New Subsea Process Cooler; Part II: High Thermal Performances and Complex 3D Free Convection Heat Transfer

Size: px

Start display at page:

Download "New Subsea Process Cooler; Part II: High Thermal Performances and Complex 3D Free Convection Heat Transfer"

Jack Parrish
6 years ago
Views:

1 New Subsea Process Cooler; Part II: High Thermal Performances and Complex 3D Free Convection Heat Transfer Julien Rolland, Stig Kanstad, Vivian Lyngvaer Framo Engineering, a Schlumberger Company

2 Introduction Installation of subsea compression systems enables to balance the reservoir depletion with time and thus to extend the plateau production and to increase total recovery of fields [1]. These systems face to harsh challenges both from a technical and commercial point of view. Actually without any upstream process on the well stream, the production flow is multiphase containing mainly gas but also condensate, water and sand. The equipment faces in addition to all subsea constrains in term of availability, flexibility and robustness. Subsea process cooling is clearly a mandatory and critical aspect for these applications. Standard heat exchangers design (see example in ref [2], [6]) are basically not suited to deal with subsea constrains. Framo Engineering has thus designed and tested a full scale passive cooler for use in combination with subsea wet gas compressors. The present study describes the high heat transfers occurring on the developed cooler. The experimental results are firstly considered. The heat transfer performances of the cooler are compared with the performances of a single pipe (SP) used as reference. These comparisons emphasize a significant improvement of the heat exchanges for the cooler. In order to characterize the phenomenon responsible for this heat transfer increase, Computational Fluid Dynamics (CFD) analyses has been performed on the considered geometry. The complex 3D flow on the ambient side is investigated and allows proposing a new correlation to represent free convection on a vertical pipe with horizontal cross flow. Abbreviations CFD FE RANS SP SST WGC amb ext inl int out Computational Fluid Dynamics Framo Engineering a Schlumberger Company Reynolds Averaged Navier-Stokes Single Pipe Shear Stress Transport Wet Gas Compressor Ambient side of the cooler Cooler external side Cooler inlet, process side Cooler internal side Cooler outlet, process side A Area [m 2 ] Cp Heat Capacity [J/kg/K] D Pipe Diameter [m] e Internal energy [J/kg] g Gravity [m/s 2 ]

3 HTC, h ext, h int Heat Transfer Coefficient [W/m 2 /K] k thermal conductivity [W/m/K] L Pipe length [m] Massflow [kg/s] Q Heat transfer [W] T Temperature [K] U Global heat transfer coefficient [W/m 2 /K] V Velocity [m/s] β Thermal expansion coefficient [/K] µ Dynamic viscosity [Pa.s] ρ Density [kg/m 3 ] τ Stress tensor [Pa] Log Mean Temperature Difference Pr Ra Nusselt number Prandtl number Rayleigh number Reynolds number Subsea cooler design Coolers principle is to transfer heat from one fluid (the cooled fluid) to another (the coolant fluid). They are usually designed using the forced convection heat transfer principle for both the cooled and the coolant fluids. This is due to the higher heat transfer rate obtained using forced convection versus free convection. Subsea environment is complex and aggressive, where routine maintenance, inspection and cleaning possibilities are limited and challenging. Difficulties are further increased by the nature and the multiplicity of equipment (pumps for example) required to generate forced convection on the ambient side (coolant fluid). Standard forced-forced convection heat exchanger technology is hence not well suited for subsea applications. Passive design based on free convection on the ambient side may thus be more appropriate to face to subsea environment challenges. The subsea passive cooler has been designed both to give a large turndown on thermal performance for operation flexibility and to handle flow assurance issues like sand accumulation, hydrates formation, wax deposition, etc [3]. One cooler illustrated in the Figure 1 consists of 33 vertical pipes and two manifolds to distribute/collect uniformly the flow. Coolers are arranged in a well designed cooling system (see Figure 2 and ref [3]) as it is symmetric and modular hence adaptable to different cooling requirements.

