6.3 Drillpipe Pressure Step-Down Schedule & Strokes to Bit / Annulus

As kill mud displaces original mud inside the drillstring, expected standpipe pressure decreases from ICP toward FCP. Wait-and-Weight uses the prepared drillpipe pressure schedule. In the standard second Driller's circulation, after the influx is removed, hold the appropriate casing-pressure reference until kill mud reaches the bit, then control drillpipe pressure at FCP. Track fluid-front volumes and pressure limits throughout.

Rig Volumetrics and Triplex Pump Output Mechanics

All well control stroke calculations depend on the volumetric displacement of the rig mud pumps. Modern rigs utilize single-acting triplex piston pumps.

Triplex Pump Output Formula

$\text{PO} = 0.000243 \times D_{\text{liner}}^2 \times L_{\text{stroke}} \times E_{\text{vol}} \quad (\text{bbl/stroke})$

Where:

• $D_{\text{liner}}$ = Inside diameter of the pump liner in inches ($\text{in}$)
• $L_{\text{stroke}}$ = Piston stroke length in inches ($\text{in}$)
• $E_{\text{vol}}$ = Volumetric pump efficiency (expressed as a decimal, typically $0.95\text{ to }0.98$)
• $0.000243$ = Geometric constant $(\frac{\pi}{4} \times \frac{3}{231 \times 42})$

Tubular and Annular Capacity Formulas

• Internal Pipe Capacity ($C_{\text{pipe}}$): $C_{\text{pipe}} = \frac{D_{\text{in}}^2}{1029.4} \quad (\text{bbl/ft})$
• Annular Capacity ($C_{\text{ann}}$): $C_{\text{ann}} = \frac{D_{\text{hole}}^2 - D_{\text{pipe, OD}}^2}{1029.4} \quad (\text{bbl/ft})$

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Strokes to Bit (STB) and Strokes Bit to Surface (STS)

To manage the kill operation, the supervisor segments the wellbore into two distinct operational volumes:

1. Drillstring Volume and Strokes to Bit (STB)

Total drillstring volume ($V_{\text{ds}}$) is the sum of the internal capacities of the drillpipe, heavyweight drillpipe (HWDP), and drill collars:

$V_{\text{ds}} = (L_{\text{dp}} \times C_{\text{dp}}) + (L_{\text{hwdp}} \times C_{\text{hwdp}}) + (L_{\text{dc}} \times C_{\text{dc}}) \quad (\text{bbl})$

With the counter referenced to kill mud entering the drillstring, Strokes to Bit (STB) is:

$\text{STB} = \frac{V_{\text{ds}}}{\text{PO}}$

If counting from the pump, account separately for the surface-line volume before kill mud enters the string. The IWCF kill sheet lists surface lines separately from drillstring volume.

2. Return-Path Volume and Strokes Bit to Surface (STS)

Total annular volume ($V_{\text{ann}}$) is calculated across each open-hole and cased-hole section:

$V_{\text{ann}} = (L_{\text{dc/oh}} \times C_{\text{ann, dc/oh}}) + (L_{\text{dp/oh}} \times C_{\text{ann, dp/oh}}) + (L_{\text{dp/csg}} \times C_{\text{ann, dp/csg}}) \quad (\text{bbl})$

For returns through this annular path, Strokes Bit to Surface (STS) is:

$\text{STS} = \frac{V_{\text{ann}}}{\text{PO}}$

For subsea BOP/choke returns, include the choke-line volume in the return-path volume; do not substitute the marine-riser annulus. With the same counter origin, the cumulative interval after bit arrival runs from STB to STB + STS.

Total Circulating Strokes (TCS) for the selected string and return path: $\text{TCS} = \text{STB} + \text{STS}$

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Pre-Tour Slow Circulating Rate (SCR) Recording Intervals and Protocols

Accurate well control requires rigorous pre-kick data acquisition. Baseline circulating pressures must be measured before any well control incident occurs.

Regulatory and Operational SCR Recording Frequency

Slow Circulating Rate (SCR) pressures ($P_{\text{scr}}$) must be taken and recorded on the active kill sheet:

1. Every Tour (Shift): At the beginning of each 8-hour or 12-hour tour;
2. Mud Weight & Rheology Changes: Whenever drilling fluid density (mud weight), viscosity, yield point, or gel strength is altered;
3. Drill Bit Changes: After every bit trip (changes in bit nozzle Total Flow Area, TFA, significantly alter system pressure drop);
4. BHA & Drillstring Reconfigurations: Whenever drill collars, HWDP, mud motors, MWD/LWD tools, or string dimensions change;
5. Significant Drilled Footage / Depth Intervals: Every $500\text{ to }1,000\text{ ft}$ ($150\text{ to }300\text{ m}$) of newly drilled open hole, or once per 24-hour period during continuous drilling;
6. Pump Maintenance or Liner Swaps: Whenever pump liners, pistons, or valves are serviced or changed;
7. Multiple Pump Speeds: At two or three designated kill speeds (e.g., $20\text{ spm}$, $30\text{ spm}$, and $40\text{ spm}$);
8. Independent Rig Pumps: Separately for each active mud pump on the rig (Pump 1, Pump 2, and Pump 3).

Surface BOP Stacks vs. Subsea BOP Stacks SCR Protocols

The configuration of the blowout preventer fundamentally dictates the circulating friction paths:

• Surface BOP Stacks: Normal drilling returns use the normal open return path; a shut-in well is circulated through the BOP side outlet and choke manifold. Measure the selected SCR and assess losses in the actual kill return path rather than assuming bell-nipple returns with the BOP closed.

• Subsea BOP Stacks & Choke Line Friction (CLF): On floating drilling vessels (semisubmersibles and drillships), the BOP stack resides on the seabed, connected to the surface rig via marine riser and small-diameter high-pressure choke and kill lines spanning thousands of feet of water depth. Circulating mud up a long, narrow subsea choke line generates massive frictional pressure resistance known as Choke Line Friction (CLF).

Measuring Subsea Choke Line Friction (Pre-Tour Procedure):

1. Riser SCR ($P_{\text{scr, riser}}$): Circulate down the drillpipe and up the marine riser at the kill rate (e.g., $30\text{ spm}$). Record the standpipe pressure.
2. Choke Line SCR ($P_{\text{scr, choke}}$): Close the subsea BOP annular preventer or pipe ram, align returns through the subsea choke line to the surface manifold, and pump at the same kill rate ($30\text{ spm}$). Record the standpipe pressure.
3. Calculate Choke Line Friction (CLF): $\text{CLF} = P_{\text{scr, choke}} - P_{\text{scr, riser}}$

Operational Consequence of CLF During a Well Kill:

In deepwater well control, when the subsea BOP is closed and circulation begins up the choke line, the CLF imposes immediate backpressure against the entire annular wellbore and casing shoe: $P_{\text{bottomhole}} = P_{\text{hyd, ann}} + P_{\text{casing surface}} + \text{CLF} + \Delta P_{\text{annular friction}}$ If the choke operator holds casing pressure constant at stabilized $\text{SICP}$ during pump startup without accounting for CLF, the bottomhole pressure will be overpressured by the full magnitude of $\text{CLF}$. In a narrow pressure window, this excess pressure can exceed the controlling formation limit and initiate losses. Evaluate the actual margin and monitor for losses or further influx; an underground blowout is a risk, not an automatic result of any extra CLF. To maintain constant bottomhole pressure during pump startup on a subsea stack, the choke operator must allow casing pressure to drop by an amount equal to $\text{CLF}$ as the pump is brought up to kill speed.

