subsea field. Stagnant fluid in horizontal deadlegs of different diameter/ length ratios was investigated by Habib et al. (0), both numerically and experimentally. A fluid mixture of 90% crude oil and % water by volume was circulated at steady state through a T-shaped pipe, where one horizontal end was inactive. It was shown that deadleg length and inlet flow velocity had an effect on oil/water separation, which is a trigger for hydrate formation. These results were validated against flow-visualization experiments. Recent studies by Mme () investigated the thermal effect of having a cold spot on the circumferential surface of a water-filled steel pipe. The heat-loss rate was found to be largest when the pipe was horizontal. Temperature measurements were compared with results from computational-fluid-dynamics (CFD) computations, Copyright 16 Society of Petroleum Engineers Original SPE manuscript received for review 26 March 16. Revised manuscript received for review 8 November 16. Paper (SPE 18170) peer approved November 16. and showed that large eddy simulation (LES) was better suited than k ε based models for predicting the temperature profile. However, the experimental temperature data were obtained solely for the pipe wall, and the velocity field and the thermal field inside the pipe were not investigated. In a study by Jensen and Grafsrønningen (14), a 3-hour-long cooldown experiment was conducted on a water-filled T-shaped acrylic-glass pipe, representing a production header with a vertical deadleg. The header was insulated, while the deadleg was kept uninsulated. The T-shaped pipe dimensions were representative of a subsea production pipe, but unlike a subsea pipeline, the experiment was set up with air at room temperature as the surrounding medium. Temperatures in the T-shaped pipe were measured internally with RTDs and externally with pipe-wall-mounted thermocouples, while velocity data were obtained in the deadleg by use of PIV. These measurements were used as benchmark data to establish a suitable numerical model. The study scrutinized the accuracy of standard RANS turbulence models in predicting the flow kinematics inside the vertical deadleg when the flow was both turbulent along the pipe wall and laminar closer to the center of the pipe at the same time. Mesh independent results were obtained by running a series of mesh convergence tests. It was shown that cooldown simulations were more sensitive to mesh design than the choice of turbulence model. Mean velocities in the deadleg compared well with experimental PIV data during the first 60 minutes, but the RANS model was not able to predict the laminar-flow kinematics that occurred after this time. The thermal field was correctly predicted with a RANS model for 3 hours of cooldown, even though the flow was laminar in the entire deadleg after 60 minutes. The heat loss in the experiment was limited by the heat-transfer rate to the surrounding air, and not by the internal natural convection. Thus, the accuracy of the RANS model for predicting the internal flow kinematics was not essential for calculating the cooldown times. Rayleigh-Benard convection in enclosures, where a fluid is heated from the bottom and cooled from above, has been the topic of many research papers. Recent experimental, numerical, and theoretical advances in Rayleigh-Benard convection were presented in Chillà and Schumacher (12). The paper scrutinized experimental and numerical data from a series of publications on Rayleigh- Benard convection in cylindrical enclosures. The underlying studies differed in terms of the temperature gradient between the top and bottom plate, the fluid inside the enclosure, and the aspect ratio Γ = L/H of the enclosure, where L is the characteristic length and H is the height of the enclosure. For 7 Ra 12, the authors showed how large-scale convection (LSC) inside the enclosure influences the overall heat loss in the system. LSC refers to the tendency for thermal plumes of the same type to cluster together and form a large-scale flow. The number of convection cells in the large-scale flow depends on the aspect ratio of the enclosure. By comparing various experimental and numerical studies with the same Ra but with different aspect ratios, it was shown how the structure of the LSC has an influence on the overall heat loss in the system, and that December 16 Oil and Gas Facilities 1

