Ecd Explanation
3
Detailed explanation of Equivalent Circulating Density calculation It is assumed that the drilling mud behaves like a Binghamplastic nonnewtonian fluid. First, the wellbore geometry must be defined with each drill string and wellbore section, including intermediate casing strings and openhole sections, such that all relevant outer and inner diameters, and length combinations are accounted the example figure shows one string and two wellbore sections. The annular area of each section can be calculated as: = !(! ! ! !! ! ! ) ! , Equation 1 where D o is the outer diameter (inner diameter of casing/openhole) and D i is the inner diameter (drill string). The annular fluid velocity within each section can be calculated as ! = ! ! , Equation 2 where Q is the volumetric flow rate. The hydraulic diameter associated with the annular section, ! = !! ! , Equation 3
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Transcript of Ecd Explanation
Detailed explanation of Equivalent Circulating Density calculation
It is assumed that the drilling mud behaves like a Bingham-‐plastic non-‐newtonian fluid. First, the wellbore geometry must be defined with each drill string and wellbore section, including intermediate casing strings and openhole sections, such that all relevant outer and inner diameters, and length combinations are accounted -‐-‐ the example figure shows one string and two wellbore sections. The annular area of each section can be calculated as:
𝐴 = !(!!!!!!!)
! , Equation 1
where Do is the outer diameter (inner diameter of casing/openhole) and Di is the inner diameter (drill string). The annular fluid velocity within each section can be calculated as
𝑣! =!!, Equation 2
where Q is the volumetric flow rate. The hydraulic diameter associated with the annular section,
𝐷! =!!!, Equation 3
where P is the wetted perimeter
𝑃 = 𝜋(𝐷! + 𝐷!). Equation 4
The Reynold's number in reference to the hydraulic diameter is
𝑅𝑒 = !!!!!!
, Equation 5
where 𝜌 is the fluid density and 𝜇 is the plastic viscosity, while the Hedstrom number is
𝐻𝑒 = !!!!!!!!
, Equation 6
where 𝜏! is the yield point (yield strength) of the fluid. Using Re and He, the laminar friction factor fL can be calculated using the Swamee and Aggarwal approximation to the exact solution,
𝑓! =!"!"+
!".!" ! !.!"!" !"!"
!.!"#
! ! !.!"#$ !"!"
!.!"!"
!"!"
, Equation 7
and the turbulent friction factor fT:
𝑓! = 10!𝑅𝑒!.!"# , Equation 8
where
𝑎 = −1.47 1 + 0.146 exp −2.9 ∗ 10!!𝐻𝑒 . Equation 9
A combined friction factor f for all flow profiles can be calculated as,
𝑓 = 𝑓!! + 𝑓!!!!, Equation 10
where
𝑚 = 1.7 + !""""!"
. Equation 11
The pressure drop through each annular section can be calculated using the Darcy-‐Weisbach equation,
∆𝑃 = !"!!!!!!!
, Equation 12
and the total pressure drop through all sections is the sum of all subsequent pressure drops. The equivalent circulating density is
𝜌!"# =∆!!"!!"
+ 𝜌, Equation 13
where g is the gravitational constant and H is the vertical depth of the well.
References
Darby, R. and Melson J.(1981). "How to predict the friction factor for flow of Bingham plastics". Chemical Engineering 28: 59–61.
Swamee, P.K. and Aggarwal, N.(2011). "Explicit equations for laminar flow of Bingham plastic fluids". Journal of Petroleum Science and Engineering. doi:10.1016/j.petrol.2011.01.015.
