Equivalent Circulating Density (ECD) with complex engineering equations

Description:

These formulas below are used for complex calculation for annular pressure loss and equivalent circulating density. These calculations will give more accurate result than a simple equation.

Equation:

n factor: $$ n = 3.32 \times \log\left(\frac{\theta_{600}}{\theta_{300}}\right) $$ k factor: $$ k = \frac{\theta_{300}}{511^{n}} $$ Annular Velocity (V): $$\text{V} = \frac{24.5 \times Q}{(D_h^2 - D_p^2)}$$ Critical Velocity (Vc): $$V_c = \left( \frac{3.878 \times 10^4 \times k}{MW} \right)^{\frac{1}{2-n}} \times \left( \frac{2.4}{D_h - D_p} \times \frac{2n + 1}{3n} \right)^{\frac{n}{2-n}}$$ Pressure loss for laminar flow (Ps): $$\text{Ps} = \frac{32 \times \mu \times L \times V}{D_h^2 - D_p^2}$$ Pressure loss for turbulent flow (Pt): $$\text{Pt} = \frac{0.052 \times MW \times L \times V^2}{D_h - D_p}$$ Equivalent Circulating Density (ECD) Calculation: $$\text{ECD} = \frac{P}{0.052 \times TVD} + MW$$

Where:

\( \text{ECD} \) = Equivalent Circulating Density, ppg

\( \text{Ps} \) = Pressure loss for laminar flow, psi

\( \text{Pt} \) = Pressure loss for turbulent flow, psi

\(P\) = Total Annular pressure loss, psi

\( \text{V} \) = Annular velocity, ft/min

\(V_c\) = Critical velocity, ft/min

\( \text{MW} \) = Mud weight, ppg

\( \text{YP} \) = Yield Point, cp

\( \text{PV} \) = Plastic Viscosity, cp

\( \text{L} \) = Pipe length, ft

\( \text{Q} \) = Flow rate, gpm

\( D_h \) = Hole size, inch

\( D_p \) = Pipe OD, inch

\( \text{TVD} \) = True Vertical Depth, ft

\( \theta_{300} \) = Viscometer dial reading at 300 rpm

\( \theta_{600} \) = Viscometer dial reading at 600 rpm

Practical Consideration:

Flow regime significantly impacts on ECD in which creating high annular pressure.