2 are usually used when calculating the insulation requirements for a subsea pipeline. However, the numerical results need to be verified through full-scale experiments before installation. If large discrepancies between the experimental and numerical results are revealed at this stage, it might be necessary to redesign the full-scale equipment and conduct the experiments again, thereby leading to a significant cost increase for the project. The aim of this study was to Obtain high-quality temperature data for 3 hours of cooldown for a system similar to that described in the preceding, where the internal flow kinematics involved Rayleigh-Benard convection. Investigate the nature of the flow kinematics inside the deadleg by acquiring velocity data through the use of PIV. Address whether main-stay RANS turbulence models are able to accurately predict the cooldown times for such a geometry, and if these models can be used to aid the insulation design for the pipeline. Fig. 1 T-shaped pipe in acrylic-glass setup to mimic a subsea production header with a vertical deadleg. The setup was equipped with temperature sensors, an aluminum lid (cold spot) on top of the deadleg, and insulation on the header. the significance of this influence decreases with increasing Rayleigh number. As an example, results from direct numerical simulation showed a variation in the Nusselt number of up to % when the structure of the LSC changed for Ra = 7, whereas it was approximately 1.6% for Ra = 12. This study was a continuation of the study by Jensen and Grafsrønningen (14). The experimental setup was modified as shown in Fig. 1, with an aluminum lid on top of the deadleg and a different insulation on the header. A mesh was created on the basis of the recommendations given by Jensen and Grafsrønningen (14). Having no insulation on the deadleg was necessary to be able to conduct optical measurements (PIV) and make observations of the internal velocity field. The fundamental difference between the previous study by Jensen and Grafsrønningen (14) and this study was the aluminum lid on top of the deadleg. The aluminum lid was made with internal channels through which cold water was circulated, thereby acting as a cold spot where the pipe wall is in direct contact with the surrounding water. This not only changed the nature of the natural convection inside the deadleg, but also made the internal natural convection the limiting factor for the heat loss through the cold spot. The Ra in the present experiment was in the range of Ra 12, hence the heat loss was not believed to depend significantly on the structure of the LSC inside the deadleg. To accurately predict the flow kinematics in such cases, LES is usually required. Setting up an LES study is known to be time consuming with respect to mesh design compared with the use of standard RANS turbulence models. Hence, RANS models Setup and Measurement Techniques The experimental setup consisted of a T-shaped acrylic-glass pipe with a wall thickness of mm, which was installed in a closed loop with various experimental components by use of flexible hoses. The experimental components are shown in Fig. 2 and include a pump for driving water from a reservoir through the T-shaped pipe, two heat exchangers for adjusting the inlet temperature, a flowmeter, and several other components. The inner diameter of the T-shaped pipe was 143 mm, and its length was 3 m horizontally (header) and 1 m vertically (deadleg). The pipe was placed on top of a wooden table with a polystyrene foam board placed beneath the pipe to limit the heat exchange with the table. The header was insulated with 19 mm of neoprene-like material, while the deadleg was kept uninsulated. Water temperatures were measured using RTDs that were inserted 0 mm into the pipe, while wall temperatures were measured with thermocouples of Type k (on the header) and Type t (on the deadleg). These sensors are sketched in Fig. 3, and their locations are given in Table 1. As illustrated, the y- and z-axis are aligned with the vertical and horizontal directions, respectively, while the x-axis points out of the figure from the center of the T-shaped pipe. In Fig. 4, the aluminum lid that was installed on top of the deadleg is shown. It was made with channels for water to flow through, and the bottom surface of the lid was in direct contact with the water inside the deadleg. The cold-spot effect was created by having water at 4 C circulate through the channels of the lid at a constant rate. A cooler enabled the water temperature at the inlet of the channel to be set with an accuracy of ±0.01 C. The cooldown experiment was also conducted without a cold spot on top of the deadleg for comparison. For these experiments, the top surface of the deadleg was replaced with a -mm-thick acrylicglass lid that had the same thermal properties as the other surfaces of the deadleg. Before initiating the experiment, water was heated to 70 C to decrease the solubility of air in water to remove air that could potentially have accumulated on the inner pipe walls and temperature sensors during the experiment. The experiment was initiated by circulating water through the header with a flow rate of 1300 kg/h. The flow rate was set by a pump with ±0.% accuracy. The water temperature at the inlet (on the right-hand side in Fig. 3) was 4 C, the ambient temperature of the surrounding air was 21 C, and the water temperature at the inlet of the cold spot was 4 C. The cooldown was initiated by closing a set of valves located upstream and downstream of the header, after turning off the pump. The flow kinematics in the deadleg were scrutinized with PIV by use of a high-resolution camera. In PIV, pattern-matching techniques on image pairs (separated by a small time interval) are used to track the movement of passive particles. Mean velocities are found through averaging over consecutive instantaneous velocity 2 Oil and Gas Facilities December 16

3 Laser head Light sheet for PIV Outlet valve Inlet valve High-speed camera Laser Computer Heat exchanger Flowmeter Water Fig. 2 setup. Pump Heat exchanger t1 PT 6 t2 PT 4 PT k1 k2 t3 PT 3 PT 2 PT 1 z y Fig. 3 T-shaped pipe geometry and sensor positions. The inlet is located on the right-hand side of the 3-m-long horizontal pipe, and the outlet is on the opposite side. The cold spot is located on top of the 1-m-long vertical deadleg. fields. A set of 31 image pairs with a resolution of pixels were acquired over a period of 186 seconds. Improved temporal resolution for consecutive image pairs was not possible because of data-transfer limitations. The passive tracers used were 0-μm polyamide particles. Post-processing of image pairs was performed with an interrogation-window size of pixels with 7% overlap. The field of view (FOV) for the PIV measurements is shown in Fig., and its location was at 0.4 m y 0.62 m, 0 m z m, and x = 0 m. During cooldown, velocity fields (31 image pairs) Sensor Position Thermocouple Position Sensor x (m) y (m) z (m) Thermocouple x (m) y (m) z (m) PT t PT t PT t PT k PT k PT Table 1 Position of internal PT sensors and external thermocouples of Types t and k. December 16 Oil and Gas Facilities 3

4 t2 y = 0. m z = m PT 3 PT k2 t3 PT 2 k1 Fig. 4 Aluminum lid. in the deadleg were acquired at -minute intervals. An industryavailable data-acquisition system was used to acquire the temperature data, and the data were recorded using related data-acquisition and analysis software. Water and wall temperatures were recorded continuously at Hz. Model A 3D numerical model of the T-shaped pipe (Fig. 6) was created in ANSYS (13a, b) geometry with the same dimensions and material properties as in the experiment, including the internal sensors. Simplifications were made in parts of the model (e.g., the cold spot was treated as a 2-mm-thick aluminum plate instead of including the geometry of the internal channels, and the valves on the inlet and outlet were not modeled). ANSYS meshing was used to create the mesh illustrated in Fig. 7, and the important mesh parameters are given in Table 2. The y z Fig. FOV for the PIV measurements. mesh parameters were set on the basis of the previous study by Jensen and Grafsrønningen (14); hence, a new grid independent study was not required. The surrounding air was not modeled, and external boundary conditions were therefore required at all external surfaces. Convective heat transfer was modeled by use of a correlation given in White (0): BRa Nu = A + C 1 Pr + ( ) ,...(1) where A, B, and C are different for horizontal and vertical cylinders, as listed in Table 3. Radiation was modeled assuming black-body radiation: q T 4 T,...(2) rad = ( ) w a where ε is the emissivity of the wall material, σ is the Stefan Boltzmann constant, T w is the wall temperature, and T a is the ambient temperature. The bottom surface (in contact with the polystyrene foam) and closed valves were modeled as adiabatic, while the cold spot was modeled as an isothermal 4 C wall. ANSYS CFX v..0 (13a, b) was used for simulating steadystate circulation and a 3-hour cooldown. Cooldown was initiated by changing the boundary conditions at the inlet and outlet to adiabatic walls. Adaptive timestepping was used to capture the abrupt changes at the beginning of the simulation. The k ω based model assumes equilibrium between the Reynolds stresses and the mean shear, and that the eddy viscosity is given by two scalar quantities υ T = k/ω. The linear-eddy-viscosity hypothesis assumes isotropic turbulence, which is usually not a valid assumption in buoyant flows. However, the previous study by Jensen and Grafsrønningen (14) on natural convective flow reported that k ω SST was able to predict flow kinematics as long as the flow remained turbulent. The k ω SST model is described in detail in ANSYS (13b). Turbulent flow is very sensitive to grid resolution close to a solid boundary, and wall functions are usually used in high-re flow to reduce computational expense. However, when simulating turbulent natural convection at low Re numbers and high Ra number, these wall functions are not valid. A near-wall resolution of y + < 2, as recommended by ANSYS (13a), was ensured for all simulations to avoid the use of wall functions. Fig. 6 The experimental and numerical geometry at the inlet of the T-shaped pipe. The numerical model of the T-shaped pipe included everything downstream of the inlet valve and upstream of the outlet valve. Results The cooldown experiment was conducted with and without a cold spot to assess its effect, and a comparison of the respective cooldown curves is shown in Fig. 8. During steady state, there was a constant flow of hot water through the header; hence, the water temperature in the header (PT1) was not lowered because of the 4 Oil and Gas Facilities December 16

