Rheology

•Fluid types
–There are two basic types of fluids, Newtonian and non-Newtonian.
–Rheological and hydraulic models have been developed to characterize the flow behavior of these two types of fluids.
•Newtonian fluids have a constant viscosity at a given temperature and pressure condition. Common Newtonian fluids include:
–Diesel
–Water
–Glycerin
–Clear brines
•Non-Newtonian fluids have viscosities that depend on measured shear rates for a given temperature and pressure condition. Examples of non-Newtonian fluids include:
–Most drilling fluids
–Cement

Rheological models

•Rheological models help predict fluid behavior across a wide range of shear rates.
•Most drilling fluids are non-Newtonian, pseudoplasticfluids.
•The most important rheological models that pertain to them are the:
–Bingham model
–Power law model
–Yield-power law or modified power law

•The Bingham model describes laminar flow using the following equation:
t = YP + (PV ×y)
–Where
–t is the measured shear stress in lb/100 ft2
–YP is the yield point in lb/100 ft2
–PV is the plastic viscosity in cP
–y is the shear rate in sec-1
•Current API guidelines require the calculation of YP and PV using the following equations:
•PV = 600rpm–300rpm
•YP = 300rpm–PV
•The power law model describes fluid rheological behavior using the following equation:
t = K ×(y)to the power n
•This model describes the rheological behavior of polymer-based drilling fluids that do not exhibit yield stress (i.e., viscosifiedclear brines).
•Some fluids viscosifiedwith biopolymers can also be described by power-law behavior.
•The general equations for calculating a fluid's flow index and consistency index are:
n =( log(t2/t1))/(log(y2/y1))
K = (t2)/(y2to the power n)
t is the calculated shear stress in lb/100 ft2
•t2is the shear stress at higher shear rate (600 rpm)
•t1is the shear stress at lower shear rate (300 rpm)
•n is the flow index
•y is the shear rate in sec-1
•y2is the higher shear rate (600)
•y1is the lower shear rate (300)
•K is the consistency index
•Because most drilling fluids exhibit yield stress, the Yield-power law [YPL]) model describes the rheological behavior of drilling muds more accurately than any other model.
•The YPL model uses the following equation to describe fluid behavior:
t = t0+ (K ×y)to the power n
–Where
–t is the measured shear stress in lb/100 ft2
–t0is the fluid's yield stress (shear stress at zero shear 0 rate) in lb/100 ft2
–K is the fluid's consistency index in cPor lb/100 ft2secn
–n is the fluid's flow index
–y is the shear rate in sec-1
•K and n values in the YPL model are calculated differently than their counterparts in the power law model.
•The YPL model reduces to the Bingham model when n = 1 and it reduces to the power law model when t0= 0.
•An obvious advantage the YPL model has over the power law model is that, from a set of data input, only one value for n and K are calculated.
–Note: The YPL model requires:
•A computer algorithm to obtain solutions.
•A minimum of three shear-stress/shear-rate measurements for solution. Model accuracy is improved with additional data input.