6.2 Kill Mud Weight, ICP & FCP Calculations

When a well is shut in following an influx, the wellbore functions as a giant hydraulic U-tube. The drill string forms one leg of the U-tube and the annulus forms the other, connected at the bottom through the bit nozzles. To safely circulate the influx out and regain primary well control without allowing additional influx or fracturing the formation, the rig team must maintain Constant Bottom-Hole Pressure (CBHP). This is accomplished by calculating three core parameters: Kill Mud Weight (KMW), Initial Circulating Pressure (ICP), and Final Circulating Pressure (FCP), and executing a drill pipe pressure step-down schedule.

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1. Kill Mud Weight (KMW) Derivation and Formulas

At shut-in, the static bottom-hole pressure ($BHP$) equals formation pore pressure ($P_f$):

$BHP = HP_{\text{string}} + \text{SIDPP} = P_f$

Because the formation influx entered the annular space, the fluid column inside the drill string remains uncontaminated and retains its original mud density ($\text{Current MW}$). Therefore, the difference between the hydrostatic pressure inside the pipe and the formation pore pressure is registered directly on the surface standpipe gauge as the Shut-In Drill Pipe Pressure (SIDPP).

To restore primary hydrostatic overbalance, the drilling fluid density must be raised to Kill Mud Weight (KMW) so that the static hydrostatic column alone equals formation pore pressure:

$HP_{\text{kill mud}} = 0.052 \times \text{KMW} \times \text{TVD} = P_f$

Substituting $P_f = (0.052 \times \text{Current MW} \times \text{TVD}) + \text{SIDPP}$:

$0.052 \times \text{KMW} \times \text{TVD} = (0.052 \times \text{Current MW} \times \text{TVD}) + \text{SIDPP}$

Dividing both sides by $0.052 \times \text{TVD}$ yields the standard Kill Mud Weight formula:

Imperial Field Formula

$\text{KMW} = \text{Current MW} + \frac{\text{SIDPP}}{0.052 \times \text{TVD}}$

Where $\text{KMW}$ and $\text{Current MW}$ are in pounds per gallon ($\text{ppg}$), $\text{SIDPP}$ is in $\text{psi}$, and $\text{TVD}$ is the True Vertical Depth of the well in feet ($\text{ft}$).

Metric Field Formula

$\text{KMW} = \text{Current MW} + \frac{\text{SIDPP} \times 10.2}{\text{TVD}}$

Where $\text{KMW}$ and $\text{Current MW}$ are in $\text{kg/l}$ (or specific gravity), $\text{SIDPP}$ is in $\text{bar}$, and $\text{TVD}$ is in meters ($\text{m}$).

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2. Initial Circulating Pressure (ICP)

The Initial Circulating Pressure (ICP) is the total standpipe drill pipe pressure required to circulate fluid through the well system at the selected Slow Circulation Rate (SCR) immediately upon initiating well kill operations.

$\text{ICP} = \text{SCR} + \text{SIDPP}$

Physical Derivation

When the mud pump is brought up to the designated kill rate:

1. Dynamic friction through the surface piping, drill string bore, bit nozzles, and annular space generates circulating pressure loss equal to the pre-recorded $\text{SCR}$.
2. To keep bottom-hole pressure balanced against the formation, the surface choke must hold an additional backpressure equal to the pore pressure deficit, represented by $\text{SIDPP}$.
3. The sum of these two pressures yields $\text{ICP}$. Bottom-hole pressure during initial circulation is: $\text{BHP} = HP_{\text{string}} + \text{ICP} - \Delta P_{\text{string+bit}} = HP_{\text{string}} + \text{SIDPP} + APL = P_f + APL$ This provides a safe dynamic overbalance equal to the annular pressure loss ($APL$) at the slow kill speed.

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3. Final Circulating Pressure (FCP)

The Final Circulating Pressure (FCP) is the dynamic standpipe drill pipe pressure required to circulate once the drill string has been completely displaced with kill mud from surface to the bit nozzles.

$\text{FCP} = \text{SCR} \times \frac{\text{KMW}}{\text{Current MW}}$

Fluid Dynamics Basis

Kill sheets use IWCF's approximation that circulating pressure at a fixed pump rate is proportional to mud density ($P_{\text{new}} \approx P_{\text{current}} \times \text{MW}_{\text{new}} / \text{MW}_{\text{current}}$). Because the kill pump speed (SPM) and string geometry remain identical to the conditions when the SCR was recorded, circulating friction scales with the ratio of mud weights.

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4. The Drill Pipe Pressure Step-Down Schedule

As kill mud is pumped from surface to the bit nozzles:

• Heavier kill mud steadily replaces original mud inside the drill string.
• The internal hydrostatic head increases continuously.
• To maintain constant bottom-hole pressure, surface drill pipe pressure must decrease linearly from $\text{ICP}$ at zero strokes to $\text{FCP}$ at the stroke count where kill mud reaches the bit ($\text{Strokes to Bit}$).

Mathematical Formulation of Step-Down

The total circulating pressure drop across the drill string displacement is:

$\Delta P_{\text{total}} = \text{ICP} - \text{FCP}$

The pressure reduction per 100 pump strokes is:

$\Delta P_{\text{100}} = \frac{\text{ICP} - \text{FCP}}{\text{Strokes to Bit}} \times 100$

Alternatively, if the schedule is divided into equal intervals of $N$ strokes:

$\Delta P_{\text{step}} = \frac{\text{ICP} - \text{FCP}}{\text{Total Steps}}$

During circulation, the choke operator monitors the pump stroke counter and manipulates the adjustable choke to maintain casing backpressure so that the drill pipe pressure gauge tracks the pre-calculated step-down table at each stroke milestone.

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5. Complete Worked Calculation Example

Well and Influx Data

• True Vertical Depth (TVD): $10{,}000\text{ ft}$ (Measured Depth = $11{,}400\text{ ft}$)
• Current Mud Weight: $10.0\text{ ppg}$
• Casing Shoe TVD: $6{,}800\text{ ft}$; LOT EMW = $14.5\text{ ppg}$
• Slow Circulation Rate (SCR): $650\text{ psi}$ at $30\text{ SPM}$
• Shut-In Data:
  • $\text{SIDPP} = 520\text{ psi}$
  • $\text{SICP} = 780\text{ psi}$
  • $\text{Pit Gain} = 15\text{ bbl}$
• Drill String Internal Volume: $140\text{ bbl}$
• Mud Pump Displacement ($V_{\text{stk}}$): $0.100\text{ bbl/stk}$

Step 1: Calculate Strokes to Bit

$\text{Strokes to Bit} = \frac{V_{\text{string}}}{V_{\text{stk}}} = \frac{140\text{ bbl}}{0.100\text{ bbl/stk}} = 1{,}400\text{ strokes}$

Step 2: Calculate Kill Mud Weight (KMW)

$\text{KMW} = 10.0 + \frac{520}{0.052 \times 10{,}000} = 10.0 + \frac{520}{520} = 10.0 + 1.0 = 11.0\text{ ppg}$ (Exact value is 11.0 ppg; if calculation had yielded 11.02 ppg, round UP to 11.1 ppg).

Step 3: Calculate Initial Circulating Pressure (ICP)

$\text{ICP} = \text{SCR} + \text{SIDPP} = 650 + 520 = 1{,}170\text{ psi}$

Step 4: Calculate Final Circulating Pressure (FCP)

$\text{FCP} = \text{SCR} \times \frac{\text{KMW}}{\text{Current MW}} = 650 \times \frac{11.0}{10.0} = 650 \times 1.10 = 715\text{ psi}$

Step 5: Construct the Drill Pipe Step-Down Schedule

$\Delta P_{\text{total}} = \text{ICP} - \text{FCP} = 1{,}170 - 715 = 455\text{ psi}$ $\Delta P_{\text{100}} = \frac{455}{1{,}400} \times 100 = 32.5\text{ psi per 100 strokes}$