HYDRAULICS

1. RHEOLOGY

• Science of deformation and flow of matter. • In the oil field: study and control of flow properties and viscosity of the mud. • 3 factors for cutting removal: ➢ MW : buoyancy ➢ Annular velocity: function of annulus size and flow rate ➢ Viscosity : to avoid slip velocity

1 Shear stress and shear rate: How to quantify viscosity

Shear stress: τ= F/A τ in dynes/cm3 F = force applied to overcome resistance of fluid to flow in dynes A = Area subjected to stress in cm2

Shear rate : γ = V/H γ in sec –1 V = Relative velocity of fluid layers in cm/sec H = Separation distance of the fluid layers in cm

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Relationship between shear stress and shear rate

The relationship between the two is:

Dynamic viscosity in cP : μ ’ τ/γ

2 Fluid flow type:

2 types depending of relation ship between shear rate and shear stress:

➢ Newtonian: water, oil ➢ Non-Newtonian: paint, drilling fluids (dissolved solids cause the relationship to be non linear))

❖ Plastic is linear but needs a specific amount of shear stress to start moving :YP (Bingham equations)

❖ Pseudo-plastic is not linear and has no YP (Power law equations)

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2. MUD PROPERTIES

A. Apparent viscosity or Funnel or MARSH viscosity in sec

B. Viscosimeter
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μp = PV= θ600 – θ300 in cP (slope of shear stress/shear rate curve)

τ0 = YP = θ300 – PV in lb/100ft2 (Be careful with Agip which uses metric unit)

Apparent viscosity: slope of the shear stress/shear rate relationship as though the fluid were Newtonian: