Hydraulics

•Once the rheological properties for a fluid have been determined and modeled to predict flow behavior, hydraulics calculations are made to determine what effect this particular fluid will have on system pressures.
•The critical pressures are total system pressure (pump pressure), pressure loss across the bit and annular pressure loss (converted to ECD)
•Many wells are drilled under pressure limitations imposed by the drilling rig and associated equipment.
–The pressure ratings of the pump liners and surface equipment and the number of mud pumps available limit the circulating system to a maximum allowable circulating pressure.
•It is imperative to optimize drilling fluid hydraulics by controlling the rheological properties of the drilling fluid to avoid reaching this theoretical limit.
–This is especially true in extended-reach drilling.
•Fluids in laminar flow “act”differently than fluids in turbulent flow.
–These differences make it necessary to use different equations to determine the pressure losses in laminar and turbulent flow.
–Different equations are also required to calculate the pressure losses in the annulus and drillstring because of different geometries.
•The first step in hydraulics calculations is to determine which stage of flow is occurring in each geometric interval of the well.
•The velocity of the fluid in each of these intervals can be determined with the following equations.

Bulk Velocity

•Average bulk velocity in pipe (Vp):
Vp (ft/min) = 24.48 x Q (gpm)/(D)*2(in.)
•Average bulk velocity in annulus:Va (ft/min) =24.48 x Q (gpm)/ ((D2)*2–(D1)*2)(in.)

–V = Velocity (ft/min)
–Q = Flow ratio (gpm)
–D = Diameter (in.)

Reynolds Number

•The Reynolds number (NRe) is a dimensionless number that is used to determine whether a fluid is in laminar or turbulent flow.
–A Reynolds number less than or equal to 2,100 indicates laminar flow.
–A Reynolds number greater than 2,100 indicates turbulent flow.
–Earlier API hydraulics bulletins and many hydraulics programs that predate the current API hydraulics bulletin define laminar and turbulent flow differently.
•The general formula for Reynolds number is:
NRe= V Dr/μ
V = Velocity
D = Diameter
r = Density
μ= Viscosity
•The Reynolds number for inside the pipe is:
NRep= 15.467 x Vp x D x r/μep
•The Reynolds number for the annulus is:
NRea= 15.467x Va x (D2-D1) x r/μea
•D = ID drill pipe or drill collars
•D2= ID hole or casing
•D1= OD drill pipe or drill collars
•μep= Effective viscosity (cP) pipe
•μea= Effective viscosity (cP) annulus

Critical Velocity

•The critical velocity is used to describe the velocity where the transition occurs from laminar to turbulent flow.
•Flow in the drill pipe is generally turbulent.
•The equations for critical velocity in the pipe and in the annulus are listed below.
•Critical Pipe Velocity Vcp(ft/min)= ((38727 x Kp)/r)*(1/(2-n)) x ((1.6/D)x((3n+1)/4n)* (n(2-n))
•Critical Pipe Flow rate Qca(gpm)= VcpD*2/24.51
•Critical Annular Velocity Vca(ft/min)= ((25818 x Ka)/r)*(1/(2-n)) x ((2.4/(D2-D1))x((3n+1)/4n) *(n(2-n))
•Critical Annular Flow rate Qca(gpm)= Vca(D2-D1)*2/24.51