Improved fluid control by proper non-newtonian flow modeling

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• 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

Improved fluid control by proper non-Newtonian flow modeling

Stein Tore Johansen, SINTEF Sjur Mo, SINTEF

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• 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

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• Assumption: the magnitude of the stress in the fluid is a pure function of strain rate (velocity gradient)

• Can be obtained from rheometer tests

Rheology

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• The steady state momentum equation for flow in a pipe gives us:

• The rheology of the fluid is Yield Power Law (Herschel-Bulkley):

A generic model for pipeflow

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The turbulent viscosity

Ref: ASHRAFIAN, A. & JOHANSEN, S. T. 2007. Wall boundary conditions for rough walls. Progress in

Computational Fluid Dynamics, 7, 230-236  

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Generic transition function Wall

viscosity

High Re dimensionless kinematic turbulent viscosity

max( , ) ; max( , ) 51.98 ( ) ( , , , ) 11.4 max( , ) ; max( , ) 51.98 w t w w S s y s y S g R S s y s y                      _ _  _     

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1 ( ) (-0.0285*max(60, )+1.61) 0 0 Transition function Non-newtonian low Re correction

( , , ) ( , , , ) 1 where , R , , R, , R, R w w wall wall u S S f R g R e U y s y s y s y                    _  _         ( ) wall U y   ( ) s  f 

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• By guessing the wall shear stress we find • The velocity profile

• The averaged velocity

• 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

Numerical solution

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2 4 4 4 8 Re_S S _U _U R R U U D U D U DS  _D U                        1/ 0 2 2 Re n w W w w U R U R K            _ _   IMPLICIT !

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Predicted effect on wall roughness of friction factors for

Newtonian flows

Roughness transition: s+<70 2 8 Re Re 8 S U D U          

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Predicted effect on wall roughness of friction factors for

non-Newtonian flow

2 8 Re Re 8 S U D U           0.806 3 (S) 2.827 Pa+0.047 S 1045 kg/m     

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Model validation (data from Chilton & Stainsby)

CHILTON, R. & STAINSBY, R. 1998. Pressure Loss Equations for Laminar and Turbulent Non-Newtonian Pipe Flow. Journal of Hydraulic Engineering, 124, 522-529

0.613 3 (S) 1.268 Pa+0.214 S 1024 kg/m      0.664 3 (S) 0.727 Pa+0.069 S 1011 kg/m     

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Model validation (data from Chilton & Stainsby)

CHILTON, R. & STAINSBY, R. 1998. Pressure Loss Equations for Laminar and Turbulent Non-Newtonian Pipe Flow. Journal of Hydraulic Engineering, 124, 522-529

0.806 3 (S) 2.827 Pa+0.047 S 1013 kg/m      0.594 3 (S) 1.273 Pa+0.189 S 1016 kg/m     

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Model validation (data from El-Nahhas et al., 2005)

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,

0.610 3 (S) 1.950 Pa+0.090 S 1170 kg/m      0.505 3 (S) 6.0 0.325 1223 kg/m Pa S      

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Model validation (data from El-Nahhas et al., 2005)

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,

0.465 3 (S) 14.0 0.755 1283 kg/m Pa S       Model inaccuracy:

Laminar – turbulent transition model issue !

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Velocity profiles

• High yield stress  velocity profile becomes more "laminar" at high Re • Log region is modified

• Velocity profile controls local viscosity and sedimentation / separation of

0.806 3 (S) 2.827 Pa+0.047 S 1013 kg/m     

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• 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

Simulations of 2.3 km long well

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Restart scenarios (pure brine or water based mud in well)

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Restart scenarios (pure brine or Water Based Mud in well)

Water based mud in well: Restart 0.80

(S) 2.5Pa 0.40 S

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Pressure distribution some time after restart

Water based mud in well: Pressure after 17331 sec Brine in well: Pressure after 12348 sec

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Profiles of mass fractions of water based mud in water

zone

Only brine in well

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Very small inflow after restart with water based mud in

well

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• 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

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• 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

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• 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