5 Uninsulated piping Water Insulation Insulated piping Sensor Bracket Fig. 7 Meshing near the branch between the header and the deadleg for a cross section in the y z plane. Mesh Number of nodes Radial cell count insulation 6 Radial cell count unisolated piping 8 Radial cell count insulated piping Circumferential cell count on piping 60 First layer height piping (m) 2 4 Numbers of layers of piping 12 Body sizing on piping (m) 4 3 Body sizing on insulation 4 3 Body sizing on fluid (m) 7 3 Table 2 Important mesh parameters. cold spot (temperature at T = 0 is the same for both curves). Meanwhile, the water temperature in the deadleg was lowered by 3 and 1. C on the top (PT6, not shown here) and bottom (PT), respectively. Cooldown was significantly accelerated because of the cold spot, leading to temperatures in the header being lowered by 9 C after 3 hours. The cold spot also triggered temperature fluctuations of ±0.3 C in the deadleg (PT), where the average period (average time between all local maximum values) of the fluctuations was 30 seconds. The nature of the temperature fluctuations (Fig. 8) was further investigated by looking at the flow kinematics in the deadleg. The deadleg was made of acrylic glass, which made it possible to visually inspect the flow. The observations revealed an LSC cell in the deadleg, which was changing rotational direction periodically during steady state and cooldown. This was important input for deciding on where to conduct the PIV measurements (see Fig. ) and how to proceed with post-processing of the results. To capture the mean velocity of the convection cell, the velocity data were filtered into two categories clockwise and counterclockwise rotation depending on whether the average vertical velocity was positive or negative close to the deadleg wall. By averaging over all instantaneous velocity fields within each category, the mean (average) velocity field for the convection cell during both rotational periods was found. Additional LSC cells were not revealed through visual inspection, and it was therefore not attempted to conduct PIV on other parts of the deadleg. In Fig. 9, the mean velocity field for the convection cell during steady state is depicted, for both a clockwise and a counterclockwise rotation. Reflection from the laser causes a discontinuity in Constants Header Deadleg A B C Table 3 Constants used for calculating the Nusselt number on both horizontal and vertical cylinder walls. the regions of 0. m < y < 0.6 m and z = 0.0 m. The repeatability of the mean vertical velocity close to the wall during steady state (a) PT No cold spot Cold spot No cold spot Cold spot (b) PT Fig. 8 ΔT between measured water temperatures at sensor positions (a) PT1 and (b) PT, and the ambient air temperature during a cooldown with (teal) and without (blue) a cold spot on top of the deadleg. December 16 Oil and Gas Facilities

6 y (m) 0.4 y (m) z (m) (a) Clockwise rotation 8.6e z (m) (b) Counterclockwise rotation Fig. 9 Convection cell rotating (a) clockwise and (b) counterclockwise during steady-state circulation. The velocity field is time averaged, and the magnitude of the velocity ranges from 0.01 m/s (red) to 0 m/s (dark blue). was found to be 4% by comparing data from three separate runs, thus suggesting that the structure of the LSC did not change significantly between experiments. The cooling rate was correctly predicted by the numerical model for 3 hours of cooldown for all internal sensors, as depicted in Fig.. However, the model overestimated temperatures in the deadleg (PT6 sensor). Obtaining experimental mean velocities for comparison with RANS velocities during cooldown was not possible with the current experimental setup. This was mainly a result of the turbulent flow being periodic and decaying with time, which made averaging over consecutive image pairs an invalid approach. Ensemble averaging over separate experiments was not possible either, because the flow kinematics of the LSC between separate runs was not phase-locked in time. However, it was possible to evaluate similarities in the experimental and numerical flow kinematics. In Fig. 11, the experimental instantaneous vertical velocity is compared with the numerical RANS velocity 1 mm from the deadleg wall at y = 0. m. Both the experimental and the numerical flow field behaved periodically, and had similar amplitudes (a) PT1 (b) PT2 (c) PT (d) PT4 (e) PT (f) PT6 Fig. A comparison of experimental and numerical results for the internal water temperature during 3 hours of cooldown. 3 6 Oil and Gas Facilities December 16

7 Velocity (m/s) Velocity (m/s) (V ) (υ) Time (minutes) (a) minutes (V ) (υ) Time (minutes) (b) minutes Fig. 11 A comparison of the numerical vertical velocity (RANS) and the measured instantaneous vertical velocity as a function of time during cooldown at y = 0. m and z = m. This study has also shown how the cooldown times are sensitive to the presence of air accumulating below the cold-spot surface. Even though the water had been heated to remove all air in the system before initiating the experiments, an insulating layer of air accumulated on top of the deadleg during the initial cooldown experiments. The layer of air prevented convection heat exchange between the water and the cold spot, thereby leading to a rapid drop in the overall cooling rate. In Fig. 12, this can be seen to cause discrepancies between experimental and numerical cooldown curves after 30 minutes in the deadleg (PT6) and minutes later in the header (PT1). temperature fluctuations in the deadleg (PT6) were also diminished because of this, which further confirmed that these fluctuations were caused by convective heat transfer with the cold spot. To prevent air voids from accumulating at the interface between the water and the cold spot during cooldown, and thereby obtain the results presented in Fig., air voids were replaced continuously by water from a reservoir at ambient temperature connected to a valve on top of the deadleg. The added water amounted to less than 0.% of the total mass of water in the system during a 3-hour cooldown and was therefore not modeled in the CFD simulations. Modeling the cold spot as a 4 C wall was found to be the best approach in this study. Another approach that was attempted was to assign a time-varying heat-flux boundary condition at the external surface of the cold spot on the basis of experimental measurements of the temperature gradient across the cold spot during the cooldown. The accuracy of this approach was found to be similar to having the cold spot defined as an isothermal surface (Hagemann 14). However, the approach required additional input data, which produced uncertainties. It was therefore concluded that setting an isothermal boundary condition on the cold spot was the best approach. Conclusion The results in this study have shown that it is possible to calculate the cooldown times for a vertical deadleg with a cold spot by use of a k ω SST RANS turbulence model. and numerical heat-transfer analysis was conducted on a T-shaped acrylicglass pipe, representing a production header in a subsea production system with a vertical deadleg. The header was insulated, while the deadleg was kept uninsulated to allow for optical measurements of the internal velocity field. The experimental conditions were set to mimic those of steady-state production, followed by a 3-hour shutdown (cooldown). The top surface of the deadleg was made of aluminum with cold water circulating on the outside, and represented an uninsulated region (a cold spot) where the pipe is in direct contact with the surrounding water. In this study, with the temperature differential between the water (production fluid) and the cold spot being 41 C, it has been shown that 1. There was an additional temperature drop of 9 C in the header after 3 hours of cooldown (compared with a cooldown without a cold spot). 2. The cold spot triggered one or several LSC cells inside the deadleg in a manner similar to that of Rayleigh-Benard convection. The resulting mean flow field was periodic, with a clockwise and counterclockwise rotation along the deadleg wall. Despite the internal flow kinematics being related to Rayleigh- Benard convection (a flow phenomenon that is not captured by RANS models), simulations in ANSYS CFX using a k ω SST turbulence model have been successfully able to predict the thermal field during a 3-hour-long cooldown. This suggests that accurate prediction of the structure of the LSC inside the deadleg was not required to predict the overall heat loss in the system. One of the reasons for this could be that the Rayleigh number in the experiment was in the range of Ra 12, a range in which the heat loss does not change significantly as a result of changes in the structure of the LSC. The successful calculation of cooldown curves further suggests that setting an isothermal boundary condition on the external surface of the cold spot, which is the main contributor to the overall heat loss, is an effective and accurate modeling approach. From an industrial point of view, the results in this study have shown that it is possible to use RANS models when estimating the cooldown times for partly insulated subsea equipment containing cold spots, where the Rayleigh number is in the range of Ra 12. In that sense, it is not necessary to use LES or other morecomplex modeling approaches when calculating the required insu Time (minutes) Time (minutes) (a) PT1 (b) PT6 Fig. 12 Water temperature for the (a) PT1 and (b) PT6 sensors. Air voids on top of the deadleg caused large discrepancies between the experimental and numerical cooldown curves. December 16 Oil and Gas Facilities 7

8 lation for the equipment. This can help increase the efficiency of the insulation-design phase and the reliability of the results, leading to reduced cost and risk for designing a full-scale cooldown experiment. Whether it is possible to increase the efficiency of the design phase further by using a 2D model was not investigated in this study. Hence, if such an approach is attempted, the results need to be verified through comparison with experimental data. This study also shows how one should proceed when designing cooldown experiments containing cold spots for the purpose of benchmarking a numerical model: 1. Avoid situating the cold spot on top of the geometry, if possible. If there is air in the system, it will accumulate at this location and create an insulating air pocket at the cold-spot surface, making the experimental data unsuitable for benchmarking the numerical model. 2. If the cold spot is situated on top of the geometry, water should be added during cooldown to replace eventual air that would have otherwise accumulated at the cold-spot surface, to make the experimental data fit for benchmarking the numerical model. Nomenclature k = turbulent kinetic energy Pr = Prandtl number (υ/α) Ra = Rayleigh number (gßδtl 3 /υα) Re = Reynolds number (UD/υ) T a = ambient temperature T w = wall temperature ε = dissipation σ = Stefan Boltzmann constant ω = turbulent-eddy frequency References ANSYS, Inc. 13a. ANSYS CFX-Solver Modeling Guide, Release.0 (November 13). Canonsburg, Pennsylvania: ANSYS, Inc. ANSYS, Inc. 13b. ANSYS CFX-Solver Theory Guide, Release.0 (November 13). Canonsburg, Pennsylvania: ANSYS, Inc. Chillà, F. and Schumacher, J. 12. New Perspectives in Turbulent Rayleigh-Bénard Convection. J. Eur. Phys. J. E. 3 (7): 8. org/.1140/epje/i Habib, M. A., Badr, H. M., Said, S. A. M. et al. 0. Characteristics of Flow Field and Water Concentration in a Horizontal Deadleg. Heat Mass Transfer 41 (4): Hagemann, O. 14. Cool Down of Subsea Dead-leg With a Cold Spot. Master s thesis, University of Oslo, Norway (November 14). Jensen, A. and Grafsrønningen, S. 14. Cool-Down Simulations of Subsea Equipment. Proc., th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries, SINTEF, Tronheum, Norway, June, Mme, U. A.. Free Convection Flow and Heat Transfer in Pipe Exposed to Cooling. Doctoral thesis, Norwegian University of Science and Technology. White, F. M. 0. Viscous Fluid Flow, third edition. New York: McGraw- Hill. Ola Hagemann graduated from the University of Oslo with a master s degree in fluid mechanics in 14. After graduating, he started working as a project engineer at Future Technology A/S, where he took part in the development of a controllable passive subsea cooler. In this position, Hagemann has contributed to the development of a robust numerical model for calculating the performance of the cooler and to the design of a full-scale technical prototype. He has also participated in testing the technical prototype in a representative environment for the purpose of demonstrating the performance of the cooler and verifying the numerical model. During his time at Future Technology A/S, Hagemann has also worked as a flow-assurance consultant on oil and gas feasibility and prefront-end engineering-design studies. Atle Jensen is a professor in the Department of Mathematics at the University of Oslo. His current research is mainly motivated by industry, conducting field work, theory, numerical simulations, and experiments. Jensen s research topics are experimental fluid mechanics, marine hydrodynamics, nonlinear waves, waves/oil and ice, and tsunami solitary waves, microfluidics, internal waves, and multiphase flow. He holds a Cand.Sci. degree in hydrodynamics and a Dr.Sci. degree, both from the University of Oslo, Norway. Stig Grafsrønningen is a senior engineer within CFD and flow assurance at Future Technology A/S. He has been with the company for the last 3 years. Previously, Grafsrønningen worked for FMC Technologies. His current interests include subsea innovation and technology, and CFD, fluid mechanics, and heat and mass transfer related to technology development. Grafsrønningen holds a PhD degree in fluid mechanics and CFD from the University of Oslo. 8 Oil and Gas Facilities December 16