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Constructing the Drillpipe Pressure Step-Down Schedule

When kill mud is pumped down the drillpipe, the hydrostatic head inside the string progressively increases because heavy fluid replaces light original mud. To prevent bottomhole pressure from exceeding formation pore pressure, the standpipe pressure must be stepped down continuously from $\text{ICP}$ at stroke 0 to $\text{FCP}$ at stroke $\text{STB}$.

Mathematical Formulation: Pressure Drop per 100 Strokes

To facilitate operational monitoring on the choke console, the step-down rate is calculated per 100 pump strokes:

$\Delta P_{100} = \frac{\text{ICP} - \text{FCP}}{\text{STB} / 100} = \frac{(\text{ICP} - \text{FCP}) \times 100}{\text{STB}} \quad (\text{psi / 100 strokes})$

For any intermediate cumulative stroke count ($S$):

$\text{SPP}(S) = \text{ICP} - \left( S \times \frac{\text{ICP} - \text{FCP}}{\text{STB}} \right)$

Assumptions Behind the Linear Schedule

The simple linear kill sheet assumes approximately constant vertical displacement per stroke and the standard ICP-to-FCP hydraulic interpolation. A uniform vertical pipe, or a constant-inclination uniform segment, gives equal vertical increments for equal pumped volumes: $\Delta P_{\text{hyd}}=0.052(\text{KMW}-\text{OMW})\Delta h_{\text{TVD}}$ Uniform bore alone is insufficient when inclination changes. Use surveyed TVD increments, measured-length capacities and the approved segmented pressure schedule for a deviated well or changing string dimensions.

Execute the Prepared Schedule

For Wait-and-Weight, follow the approved geometry-dependent drillpipe schedule to bit arrival, then hold FCP through the planned return displacement. Keep pump flow steady and monitor annular pressure limits.

For subsea returns, a static kill-line monitor can provide a nonflowing pressure reference. Include its known fluid head and gauge elevation when relating that reading to stack or bottomhole pressure. A flowing choke gauge requires CLF compensation on rate changes; do not equate either raw surface reading with seabed pressure.

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Pipe Tripping Mechanics: Heavy Slug Sizing and Pit Gain Calculations (IWCF EX-0035)

Prior to pulling the drillstring out of the hole (POOH) for a bit change or BHA trip, drillers pump a small volume of high-density drilling fluid—termed a heavy slug—into the top of the drillpipe.

Operational Rationale for Pumping a Slug

1. Preventing Wet Pulling (Mud Spills): If upper pipe remains filled when a connection is broken, mud can spill onto the rig floor, creating slip hazards, mud loss and contamination. A correctly planned slug lowers the internal fluid level so the selected upper stands can be pulled dry.
2. Controlling Mud Drainage: The dry upper interval reduces mud spilling from disconnected pipe. It does not eliminate annular swabbing; pull speed, fluid rheology and clearance still require control.
3. Ensuring Accurate Hole Fill Monitoring: A dry string allows precise measurement of steel displacement in the trip tank without contamination from surface drainage.

U-Tube Mechanics of a Heavy Slug

Once the heavy slug is pumped into the drillstring and the top of the string is opened (vented) to atmosphere at the surface, a U-tube imbalance exists between the heavy slug column inside the drillpipe and the lighter mud in the annulus.

Gravity pulls the heavy slug down the drillstring until the hydrostatic pressure inside the pipe balances the hydrostatic head in the annulus:

$P_{\text{hyd, pipe}} = P_{\text{hyd, annulus}}$ $0.052 \times \rho_{\text{slug}} \times L_{\text{slug}} = 0.052 \times \rho_{\text{current}} \times (L_{\text{slug}} + L_{\text{dry}})$

Where:

• $\rho_{\text{slug}}$ = Density of the heavy slug ($\text{ppg}$)
• $\rho_{\text{current}}$ = Density of the active drilling mud ($\text{ppg}$)
• $L_{\text{slug}}$ = Vertical length of the slug column inside the drillpipe ($\text{ft}$)
• $L_{\text{dry}}$ = Desired vertical length of dry (evacuated) drillpipe below the rotary table ($\text{ft}$)

