Tekna Flow Assurance 2015, Larvik Improved fluid control by proper non-newtonian flow modeling Stein Tore Johansen, SINTEF Sjur Mo, SINTEF A general wall friction model for a non-newtonian fluid has been developed and compared successfully to experimental data. The model computes the velocity profiles, for given rheology, velocity, pipe diameter and wall roughness, and results in a generic friction factor which can be applied to fluids with non-newtonian behavior. The transition between laminar and turbulent flow is included. In the presentation we compare model and experimental pressure drops for various rheologies. A case of cleanup of a well containing water based mud is discussed Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 1
Introduction Non-Newtonian flows are present in many situations All oils where precipitation is thermodynamically possible Precipitated particles may cause non-newtonian rheology Precipitates, such as asphaltenes, wax, naphthenic acids, inorganic salts Emulsions formed by the flow and where fluid interfaces are modified and stabilized by surfactants or particles Drilling operations. The drilling fluids contain different types of particles. The fluid base may be some stabile emulsion. Completion fluids Typical flow assurance situations where non-newtonian effects must be respected Flows with precipitated wax, hydrates, as well as emulsions Well clean-up: Leftover drilling fluids and completion fluids Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 2
Rheology Assumption: the magnitude of the stress in the fluid is a pure function of strain rate (velocity gradient) Can be obtained from rheometer tests n U n1 ( S) 0 KS ; S ( S) / S 0 / S KS y Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 3
A generic model for pipeflow The steady state momentum equation for flow in a pipe gives us: y U w(1 ) y ( S) U R (1 ) w t R S y y ( S) t S The rheology of the fluid is Yield Power Law (Herschel-Bulkley): ( S) KS ; S U y n 0 Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 4
The turbulent viscosity 2 max( s, y ) ( S ) ;max(, ) 51.98 w s y t g( S, 0, R, w) 11.4 S w Generic transition function max( s, y ) ; max( s, y ) 51.98 Wall viscosity High Re dimensionless kinematic turbulent viscosity s f( ) f( S, 0, R ) g( S, 0, R, w) 1 e w 1 ( ) (-0.0285*max(60, R )+1.61) Transition function Non-newtonian low Re correction u U where y, R, s y, R, s y, R, s wall y U ( wall y ) wall Ref: ASHRAFIAN, A. & JOHANSEN, S. T. 2007. Wall boundary conditions for rough walls. Progress in Computational Fluid Dynamics, 7, 230-236 Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 5
Numerical solution (1 ) By guessing the wall shear stress we find The velocity profile The averaged velocity y U w R y ( S) t S If the required velocity is not met correct wall shear stress until convergence Compute friction factor versus Re Re S : Use U/ y Wall based on laminar Newtonian flow Re W : Use actual U/ y Wall 4U UD UDS UD 8U R R 2 Re S D S 4U 4U Re W 2UR 2UR w 0 w w K 1/ n IMPLICIT! Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 6
Predicted friction factors for Newtonian flows Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 7
Predicted effect on wall roughness of friction factors for Newtonian flows Roughness transition: s+<70 Re Re S 2 8U 8U D Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 8
Predicted effect on wall roughness of friction factors for non-newtonian flow (S) 2.827 Pa+0.047 S 1045 kg/m 3 0.806 Re Re S 2 8U 8U D Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 9
Model validation (data from Chilton & Stainsby) (S) 1.268 Pa+0.214 S 1024 kg/m 3 0.613 (S) 0.727 Pa+0.069 S 1011 kg/m 3 0.664 CHILTON, R. & STAINSBY, R. 1998. Pressure Loss Equations for Laminar and Turbulent Non-Newtonian Pipe Flow. Journal of Hydraulic Engineering, 124, 522-529 Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 10
Model validation (data from Chilton & Stainsby) (S) 2.827 Pa+0.047 S 1013 kg/m 3 0.806 (S) 1.273 Pa+0.189 S 1016 kg/m 3 0.594 CHILTON, R. & STAINSBY, R. 1998. Pressure Loss Equations for Laminar and Turbulent Non-Newtonian Pipe Flow. Journal of Hydraulic Engineering, 124, 522-529 Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 11
Model validation (data from El-Nahhas et al., 2005) (S) 1.950 Pa+0.090 S 1170 kg/m 3 0.610 (S) 6.0Pa 0.325 S 1223 kg/m 3 0.505 EL-NAHHAS, K., GAD EL-HAK, N., ABOU RAYAN, M. & EL-SAWAF, I. FLOW BEHAVIOUR OF NON-NEWTONIAN CLAY SLURRIES. Ninth International Water Technology Conference, IWTC9 2005, 2005 Sharm El-Sheikh, Egypt. 627-640 Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 12
Model validation (data from El-Nahhas et al., 2005) (S) 14.0Pa 0.755 S 1283 kg/m 3 0.465 Model inaccuracy: Laminar turbulent transition model issue! EL-NAHHAS, K., GAD EL-HAK, N., ABOU RAYAN, M. & EL-SAWAF, I. FLOW BEHAVIOUR OF NON-NEWTONIAN CLAY SLURRIES. Ninth International Water Technology Conference, IWTC9 2005, 2005 Sharm El-Sheikh, Egypt. 627-640 Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 13
Velocity profiles (S) 2.827 Pa+0.047 S 1013 kg/m 3 0.806 High yield stress velocity profile becomes more "laminar" at high Re Log region is modified Velocity profile controls local viscosity and sedimentation / separation of particles, droplets and bubbles Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 14
Simulations of 2.3 km long well Reservoir pressure : 91 bar Exit pressure: 16 bar Well PI = 0.5 kg/(bar sec) Initially well is filled with stagnant water, oil and gas Oil zone Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 15
Restart scenarios (pure brine or water based mud in well) Brine in well: Restart Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 16
Restart scenarios (pure brine or Water Based Mud in well) Water based mud in well: Restart (S) 2.5Pa 0.40 S 0.80 Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 17
Pressure distribution some time after restart Brine in well: Pressure after 12348 sec Water based mud in well: Pressure after 17331 sec Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 18
Profiles of mass fractions of water based mud in water zone Burst of produced water entering well Only brine in well Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 19
Very small inflow after restart with water based mud in well Need to simulate for very long time to see if well can be restarted! Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 20
Summary - model A numerical model is established for friction in non-newtonian flows The model can represent available experimental data well The model gives for the first time a method to include wall roughness into non- Newtonian wall friction predictions The model can be applied directly as boundary condition in CFD (Computational Fluid Dynamics) simulations The model can easily be extended to represent heat transfer (mildly temperature dependent rheologies) The model is quite computationally intensive: i) Huge potential for speed optimization ii) Easy to generate pre-calculated friction factor curves for any fluid rheology allows superfast friction calculations Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 21
Summary of sample simulation A non-newtonian model has been implemented into LedaFlow Here we investigated the "water phase" as a mixture of brine and WBM. Water based mud sitting in a well is very challenging to clean out due to Yield stress of mud High effective viscosity of mud A combined effect of the two above is that initial velocity during clean-up may be too low, such that only trapped gas can escape, making the situation worse Mud may only partially be cleaned out, restricting wellbore area and limiting production Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 22
Acknowledgements The sponsors contributing to this development are gratefully acknowledged: The NFR sponsored project Advanced Wellbore Transport Modelling, with partners Statoil, GDF SUEZ E&P Norge, IRIS, UiS, NTNU and SINTEF LedaFlow Technologies DA Tekna Flow Assurance 2015, Larvik Teknologi for et bedre samfunn 23