Inlet manifold Cooling pipes Baffles Gravity Outlet manifold Figure 1: Cooler design As sea current is unpredictable and constantly variable, the cooler design does not take into account this effect.

4 Inlet manifold Cooling pipes Baffles Gravity Outlet manifold Figure 1: Cooler design As sea current is unpredictable and constantly variable, the cooler design does not take into account this effect. Sufficient cooling in the worst scenario is hence ensured. Currents will have a positive influence on the thermal performances as it will generate additional forced convection heat transfer on the ambient side. Figure 2: Cooling system assembly Full scale test setup In order to evaluate the cooler performance and to compare it with empirical correlation given for simple geometries [2], the cooler and a single pipe are run in parallel. The single pipe has exactly the same characteristics (diameter, length, thickness, material ) as the cooler pipes. A picture of the test set up is given Figure 3 and illustrates the wide dimensions of the pit and the test skid (the cooling pipe length is 4.3 m).

Cooler Single pipe Figure 3: Cooler and single pipe in dry pit prior to submerge testing A slip stream of dry nitrogen was provided from the existing WGC discharge and routed through the test objects.

5 Cooler Single pipe Figure 3: Cooler and single pipe in dry pit prior to submerge testing A slip stream of dry nitrogen was provided from the existing WGC discharge and routed through the test objects. A schematic of the test loop is shown Figure 4. Flow/pressure at test objects was controlled by means of the chokes on WGC outlet and control valves downstream test objects. The test operating conditions are listed in Table 1. It should be noted that only a part of the test matrix is presented in this study. Actually the inlet temperature and pressure effects have also been investigated to fully qualify the cooler. Moreover these tests were the last ones of a global tests campaign which included amongst other the heat transfer characterization with wet gas. Figure 4: Test set up schematic

6 The process flow was measured by means of Coriolis mass flow meters. Temperature was measured upstream and downstream the test objects. Pressure was measured upstream the test objects. Six individual temperature measurements were made in the sea water along the test objects to determine ambient temperature and to check any temperature layering in the pit. The head loss across the bundle was in addition measured using a differential pressure sensor. Table 1: Operating conditions Units Value Inlet temperature [ C] 90 Ambient temperature [ C] 12 Inlet pressure [bara] 40 Massflow (per pipe) [kg/s] Using pressure and temperature measurements at the test objects inlet, the gas thermodynamic properties (density and heat capacity) are calculated and hence the amount of heat removed to the process fluid true the cooling pipes is obtained. Experimental results The thermal performances of the two test objects (cooler and single pipe) have been characterized for different massflow. The global heat transfer coefficient U is calculated according to the following equations. The heat transfer is defined by: with A the object area and ΔT the temperature difference between the process gas and the ambient water. The heat transfer Q is directly related to the heat removed to the gas: Replacing the temperature difference between the process gas and the ambient water by the Log Mean Temperature Difference (LMTD) as the process gas is not constant all along the cooling pipes [2], the global heat transfer coefficient is calculated using the following formula: It should be stressed that the experimental data obtained during this tests campaign are very promising to investigate free convection behavior as the global range is quite uncommon [2] thanks to the wide dimensions and cooling capacities of the studied case (see Table 2). Actually the length scale, the temperature difference and the total cooling load are most likely

7 way outside normal test conditions used to define the empirical correlations. Comparison of Nusselt number based on 3 different approaches which are experimental, analytical and numerical, for such as high Rayleigh number range up to makes this study very valuable. Table 2: Global results Units Min Value Max Value Massflow (cooler) [kg/s] Heat transfer (cooler) [kw] Reynolds number (gas) [-] Rayleigh number (ambient) [-] The cooler and single pipe cooling performances versus the massflow are plotted on Figure 5. Using 2 nd order polynomial interpolation the performance ratio is obtained (dot line using right scale). The cooler performance is about 23% higher than the single pipe one. The measured performance increase given in the Figure 5 is defined by:. U value (W/m2/K) Bundle vs single pipe measured single pipe measured bundle Measured delta % 40 % 35 % 30 % 25 % 20 % % % 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 Massflow (kg/s) Figure 5: Cooler and single pipe thermal performance This tendency is explained by the pipes interaction for the cooler. The heat transfer from the pipe external faces to the ambient sea water is driven by free convection activities. An external flow is generated due to the density variation induced by the temperature increase in the pipes vicinity. For the cooler case, the pipes closeness makes these flows interacting, the obtained momentum is thus higher than the one obtained with a single pipe. This phenomenon called chimney effect is illustrated below.

8 Simulations The heat transfer from the process gas to the ambient observed on the test objects can be decomposed in the 3 following features: Internal forced convection between the bulk gas and the pipes internal faces Conduction across the pipes wall External free convection between the pipes external faces and the ambient water Based on the physical mechanisms split above, the global heat transfer coefficient is defined by the following formula: The thermal performance difference obtained between the SP and the cooler is related to the free convection pattern and intensity on the ambient side. In order to characterize and to understand in detail the phenomena occurring and the complex 3D flow that develops around pipes, CFD simulations are performed on both the cooler and the single pipe. The case with a massflow of 0.22 kg/s has been studied using CFX software [4]. Numerical method The geometry simulated consists of 3 domains (see Figure 6): the gas flowing inside pipes, the solid part and the ambient side. The two flows (ambient and gas) are described by the RANS system coupled to the internal energy equation for the ambient side by the buoyancy force based on the Boussinesq assumption [4] kT.: The momentum source is hence for the water domain: Turbulence is solved using the SST model [5]. Both fluids water and gas are considered incompressible. The solid domain material is stainless steel described by its thermal conductivity. The boundary condition for the top and bottom faces of the ambient domain is set to opening. The lateral face representing infinite is set to wall with free slip condition and imposed temperature to 12 C. For the gas domain, standard incompressible boundary conditions are

9 used, i.e. massflow imposed at the inlet (top) and static pressure imposed at the outlet (bottom). The inlet temperature is fixed to 90 C. g Figure 6: Simulation domains Single pipe simulation As shown in Table 3, the heat transfer for the single pipe is very well simulated. The discrepancy between test data and simulation is only 5%. The difference between test data and empirical correlation is 10% which is acceptable too regarding correlations accuracy [2], [6], [7]. Comparison of the CFD and test results for the single pipe is an important step which validates the numerical approach. Method Units Value Variation Experimental data 175 CFD W/m 2 /K 167 5% Empirical correlation % Table 3: Global HTC for the SP; comparison between numerical and analytical approaches [6] with test results On the Figure 7 the development of thermal boundary layers is given. As internal and external heat transfer coefficients (HTC) cannot be extracted from test results, estimated values from empirical correlations (dot line on the right Figure 7) are compared with HTC obtained from CFD simulation.

100 90 80 Temperature [⁰C] 70 60 50 40 30 gas center pipe gas bulk wall internal wall external wall dt 6.5 500 5.5 4.5 3.

10 Temperature [⁰C] gas center pipe gas bulk wall internal wall external wall dt Temperature difference [⁰C] heat transfer coefficient [W/m2/K] hint hext U hint emp hext emp U emp Y [m] Y [m] Figure 7: Single pipe simulation results (Y=0 is the gas inlet) The temperatures plotted on the Figure 7 (left) are used to determine the internal and external heat transfer coefficients (HTC) (right) from CFD analysis. The gas bulk temperature is obtained using massflow averaged the temperature on cross-sections inside the pipe. This temperature is used to calculate the internal HTC. The pipe inlet (on the top) refers to y=0; and the outlet (bottom of the pipe) is at y=4.3m. Extreme values obtained for y=0 and y=4.3 are only due to the imposed conditions on the boundaries. Cooler simulation Due to the compressed gas flowing inside the pipes, pipes external wall is warm and thus a vertical flow in the ambient is generated due to free convection. As shown on the Figure 8, the gas flow delivers continuously heat to the ambient and the averaged gas temperature drops off from 90 C down to 60 C. g Figure 8: Gas temperature (streamline) and outlet velocity On the sea side, starting from the bottom the water free convection flow is routed from the ambient into the pipes neighborhood (Figure 9 and Figure 10). What is outstanding with the cooler design is that the baffles block the vertical flows and force the ambient water inside

increases the turbulence level and the flow mixing around the cooling pipes. It breaks the thermal layer with transverse flow and unsteady drag effects.

design generates secondary flows around the baffles.

11 the bundle to flow out and in again. This phenomenon which generates radial flows around the baffles and the domes has a very positive effect on the heat transfers as: It increases the mean velocity field and hence the heat transport It increases the turbulence level and the flow mixing around the cooling pipes. It breaks the thermal layer with transverse flow and unsteady drag effects. g Figure 9: Flow pattern on the ambient side (sea water) g Figure 10: Radial velocity field along the cooler; red surface +2cm/s, blue surface -2 cm/s As observed on the Figure 10 the cooler specific design generates secondary flows around the baffles. In red (positive radial velocity) the water is ejected from the bundle where in blue (negative radial velocity) the water is routed into the pipes vicinity. This transverse flow generated firstly increases the momentum level and by consequence the heat removal is improved. A second aspect is that it increases the turbulence level creating some turbulent structures as identified in the Figure 11. On the lowest side of the baffle, the shape of the helicity isosurfaces is typically representative of the Von Karman vortex development. The generation of these turbulent structures in a staggered bank has been largely studied in the past [2], [7], [8] and its positive impact on heat transfer is widely known.

g Figure 11: Helicity isosurface around the second baffle Discussion Test results and comparisons of the thermal performance between the single pipe and the cooler highlighted an increase of the heat

12 g Figure 11: Helicity isosurface around the second baffle Discussion Test results and comparisons of the thermal performance between the single pipe and the cooler highlighted an increase of the heat transfer for the cooler. Due to the similarity of the two test objects and the physical mechanisms decomposition of heat transfer, the free convection on the ambient side has been identified as the key phenomena to explain test results deviation. 800 heat transfer coefficient [W/m2/K] hext SP hext cooler U SP U cooler Y [m] 4 Figure 12: External and global HTC; cooler vs. SP (Y=0 is the gas inlet) The CFD analyses performed on the two objects revealed a complex 3D flow development for the cooler. This 3D flow is responsible for the external HTC increase as illustrated in the Figure 12. It has been identified that two effects interact and are coupled enhancing heat transfer. First the pipes bundle generates the high intensity vertical momentum due to free convection and secondly the baffles transfer this vertical flow into radial and azimuthal flows. This flow pattern increases the momentum in the pipe vicinity which amplifies the heat removal and

likewise generates Von Karman structures with high turbulence level. This decomposition of the heat transfer mechanisms on the ambient side is illustrated on the Figure 13.

Nevertheless the pipes interaction makes the free convection flow generated by one pipe acting as a forced convection flow for the neighboring pipes.

13 likewise generates Von Karman structures with high turbulence level. This decomposition of the heat transfer mechanisms on the ambient side is illustrated on the Figure 13. Figure 13: Heat transfers combination on the ambient side Based on the analysis presented above, a new empirical correlation is proposed. The cooler is a passive design i.e. no additional equipment is used to create forced flow on the ambient side. Nevertheless the pipes interaction makes the free convection flow generated by one pipe acting as a forced convection flow for the neighboring pipes. Combined free and forced convection has already been investigated in the pa st [2], [9]. One of the common practices is basically to use an expression of the follo wing form to describe the mixed convection: It is important to stress that analysis and results are strongly dependent of the configuration. Three special cases can be identified: Buoyancy induced flow and forced flow parallel with the same direction Buoyancy induced flow and forced flow parallel in opposite directions Buoyancy induced flow and forced flow perpendicular Finally in the last case which is of interest in the study presented, different configurations can be investigated. One of the most extensively studied is probably the horizontal cylinder with horizontal cross flow [9]. The novelty and the difficulties for the typical case analyzed are related to the fact that two different characteristic lengths representative of the combined mechanism come out. It hence makes it difficult to establish the combination of the characteristic dimensionless numbers for the free and the forced convections. Actually the characteristic length to build the Nusselt number and quantify the free convection intensity is the total vertical pipe length (L) while the one representative of the forced convection in a staggered bank is the pipe diameter (D). For this reason, the formula proposed above is not suited anymore as the Nusselt magnitude based on different length scale strongly deviates. The following formula is hence used to correlate mixed convection heat transfer for the cooler external heat transfer:. _

14 The Nusselt number for a free convection vertical boundary layer development [6] is:. _. The Nusselt number for forced convection in staggered bank [8] is: _. where the constant has the following values according to the geometry configuration: C 1 =0.416, C 2 =0.75 and m= Therefore the external heat transfer for the cooler corresponds to the single pipe ones in addition with a component representing the pseudo forced convection in the baffles vicinity. According to the Figure 10 and the previous simulation analysis, only one third of this component is included as only one third of the total pipe area is affected by this horizontal flow pattern. The test results presented in the Figure 5 are compared with the estimated global HTC obtained using the proposed empirical correlations combination for the external HTC (Figure 14). The good matching between the measured and estimated values for the cooler is very promising and it supports the method used to define the mixed convection correlation for this specific configuration. U value (W/m2/K) Bundle vs single pipe measured single pipe estimate single pipe measured bundle estimate bundle ,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 Massflow (kg/s) Figure 14: Calculated and measured thermal performances for the cooler and the SP

15 Conclusion As part of a modular cooling system integrated inside a subsea compression system, FE has designed and tested a robust and high-performance subsea wet gas cooler. All the subsea and multiphase constrains have been carefully managed fulfilling the demanding requirements. This qualification step actually validates one of the crucial technical parts initially identified on the Statoil s Gullfaks 2030 Subsea Compression project [1], [3]. The cooler has been fully tested in subsea conditions. The good thermal performances obtained have been analyzed using CFD approach. It enabled to understand and to characterize the complex 3D flow pattern which developed on the ambient side around the cooler. Based on these analyses, a new formula for combined free convection and crossflow for vertical pipe has been used. The overall heat transfer coefficient obtained from these correlations matches very well the experimental data. Thanks to the understanding and the good control of all the physical mechanisms involved, investigations of optimized design are ongoing to improve even more the cooler performances. Acknowledgments The authors wish to express their gratitude to Statoil for their continuous interest in the development of the cooler design.

16 References [1] World first submerged testing of Subsea Wet Gas Compressor Knudsen T., Solvik N. Offshore Technology Conference, Houston, May 2011 [2] Fundamentals of heat and mass transfer, Incropera F., DeWitt D., Bergman T., Lavine A. John Wiley & Sons, sixth edition, 2006 [3] New Subsea Process Cooler Design; Part I: Focused On Flow Assurance, Operation and Reliability Kanstad S., Rolland J., Lyngvaer V., Boe C., Henning B. Deep Offshore Technology International, Perth, November 2012 [4] CFX Users Manual, November 2009 [5] Two-equation eddy-viscosity turbulence models for engineering applications Menter F.R. AIAA Journal, Vol. 32, No. 8, pp (1994) [6] An analysis of turbulent free convection heat transfer Bayley F.J. Institution of Mechanical Engineers (London) Proceedings, vol. 169 pp. 361, 1955 [7] Transferts thermiques Bianchi A.M., Fautrelle Y., Etay J. Presses polytechniques et universitaires romandes, 2004 [8] Correlation and utilization of new data on flow resistance and heat transfer for cross flow of gases over tube banks Grimison E.D. Trans. ASME 59 (1937) pp [9] Combined natural and forced convection heat transfer from horizontal cylinders to water Fand R. M., Keswani K. K. Int. J. Heat Mass Trasnfer, Vol. 16, pp (1973)

PHYSICAL MECHANISM OF CONVECTION

Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter