Multiphase flow metrology in oil and gas production: Case study of multiphase flow in horizontal tube

Transcription

1 Multiphase flow metrology in oil and gas production: Case study of multiphase flow in horizontal tube Deliverable of Work Package WP5 (Creating Impact) Authors: Stanislav Knotek Czech Metrology Institute (CMI), CZ André Fiebach, Sonja Schmelter, Ellen Schmeyer Physikalisch-Technische Bundesanstalt (PTB), DE A report of the EMRP joint research project ENG58 Multiphase flow metrology in oil and gas production

2 1. Work package WP 5 2. Deliverable number D Reporting date June Title Case study of multiphase flow in horizontal tube 5. Author(s) Knotek, Fiebach, Schmelter, Schmeyer 6. Lead author ( ) sknotek@cmi.cz 7. Contributing researches (institutes) PTB (DE), CMI (CZ) 8. Supplementary notes None 9. Abstract The paper deals with case study of CFD models created for research of liquid flow patterns established for different flow rates and fluid properties in large diameter long horizontal tube which is part of the multiphase flow rate measurement system described in project deliverables. The paper deals with mesh dependency study, influence of boundary conditions and impact of fluid properties on resulting flow patterns. 10. Key words CFD model, flow patterns, mesh study, parametric influence I

3 Contents 1 Introduction 1 2 Geometry 1 3 Mesh 1 4 Boundary conditions 3 5 Solvers and numerical settings 3 6 Test cases Physical and Material properties Results and discussions Mesh dependency study Influence of the inlet boundary conditions Influence of artificial perturbation Influence of phase distribution at inlet section Influence of the fluid properties Conclusion 8 Acknowledgements 9 References 9 II

4 1 Introduction The paper deals with case study of CFD models created for research of liquid flow patterns established for different flow rates and fluid properties in large diameter long horizontal tube which is part of the multiphase flow rate measurement system described in project deliverables. Note that the results described in this paper have been received using OpenFOAM, open source CFD software. 2 Geometry The considered geometry is defined by the transfer package, which is used within the experimental intercomparison in WP 1. It consists of a m long horizontal pipe required for pattern formation and for damping of the influence of different injection points. Therefore a 12 m long horizontal pipe has been constructed. The diameter of the tube is 104 mm, thus the ratio of diameter to the length of the tube is nearly 115 which should be enough for the flow pattern development. 3 Mesh The meshes have been developed using the internal OpenFOAM mesher. For use with interfoam solver the static mesh has been constructed using blockmesh. An adaptive mesh refinement has been used during the solution with interdymfoam solver. Using the blockmesh, four different meshes has been created using increasing refinement in axial and radial direction. The mesh parameters are summarized in Table 1 and the cross sections are shown in Figure 1. Note that in case of extra fine mesh, the symmetry boundary condition has been prescribed in longitudinal section, so that only mesh of half geometry has been used in simulation. However, the number of cells in Table 1 for extra fine mesh is recalculated for hypothetical mesh of whole geometry. Mesh no. of cells per diameter per 1 m in total Coarse Normal Fine Extra fine Table 1: Cell statistics of meshes used for mesh dependency study in OpenFoam. For use with interdymfoam the mesh similar to coarse mesh in Table 1 has been used as basis for adaptive mesh refinement. In every time step, the cells on interface between phases are refined up to the enabled amount of cells. The comparison between coarse static mesh used for interfoam and dynamicaly refined mesh created by interdymfoam is show in Figure 2. 1

5 Figure 1: Cross section of the meshes used for mesh dependency study. Figure 2: Comparison of static and dynamic mesh and corresponding fluid interface. 2

6 4 Boundary conditions The inlet section is divided in two subdomains which have been constructed in several topological schemes as can be seen in Figure 3. The red colour represents the inlet area of liquid phase whereas the blue colour stands for the inlet of gaseous phase. The forms a) - c) have been used in dependence on the supposed level of liquid, i.e. for the cases with low liquid level, the inlet a) has been used, whereas the inlet c) has been used for cases with expected high liquid level. The inlet d) has been constructed for imposing bigger fluctuations in order to accelerate the perturbations on the surface. However, the results have shown, that for cases with enough big flow rate the same flow pattern have been established independently on the used inlet scheme. On the other side for low flow rates, the expected flow pattern was not established in whole length of the computed domain. For these reasons the artificial velocity fluctuations in y- and z- direction have been prescribed in the inlet velocity boundary condition according to formula u i = A i sin( 1 πfφ), (1) 9 where i stands for y and z, f=100 Hz, φ is random number with zero mean value and variance equals 0.5. Using this perturbation, the symmetric inlet c) seems to be appropriate as universal scheme. The impact of different inlet subdomains and influence of inlet perturbation is discussed further in section 7.2. The uniform velocity profile has been prescribed for each liquid phase on inlet whereas the pressure outlet boundary condition has been used at the end of the pipe. No-slip boundary condition has been prescribed on the walls. Figure 3: Phase distribution at inlet section. 5 Solvers and numerical settings Since the fluids are supposed to be separated (evident interface between phases), the volume of fluid method (VOF) has been suggested for numerical solution. Corresponding solvers for incompressible flows in Open- FOAM are interfoam and interdymfoam (solver for dynamic mesh). As was mentioned in [4], second order schemes have been used for spatial discretization, while the time discretization is done by classical first order Euler scheme. 3

7 6 Test cases For this study, eight test cases from the project test envelope have been selected. All these cases are two-phase cases, one half is for oil-gas, the other one for water-gas. The superficial velocities can be read from the Table 2, where the numbering in column signed with No. corresponds to the old internal numbering in the project. The numbering in column signed with Matrix Ref. No. corresponds to the actual numbering, see deliverable It can be seen that each oil-gas case has a corresponding water-gas case with same superficial velocities. Thus, the influence of the fluid can be considered, see Section 7.3. No. Matrix Ref. No. Q W Q O Q G u sw u so u sg l/s l/s l/s m/s m/s m/s Table 2: Volume flow rates Q W, Q O, Q G and superficial velocities u sw, u so, u sg of the water phase, oil phase and gaseous phase, respectively, used for the numerical simulations. 6.1 Physical and Material properties Physical and material properties used for simulations discussed in this paper are set according to published deliverable D [1], D [3] and D and are listed in Table 3. Note that cases No. 5a) - 5d) correspond to case No. 5 in Table 2. 7 Results and discussions 7.1 Mesh dependency study Mesh dependence study based on case No. 1 has been done in [4]. It was shown, that observed flow patterns remain nearly the same for coarse, normal and fine mesh as defined in Table 1. Only the wave origin and pressure loss were slightly dependent on the mesh refinement. For finer mesh, the velocity gradient is bigger on the interface between the phases as can be seen in Figure 4 from the comparison of velocity profiles corresponding to results of case No. 5 using coarse, fine and dynamic mesh. From alpha profiles (liquid volume 4

8 No. M. Ref. No. Temp. Gas density G. viscosity Liquid density L. viscosity Surface tension C kg/m 3 m 2 /s 10 6 kg/m 3 m 2 /s 10 6 kg/s (0.07) (0.07) 5a b c d a b Table 3: Physical and material properties used for the numerical simulations. fraction) in the same figure, it can be seen that the interface resolution is better for the dynamic mesh, since the mesh refinement on the interface is the finest from these three assessed meshes. On the other hand, there are no differences between the liquid velocity profile on the wall as can be seen from the same near wall velocity profiles depicted in logarithmic coordinates in Figure 6. Thus, the near wall region seems to be well resolved for all meshes. Figure 4: Profiles of alpha and velocity in dependence on mesh refinement. Figure 5: Velocity profiles in dependence on mesh refinement. 5

9 Figure 6: Phase interface using dynamic mesh in comparison with coarse and fine static mesh. The bigger velocity gradient on the interface implicates the bigger shear stress between phases, thus the surface instabilities are influenced by the mesh refinement on the interface more than by the mesh refinement in general. Figure 7 shows the comparison of alpha field computed using fine, extra fine and dynamic mesh. In case of extra fine and dynamic mesh, the instabilities are developed earlier and moreover the flow patterns seems to be quite different than in case of fine mesh. The arrows in Figure 7 point on the broad locations where the liquid touches the top wall of the tube and the flow pattern can be named as slug or plug/elongated bubble in dependence on the definitions. In contrast, only classical sharp solitary waves touching the wall in one point are observed using the static coarse, normal and fine mesh. Figure 7: Comparison of alpha field computed using fine, extra fine and dynamic mesh. 6

10 As is shown below, see Figure 9, similar flow patterns are obtained also using coarse mesh with suitable phase inlet distribution. Thus, it can be concluded that appropriate mesh refinement and phase inlet distribution are essential for right flow pattern resolution. Because even fine mesh defined in Table 1 does not reproduce the same flow pattern as extra fine mesh, the mesh study just presented is not completed and some other meshes should be used for mesh dependency study. In Figures 10-13, the comparison of time evolution of alpha computed using dynamic and static meshesh for different fluid properties is depicted. The values of alpha are received as mean values of alpha field in cross-section located in z=11 m. The time intervals are selected so as the mean values over the interval are not affected by the signal representing disturbance which has not been evolved yet. The results in all cases No. 5a) - 5d) show, that the flow patterns are nearly the same for coarse, normal and fine meshes, while different flow pattern is established for dynamic mesh, as was discussed above. Next, the main frequencies decrease with increasing mesh density. Thus, the flow pattern frequency seems to be the appropriate parameter for assessment of the mesh convergence. The summary of these results is shown in Figure 8. The squares correspond to the mean values of alpha in chosen time interval, while the upper and lower points of lines correspond to maximum and minimum alpha values, respectively. As can be seen, the alpha mean values and alpha ranges are nearly the same for all static meshes. The adaptive meshing leads to bigger alpha ranges, which is explained by different flow pattern as can be seen from corresponding plots. Figure 8: Comparison of mean alpha over time in section z=11m for cases No. 5a) - No. 5d). 7

11 7.2 Influence of the inlet boundary conditions Influence of artificial perturbation As was mentioned in section 4, the velocity perturbation is important for right flow pattern development. It was found, see [2], that using uniform velocity profile without artificial perturbation described by formula (1) only stratified flow has been developed even in cases where slug flow should be found according to experimental observations. For these reasons the artificial perturbation has been used in all cases. The velocity fluctuations defined by formula (1) can be driven by amplitude A i. However, no influence has been found for any reasonable values Influence of phase distribution at inlet section The Figure 9 shows the comparison of results computed for case No. 5b) using phase inlet distribution a) - c), see Figure 3, with coarse meshes and using inlet distribution b) with extra fine mesh. As can be seen, the impact of phase inlet distribution is quite important. From the comparison of the alpha evolution for coarse mesh with inlet c) with extra fine mesh results follows, that the inlet distribution should be imposed in similar manner as is the natural established distribution downstream. The impact of this boundary condition in case of enough fine mesh should be the object of next study. 7.3 Influence of the fluid properties Influence of the fluid properties has been studied using case No. 5 for fluid properties 5a) - 5d), see Table 3. The corresponding results are depicted in Figures and in Figure 8. The fluid properties does not influence the mean alpha value, what is the essential need, since it represents the average volume flow rate, which should be similar in all cases. The alpha ranges seem to be wider for oils with higher viscosities, although we should have in mind, that all fluid properties change according to defined temperature. Thus, more detailed study of each fluid property should by done. 8 Conclusion This study gives an overview of the main conclusions from number of simulations computed using OpenFOAM. The aim has been focused on study of mesh dependency, impact of boundary conditions and influence of fluid properties. As was shown in section 7.1, the results using the finest mesh differ from results computed using other meshes. Hence, the presented mesh study can not be assessed as completed and more finer meshes should be used for examination of mesh convergence. Although it was shown, that suitable combination of mesh density and boundary condition can be succesful in flow pattern resolution, the quantitative parameters as slug frequency are still mesh dependent, which also supports the need of better refinement. 8

12 Since the time requirements for numerical solution bounded the number of cells of using meshes, the presented influence of fluid properties can be used rather in qualitative sense. The study suggests, that higher oil viscosity (reached for lower temperature) supports establishing of bigger waves and the resulting flow pattern could be more inclinable to slug creation. Acknowledgements The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. References [1] G. Kok, P. Lucas, D. van Putten, T. Leonard, E. Graham, R. Harvey, A. Lupeau, M. T. Smith, L. Zakharov and R. de Leeuw. Test protocols for single and multiphase intercomparisons. Deliverable of WP1 Multiphase Laboratory Intercomparison in EMRP project ENG58 Multiphase flow metrology in oil and gas production, [2] A. Fiebach, S. Knotek, and S. Schmelter. 5 validated and verified CFD models to determine the influences of selected process / fluid property parameters on flow patterns. Deliverable of WP2 Determination of Multiphase Flow Pattern in EMRP project ENG58 Multiphase flow metrology in oil and gas production, [3] A. Fiebach, S. Knotek, and S. Schmelter. Specification of parametric values, geometry and boundary conditions for multiphase flow simulations covering the conditions of the intercomparison tests. Deliverable of WP3 Advanced Numerical Modelling in EMRP project ENG58 Multiphase flow metrology in oil and gas production, [4] S. Knotek, A. Fiebach and S. Schmelter. Numerical simulation of multiphase flows in large horizontal pipes Flomeko 2016 Sydney, Australia, September 26-29,

13 Figure 9: Mean alpha over time in section z=11m computed using coarse mesh for case No. 5b) with inlet subdomains a) - c) in comparison with mean alpha computed using extra fine mesh with inlet subdomain b). 10

14 Figure 10: Comparison of alpha field computed using static and dynamic mesh for case No. 5a (15 C) defined in Table 2 and 3. 11

15 Figure 11: Comparison of alpha field computed using static and dynamic mesh for case No. 5b defined in Table 2 and 3. 12

16 Figure 12: Comparison of alpha field computed using static and dynamic mesh for case No. 5c defined in Table 2 and 3. 13

17 Figure 13: Comparison of alpha field computed using static and dynamic mesh for case No. 5d defined in Table 2 and 3. 14