Calculate the equivalent circulating density ECD (in ppg) during circulation through partially closed choke using the following information:
a. Fluid density is 1.162 g/cc,
b. Well total depth is 9529 ft
c. Pump flow rate is 426 gpm,
d. Drill string pressure loss is 1389 psi,
e. Annulus pressure loss is 309 psi,
f. Choke backpressure is 383 psi,
The Correct Answer and Explanation is:
- Fluid density, $\rho = 1.162 \, \text{g/cc}$
- Total depth, $TVD = 9529 \, \text{ft}$
- Pump flow rate = 426 gpm (not directly needed for ECD calculation here)
- Drill string pressure loss, $\Delta P_{ds} = 1389 \, \text{psi}$
- Annulus pressure loss, $\Delta P_{ann} = 309 \, \text{psi}$
- Choke backpressure, $\Delta P_{choke} = 383 \, \text{psi}$
Step 1: Understand Equivalent Circulating Density (ECD)
ECD represents the effective mud density when circulating, accounting for frictional pressure losses due to fluid movement inside the wellbore (drill string and annulus) plus any additional choke backpressure. ECD is critical in drilling operations because it affects wellbore pressure and stability.
The general formula for ECD is:
$$
ECD = \text{Static Mud Density} + \frac{\text{Total Pressure Losses}}{0.052 \times \text{TVD}}
$$
Where:
- Pressure losses include drill string pressure loss, annulus pressure loss, and choke backpressure.
- 0.052 is a constant used to convert psi/ft to ppg.
Step 2: Convert Fluid Density to ppg
Density is given in g/cc, convert it to ppg:
$$
1 \, \text{g/cc} = 8.34 \, \text{ppg}
$$
$$
\text{Static mud density} = 1.162 \times 8.34 = 9.69 \, \text{ppg}
$$
Step 3: Calculate total pressure loss during circulation
Add all pressure losses:
$$
\Delta P_{total} = \Delta P_{ds} + \Delta P_{ann} + \Delta P_{choke} = 1389 + 309 + 383 = 2081 \, \text{psi}
$$
Step 4: Calculate the pressure gradient in ppg
$$
\text{Pressure gradient (ppg)} = \frac{\Delta P_{total}}{0.052 \times TVD} = \frac{2081}{0.052 \times 9529}
$$
Calculate denominator:
$$
0.052 \times 9529 = 495.5
$$
Calculate pressure gradient:
$$
\frac{2081}{495.5} = 4.2 \, \text{ppg}
$$
Step 5: Calculate Equivalent Circulating Density (ECD)
$$
ECD = \text{Static Mud Density} + \text{Pressure gradient due to losses} = 9.69 + 4.2 = 13.89 \, \text{ppg}
$$
Final Answer:
$$
\boxed{ECD = 13.89 \, \text{ppg}}
$$
Explanation (300 words):
Equivalent Circulating Density (ECD) is a vital concept in drilling engineering because it helps assess the effective hydrostatic pressure exerted by the drilling fluid when it is circulating. While static mud density determines the hydrostatic pressure under static conditions, circulating mud experiences frictional losses inside the drill string, annulus, and choke. These losses increase the bottom hole pressure beyond the static value, potentially risking formation fracturing or well control issues if not properly monitored.
To calculate ECD, we start by converting the static mud density from grams per cubic centimeter (g/cc) to pounds per gallon (ppg), since ppg is the standard unit used in drilling operations for mud density. Using the conversion factor $1 \, \text{g/cc} = 8.34 \, \text{ppg}$, the given fluid density of 1.162 g/cc corresponds to about 9.69 ppg.
The total pressure loss includes the drill string pressure loss, annulus pressure loss, and choke backpressure. These losses together sum to 2081 psi. These pressure losses increase the effective mud density during circulation.
Using the formula $ECD = \text{Static Mud Density} + \frac{\text{Total Pressure Loss}}{0.052 \times TVD}$, where 0.052 is a constant to convert psi/ft into ppg, and TVD (True Vertical Depth) is 9529 ft, we calculate the pressure gradient caused by friction losses as 4.2 ppg.
Adding this to the static mud density gives an ECD of 13.89 ppg.
This elevated mud density means the wellbore pressure while circulating is significantly higher than the static pressure. Accurate ECD calculation ensures proper mud weight selection to prevent fracturing the formation or causing a kick, which is critical for safe and efficient drilling operations.