Expanding and rearranging: $\rho_{\text{slug}} \times L_{\text{slug}} = \rho_{\text{current}} \times L_{\text{slug}} + \rho_{\text{current}} \times L_{\text{dry}}$ $L_{\text{slug}} \times (\rho_{\text{slug}} - \rho_{\text{current}}) = \rho_{\text{current}} \times L_{\text{dry}}$ $L_{\text{slug}} = \frac{L_{\text{dry}} \times \rho_{\text{current}}}{\rho_{\text{slug}} - \rho_{\text{current}}}$

IWCF Formula 24: Slug Volume Calculation

Multiplying the required slug column length ($L_{\text{slug}}$) by the internal capacity of the drillpipe ($C_{\text{pipe}}$ in $\text{bbl/ft}$), where $\text{Slug Volume} = L_{\text{slug}} \times C_{\text{pipe}}$:

$\text{Slug Volume (bbl)} = \frac{\text{Length of Dry Pipe (ft)} \times \text{Pipe Capacity (bbl/ft)} \times \rho_{\text{current}} (\text{ppg})}{\rho_{\text{slug}} (\text{ppg}) - \rho_{\text{current}} (\text{ppg})}$

In Metric / SI Units ($\text{m}^3$, $\text{m}$, $\text{m}^3/\text{m}$, and $\text{SG}$ or $\text{kg/m}^3$):

$\text{Slug Volume } (\text{m}^3) = \frac{\text{Length of Dry Pipe (m)} \times \text{Pipe Capacity } (\text{m}^3/\text{m}) \times \rho_{\text{current}}}{\rho_{\text{slug}} - \rho_{\text{current}}}$

IWCF Formula 25: Pit Gain Due to Slug U-Tubing

As the heavy slug falls down the drillstring to achieve hydrostatic balance, it displaces an equivalent volume of mud out of the annulus and into the surface active pits. This pit volume increase is calculated as:

$\text{Pit Gain (bbl)} = \text{Slug Volume (bbl)} \times \left( \frac{\rho_{\text{slug}} (\text{ppg})}{\rho_{\text{current}} (\text{ppg})} - 1 \right)$

In Metric / SI Units:

$\text{Pit Gain } (\text{m}^3) = \text{Slug Volume } (\text{m}^3) \times \left( \frac{\rho_{\text{slug}}}{\rho_{\text{current}}} - 1 \right)$

Physical Proof of the Pit Gain Identity

Substituting Formula 24 into Formula 25 reveals a fundamental physical property of the wellbore U-tube:

$\text{Pit Gain} = \left[ \frac{L_{\text{dry}} \times C_{\text{pipe}} \times \rho_{\text{current}}}{\rho_{\text{slug}} - \rho_{\text{current}}} \right] \times \left[ \frac{\rho_{\text{slug}} - \rho_{\text{current}}}{\rho_{\text{current}}} \right] = L_{\text{dry}} \times C_{\text{pipe}}$

$\mathbf{\text{Pit Gain Due to U-Tubing} \equiv \text{Internal Capacity Volume of Dry Pipe}}$

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Step-by-Step Worked Field Problem: Heavy Slug Sizing & Pit Gain

A drilling crew is preparing to trip pipe out of the hole. The supervisor requires a dry drillstring interval to ensure clean, safe handling on the rig floor.

• Well Depth: $10,500\text{ ft TVD} / 11,800\text{ ft MD}$
• Current Mud Weight ($\rho_{\text{current}}$): $12.0\text{ ppg}$
• Heavy Slug Mud Weight ($\rho_{\text{slug}}$): $14.5\text{ ppg}$
• Desired Length of Dry Drillpipe ($L_{\text{dry}}$): $200\text{ ft}$ (approximately 2 stands)
• $5\text{ in}$, $19.5\text{ lb/ft}$ Drillpipe Capacity ($C_{\text{pipe}}$): $0.0178\text{ bbl/ft}$
• Mud Pump Output ($\text{PO}$): $0.119\text{ bbl/stroke}$

Step 1: Calculate the Internal Volume of Dry Pipe Desired

$V_{\text{dry}} = L_{\text{dry}} \times C_{\text{pipe}} = 200\text{ ft} \times 0.0178\text{ bbl/ft} = \mathbf{3.56\text{ bbl}}$

Step 2: Calculate Required Heavy Slug Volume (IWCF Formula 24)

$V_{\text{slug}} = \frac{200\text{ ft} \times 0.0178\text{ bbl/ft} \times 12.0\text{ ppg}}{14.5\text{ ppg} - 12.0\text{ ppg}}$ $V_{\text{slug}} = \frac{3.56\text{ bbl} \times 12.0}{2.5} = \frac{42.72}{2.5} = \mathbf{17.088\text{ bbl}} \approx \mathbf{17.1\text{ bbl}}$

Step 3: Calculate Expected Pit Gain Due to U-Tubing (IWCF Formula 25)

$\text{Pit Gain} = 17.088\text{ bbl} \times \left( \frac{14.5\text{ ppg}}{12.0\text{ ppg}} - 1 \right)$ $\text{Pit Gain} = 17.088 \times (1.20833 - 1) = 17.088 \times 0.20833 = \mathbf{3.56\text{ bbl}}$ (Notice that the calculated pit gain of $3.56\text{ bbl}$ exactly equals the internal volume of the $200\text{ ft}$ dry drillpipe calculated in Step 1.)

Step 4: Calculate Pump Strokes to Mix and Place Slug

• Strokes to pump slug into drillstring: $\text{Strokes}_{\text{slug}} = \frac{17.088\text{ bbl}}{0.119\text{ bbl/stroke}} = \mathbf{144\text{ strokes}}$
• Displacement: Depending on company policy, the slug is pumped into the string and either left at surface or displaced down the drillstring with a predetermined volume of active mud before disconnecting the top drive/kelly. The string is then vented to atmosphere, allowing the slug to drop and the expected $3.56\text{ bbl}$ pit gain to register on the PVT.

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Choose the Pressure Reference for the Kill Phase

During Wait-and-Weight, the annulus still contains the influx. Follow the prepared drillpipe pressure schedule as kill mud moves down the string; do not force casing pressure to follow the same curve. Continue monitoring casing pressure, returns and current formation/equipment limits.

During the standard second Driller's circulation, the influx has already been removed and the annulus initially contains original mud. Hold the appropriate casing-pressure reference (original SIDPP in the simple surface case) until kill mud reaches the bit. Drillpipe pressure declines as string hydrostatic head increases. Then hold drillpipe pressure at FCP while kill mud displaces the annulus. Include subsea CLF and actual fluid-head corrections where applicable.

Worked Field Problem: Step-Down Schedule Construction

• For this arithmetic exercise, use the supplied linear ICP-to-FCP interpolation. A field schedule for $11,000\text{ ft TVD} / 12,500\text{ ft MD}$ would additionally require survey and string-segment data.
• Pump Displacement: $\text{PO} = 0.1183\text{ bbl/stroke}$
• Drillstring Volume: $V_{\text{ds}} = 213.9\text{ bbl}$
• $\text{STB} = \frac{213.9\text{ bbl}}{0.1183\text{ bbl/stroke}} = 1,808\text{ strokes}$
• $\text{ICP} = 1,220\text{ psi}$
• $\text{FCP} = 740\text{ psi}$

Calculation of Step-Down Rate:

$\Delta P_{\text{total}} = \text{ICP} - \text{FCP} = 1,220 - 740 = 480\text{ psi}$ $\Delta P_{100} = \frac{480}{1,808 / 100} = \frac{480}{18.08} = \mathbf{26.55\text{ psi per 100 strokes}}$

Step-Down Table for Rig Floor Choke Console: