# Chapter 10 — Well Control Calculations ## Learning Objectives By the end of this chapter, students should be able to: 1. Calculate kill mud weight from shut-in drill pipe pressure (SIDPP) and TVD. 2. Calculate initial circulating pressure (ICP) and final circulating pressure (FCP) for a given kick scenario. 3. Construct a choke pressure schedule for the Wait-and-Weight Method. 4. Describe how drill pipe pressure and casing pressure evolve during the Driller's Method (both circulations) and the Wait-and-Weight Method. 5. Calculate MAASP and verify that the chosen kill method will not fracture the shoe. 6. Interpret the choke pressure schedule and identify deviations that indicate a problem. --- ## 10.1 The Constant Bottomhole Pressure Principle All kill methods are built on a single underlying principle: **keep the bottomhole pressure (BHP) constant and greater than the formation pore pressure throughout the kill operation**. If BHP falls below pore pressure, more formation fluid enters the well. If BHP rises above the fracture gradient, the shoe breaks down and mud is lost to the formation. The bottomhole pressure at any instant during a kill operation is the sum of the hydrostatic pressure of the fluid in the drill string plus the surface standpipe pressure: $$\text{BHP} = \rho_\text{fluid,in} \times 0.052 \times \text{TVD} + P_\text{standpipe}$$ Equivalently, it can be expressed from the annulus side: $$\text{BHP} = \rho_\text{fluid,ann} \times 0.052 \times \text{TVD} + P_\text{casing}$$ At shut-in, the system is static and BHP equals the formation pressure: $$P_\text{formation} = \rho_\text{mud} \times 0.052 \times \text{TVD} + \text{SIDPP}$$ The kill mud weight is chosen so that the mud alone (with no surface pressure) balances formation pressure: $$\rho_\text{kill} \times 0.052 \times \text{TVD} = P_\text{formation}$$ $$\boxed{\rho_\text{kill} = \rho_\text{mud} + \frac{\text{SIDPP}}{0.052 \times \text{TVD}}}$$ ```{admonition} Key Term :class: tip The **constant bottomhole pressure** principle is the foundation of all well control kill methods. Surface choke pressure is adjusted continuously to maintain BHP = formation pressure throughout the kill operation, regardless of what fluid is in the drill string or annulus at any given moment. ``` --- ## 10.2 Circulating Pressures During a Kill ### 10.2.1 Slow Circulating Rate (SCR) Pressure Before calculating ICP and FCP, the engineer must know the **slow circulating rate (SCR) pressure**, the standpipe pressure measured while circulating at the kill pump rate (typically 20–40 spm), with the original mud weight and with the well under control (no kick in the hole). This is recorded regularly during drilling. SCR pressure represents all frictional pressure losses in the circulating system at the kill rate: $$\text{SCR} = \Delta P_\text{ds,friction} + \Delta P_\text{bit} + \Delta P_\text{ann,friction} \quad \text{(at kill rate)}$$ ### 10.2.2 Initial Circulating Pressure (ICP) When the pump is started to begin a kill circulation, BHP must be maintained at formation pressure. At the start of circulation, the fluid in the drill string is the original mud (weight $\rho_\text{mud}$). The hydrostatic pressure of that mud column already accounts for most of BHP, with SIDPP making up the remainder. Adding friction by circulating tends to raise annular pressure. To hold BHP constant while adding friction, the standpipe pressure target at the start of circulation is: $$\boxed{\text{ICP} = \text{SIDPP} + \text{SCR pressure}}$$ ICP is the **drill pipe pressure target when the pump first reaches kill speed** at the beginning of any kill circulation. ```{admonition} Key Term :class: tip **Initial circulating pressure (ICP)** is the drill pipe pressure target when the pump first reaches kill speed. It equals SIDPP + SCR. This is the starting drill pipe pressure for both the Driller's Method (both circulations) and the Wait-and-Weight Method. ``` ### 10.2.3 Final Circulating Pressure (FCP) By the time kill mud fills the drill string completely (kill mud just reaches the bit), the hydrostatic pressure of the kill mud column has replaced the hydrostatic pressure of the original mud plus the SIDPP. At this point, the only contribution to BHP needed from surface pressure is the friction in the circulating system — which is just the SCR pressure, but scaled for the higher density of the kill mud: $$\boxed{\text{FCP} = \frac{\rho_\text{kill}}{\rho_\text{mud}} \times \text{SCR pressure}}$$ FCP is the **drill pipe pressure target when kill mud just reaches the bit** (drill string fully displaced to kill mud). After this point, no further change in drill pipe pressure is expected, the system circulates at FCP until the kill mud has filled the entire annulus and exits at surface. ```{admonition} Key Term :class: tip **Final circulating pressure (FCP)** is the drill pipe pressure target once kill mud fills the entire drill string and is just reaching the bit. It equals (ρ_kill / ρ_mud) × SCR. Drill pipe pressure holds constant at FCP for the remainder of the kill. ``` --- ## 10.3 Driller's Method: Pressure Profiles The Driller's Method consists of two complete circulations. Understanding how drill pipe pressure and casing pressure behave during each helps the driller recognize whether the operation is proceeding correctly. ```{figure} ../figures/ch10/fig_drillers_method_pressures.png :name: fig-drillers-method-pressures :width: 90% :align: center Standpipe, choke, and drill pipe pressures versus strokes pumped through both circulations of the Driller's Method. The kick is circulated across the choke in the first circulation; kill mud displaces the well in the second. ``` ### 10.3.1 First Circulation: Circulate Out the Kick **Objective:** Pump with original mud at kill rate; hold BHP constant at formation pressure; circulate the kick influx from the annulus to surface and out through the choke. **Drill pipe pressure:** Held constant at ICP throughout the first circulation by adjusting the choke. As long as original mud is in the drill string (constant hydrostatic), the friction contribution is also constant, so drill pipe pressure stays at ICP. **Casing pressure:** More complex. Casing pressure reflects the annulus-side pressure balance. As the kick migrates upward and gas expands, casing pressure increases. The choke must be opened to allow expanding gas to exit while keeping BHP (and therefore drill pipe pressure) constant. Casing pressure peaks when the gas enters the choke and choke manifold, then decreases as gas is bled off. ```{figure} ../figures/ch10/fig_drillers_method_depth_profiles.png :name: fig-drillers-method-depth-profiles :width: 90% :align: center Pressure-depth profiles during the first circulation of the Driller's Method, with the influx on bottom, at the shoe, and at surface. Surface pressures rise as the influx approaches surface while bottomhole pressure is held constant. ``` ```{admonition} Warning: Gas Expansion at Surface :class: warning As a gas kick rises in the annulus, it expands. The choke must be opened progressively to allow the gas to exit at the same rate it expands. Failure to do so will cause SICP to rise rapidly, potentially exceeding MAASP and fracturing the shoe. The choke operator must watch casing pressure and open the choke to hold drill pipe pressure (not casing pressure) constant. ``` **After first circulation:** Kick has been removed. Well is shut in. Drill pipe and casing pressures should equilibrate and reflect the residual underbalance, SIDPP should be unchanged (still reflecting the same pore pressure). Now mix and pump kill mud in the second circulation. ### 10.3.2 Second Circulation: Pump Kill Mud **Objective:** Pump kill mud down the drill string and fill the annulus. Hold BHP constant throughout. **Drill pipe pressure:** Starts at ICP (same as the first circulation, because the kill mud has not entered the string yet when the pump starts). As kill mud fills the drill string, it displaces original mud, and the drill string hydrostatic increases. To hold BHP constant, the choke must be closed slightly, and drill pipe pressure decreases. When kill mud reaches the bit, drill pipe pressure has decreased linearly from ICP to FCP. **Linear pressure decrease:** The relationship is linear because the volume of kill mud entering the string is proportional to strokes pumped, and the additional hydrostatic it provides is proportional to its volume. Therefore: $$P_\text{dp}(n) = \text{ICP} - (\text{ICP} - \text{FCP}) \times \frac{n}{N_\text{ds}}$$ where $n$ is the number of strokes pumped since the start of the second circulation and $N_\text{ds}$ is the total strokes to fill the drill string. **After kill mud reaches the bit:** Drill pipe pressure holds at FCP. As kill mud fills the annulus, SICP (casing pressure) decreases as the heavier mud replaces the lighter original mud and the kick fluid in the annulus. When kill mud exits the choke, SICP should be zero and the well is dead. --- ```{figure} ../figures/ch10/fig_drillers_method_notes.png :name: fig-drillers-method-notes :width: 80% :align: center Instructor's worked notes tracing SIDPP, SICP, and pump pressure through each step of the Driller's Method, from initial shut-in through kill mud displacement (from PETE 355 lecture notes). ``` ## 10.4 Wait-and-Weight Method: Pressure Profiles The Wait-and-Weight Method uses a single circulation. Kill mud is mixed first, then pumped in one pass from drill string to annulus. ```{figure} ../figures/ch10/fig_ww_influx_taken.png :name: fig-ww-influx-taken :width: 90% :align: center Pressure-depth diagram at shut-in, before the Wait-and-Weight circulation begins: the influx of height $H_\text{influx}$ sits at the bottom of the annulus, and the gradients of the original mud ($\rho_1$), kill mud ($\rho_2$), and influx determine the surface pressures. ``` ### 10.4.1 Choke Pressure Schedule Construction The choke operator needs a schedule that tells them the exact target drill pipe pressure at each stroke count during the kill. This is the choke pressure schedule (also called the kill sheet pressure schedule). The schedule is linear from ICP (at the start of pumping) to FCP (when kill mud reaches the bit): $$P_\text{dp}(n) = \text{ICP} - (\text{ICP} - \text{FCP}) \times \frac{n}{N_\text{ds}}$$ In practice, the schedule is tabulated at regular stroke intervals (e.g., every 10% of $N_\text{ds}$): | Strokes pumped | Fraction of drill string displaced | Target drill pipe pressure | |---------------|-----------------------------------|---------------------------| | 0 | 0% | ICP | | $0.1 \times N_\text{ds}$ | 10% | $\text{ICP} - 0.1(\text{ICP} - \text{FCP})$ | | $0.2 \times N_\text{ds}$ | 20% | $\text{ICP} - 0.2(\text{ICP} - \text{FCP})$ | | ... | ... | ... | | $0.9 \times N_\text{ds}$ | 90% | $\text{ICP} - 0.9(\text{ICP} - \text{FCP})$ | | $N_\text{ds}$ | 100% (kill mud at bit) | FCP | After $N_\text{ds}$ strokes, drill pipe pressure holds at FCP. The well is dead when kill mud appears at the choke outlet (after $N_\text{ds} + N_\text{ann}$ total strokes, where $N_\text{ann}$ is strokes to displace the annulus). ### 10.4.2 Casing Pressure During Wait-and-Weight As kill mud fills the drill string, the annulus side initially remains unchanged (original mud and kick fluid). Casing pressure during this phase is held at the value needed to maintain BHP = formation pressure, given the changing drill string hydrostatic. Casing pressure is not directly scheduled — it follows naturally from maintaining the drill pipe pressure schedule on the choke. Once kill mud reaches the bit and enters the annulus, the heavier kill mud displaces both the original mud and the kick fluid upward. The kick gas rises through the annulus and is eventually bled through the choke. As kill mud fills the annulus from bottom to top, casing pressure decreases steadily until it reaches zero when kill mud arrives at the choke. ```{figure} ../figures/ch10/fig_ww_phase1.png :name: fig-ww-phase1 :width: 90% :align: center Wait-and-Weight Phase 1: kill mud ($\rho_2$) displaces the drill string while the influx remains in the annulus. Drill pipe pressure declines from ICP toward FCP along the choke pressure schedule. ``` ```{figure} ../figures/ch10/fig_ww_phase2.png :name: fig-ww-phase2 :width: 90% :align: center Wait-and-Weight Phase 2: the influx is circulated up the annulus ahead of the kill mud, expanding as it rises; casing pressure peaks as the influx reaches the choke. ``` ```{figure} ../figures/ch10/fig_ww_phase3.png :name: fig-ww-phase3 :width: 90% :align: center Wait-and-Weight Phase 3: with the influx removed, kill mud fills the annulus and casing pressure declines toward zero as the well is displaced to kill weight. ``` --- ## 10.5 Worked Examples ### Example 10.1 — Kill Sheet Completion **Given:** - Current mud weight: 10.5 ppg - TVD: 12,000 ft - Drill string: 9,500 ft of 5" drill pipe (capacity 0.0176 bbl/ft) + 500 ft of 6.5" drill collars (capacity 0.0087 bbl/ft) - Pump output: 0.112 bbl/stroke - SCR pressure at 30 spm: 600 psi - Casing shoe at 8,500 ft TVD; LOT EMW: 14.2 ppg - After shut-in: SIDPP = 400 psi, SICP = 650 psi, pit gain = 25 bbl - Annular capacity opposite collars: 0.0245 bbl/ft; opposite drill pipe: 0.0505 bbl/ft **Required:** Complete the kill sheet — compute kill mud weight, ICP, FCP, $N_\text{ds}$, kick height, kick density, MAASP, and the choke pressure schedule at 10% intervals. **Solution:** **Kill mud weight:** $$\rho_\text{kill} = 10.5 + \frac{400}{0.052 \times 12000} = 10.5 + 0.641 = 11.14 \text{ ppg}$$ Round up to **11.2 ppg** (always round kill mud weight up to the nearest 0.1 ppg). **ICP:** $$\text{ICP} = 400 + 600 = 1000 \text{ psi}$$ **FCP:** $$\text{FCP} = \frac{11.2}{10.5} \times 600 = 640 \text{ psi}$$ **Drill string internal volume and strokes to displace:** Drill pipe volume: $9500 \times 0.0176 = 167.2$ bbl Drill collar volume: $500 \times 0.0087 = 4.35$ bbl Total $V_\text{ds} = 171.6$ bbl $$N_\text{ds} = \frac{171.6 \text{ bbl}}{0.112 \text{ bbl/stroke}} = 1532 \text{ strokes}$$ **Kick height:** Assume kick fills the annulus opposite the drill collars first: $V_\text{collars} = 500 \times 0.0245 = 12.25$ bbl → not enough to hold 25 bbl Remaining kick volume after collars are filled: $25 - 12.25 = 12.75$ bbl in the drill pipe annulus: $H_\text{in dp annulus} = 12.75 / 0.0505 = 252$ ft Total kick height: $H_\text{kick} = 500 + 252 = 752$ ft **Kick density:** $$\rho_\text{kick} = 10.5 - \frac{650 - 400}{0.052 \times 752} = 10.5 - \frac{250}{39.1} = 10.5 - 6.4 = 4.1 \text{ ppg}$$ A density of 4.1 ppg is consistent with a **gas kick** (water ≈ 8.3 ppg, oil ≈ 6–7 ppg, gas ≈ 1–4 ppg). **MAASP:** $$\text{MAASP} = (14.2 - 10.5) \times 0.052 \times 8500 = 3.7 \times 0.052 \times 8500 = 1634 \text{ psi}$$ Current SICP (650 psi) is well below MAASP (1634 psi). ✓ **Choke pressure schedule (W&W, $N_\text{ds}$ = 1532 strokes):** Pressure drop per 10% interval: $(1000 - 640) / 10 = 36 \text{ psi}$ | Strokes | % displaced | Target DP pressure (psi) | |---------|------------|--------------------------| | 0 | 0% | 1000 (ICP) | | 153 | 10% | 964 | | 306 | 20% | 928 | | 459 | 30% | 892 | | 612 | 40% | 856 | | 766 | 50% | 820 | | 919 | 60% | 784 | | 1072 | 70% | 748 | | 1225 | 80% | 712 | | 1379 | 90% | 676 | | 1532 | 100% | 640 (FCP) | --- ### Example 10.2 — Driller's Method vs. Wait-and-Weight: Shoe Integrity Check **Given:** Same well as Example 9.1. The operator is evaluating whether to use the Driller's Method or the Wait-and-Weight Method. A key constraint is the shoe at 8,500 ft with MAASP = 1,634 psi. **Required:** During the first circulation of the Driller's Method, estimate the maximum expected casing pressure. Will it exceed MAASP? **Solution:** During the first circulation (Driller's Method), the kick is being circulated out. The maximum casing pressure occurs when the gas kick is near the surface and is expanding. A conservative estimate of the maximum casing pressure can be made by assuming the gas kick migrates to the shoe and expands to fill the casing above the shoe, then checking the surface pressure required to hold BHP constant. An approximate upper bound: at the moment the gas enters the choke, the gas has risen through the entire annulus. If the gas column has replaced the mud from TD to surface, the hydrostatic contribution from the gas column is approximately: $$P_\text{gas column} = \rho_\text{kick} \times 0.052 \times H_\text{kick,surface}$$ However, at surface the gas has expanded. A rigorous treatment requires tracking gas expansion with depth (using the real gas law), which is beyond the scope of this example. A simpler bounding check: the maximum casing pressure will not exceed the shut-in casing pressure plus the additional pressure from gas expansion as it rises. For a shallow-gas kick (4.1 ppg, 752 ft at bottom), the initial SICP was 650 psi. As the gas rises, its volume expands and SICP increases. A common field rule of thumb is that the maximum casing pressure during the first Driller's Method circulation may approach 1.5–2× SICP for a gas kick. Estimate: Max casing pressure ≈ $2 \times 650 = 1300$ psi (rough estimate). MAASP = 1,634 psi > 1,300 psi. ✓ The shoe is likely safe. ```{admonition} Note :class: tip A rigorous calculation of maximum casing pressure during a Driller's Method first circulation requires tracking gas migration and expansion using the real gas law. The estimate above is a rough bound only. In practice, the driller monitors casing pressure continuously and adjusts the choke if it approaches MAASP. ``` For the Wait-and-Weight Method: the gas kick remains at the bottom during the entire drill string displacement phase (kill mud has not yet reached the bit), so casing pressure behavior is governed by the changing drill string hydrostatic, not by gas expansion. The W&W method generally exposes the annulus to lower maximum pressures than the Driller's Method for the same kick, because the kill mud is immediately in the string, progressively increasing bottomhole pressure. --- ### Example 10.3 — Negative MAASP Scenario **Given:** - Mud weight: 14.0 ppg - TVD: 15,000 ft - Casing shoe at 10,000 ft TVD; LOT EMW: 14.5 ppg - SIDPP after kick: 350 psi **Required:** (a) Calculate kill mud weight. (b) Calculate MAASP with current mud weight. (c) Can a standard kill circulation be executed? **Solution:** **(a) Kill mud weight:** $$\rho_\text{kill} = 14.0 + \frac{350}{0.052 \times 15000} = 14.0 + 0.449 = 14.45 \text{ ppg}$$ **(b) MAASP with current mud weight:** $$\text{MAASP} = (14.5 - 14.0) \times 0.052 \times 10000 = 0.5 \times 0.052 \times 10000 = 260 \text{ psi}$$ **(c) Can a standard kill be executed?** The ICP would be $\text{SIDPP} + \text{SCR} = 350 + \text{SCR}$. Even if the SCR pressure is only 200 psi (slow pump rate), ICP = 550 psi, which already exceeds MAASP (260 psi). Furthermore, the kill mud weight (14.45 ppg) exceeds the LOT EMW at the shoe (14.5 ppg is very close, and rounding to 14.5 ppg would exactly equal the fracture gradient). During circulation, the ECD at the shoe will be even higher than the static kill mud hydrostatic. **This is a dangerous situation.** The well cannot be killed with a conventional circulation without risking fracturing the shoe. Options include: - Bullheading the kick back into the formation (if formation is permeable enough). - Setting a casing string before proceeding. - Using managed pressure drilling (MPD) equipment to control circulating pressures. - Calling a well control specialist immediately. This scenario is a reminder that MAASP is a hard constraint — not a target — and that some kick situations require engineering solutions beyond the standard kill methods. --- ### Example 10.4 — Kick Identification from SIDPP, SICP, and Pit Gain **Given:** A well is shut in after a suspected kick. The wellbore configuration is: - 500 ft of drill collars (OD = 5 in, open hole = 6 in) - 9,500 ft of drill pipe above (OD = 4 in, open hole = 6 in above drill collars) - Casing set above the open hole section - Mud weight: 10.0 ppg At shut-in: SIDPP = 300 psi, SICP = 500 psi, pit gain = 10 bbl. **Required:** (a) Determine kick height. (b) Determine kick density. (c) Identify the kick fluid type. (d) Calculate kill mud weight. **Solution:** **Step 1 — Annular capacities (bbl/ft).** The capacity formula for an annular section is: $$C_\text{ann} = \frac{D_\text{hole}^2 - D_\text{pipe}^2}{1029.4}$$ Opposite drill collars (5 in OD in 6 in hole): $$C_\text{dc} = \frac{6^2 - 5^2}{1029.4} = \frac{11}{1029.4} = 0.01069 \text{ bbl/ft}$$ Opposite drill pipe (4 in OD in 6 in hole): $$C_\text{dp} = \frac{6^2 - 4^2}{1029.4} = \frac{20}{1029.4} = 0.01943 \text{ bbl/ft}$$ **Step 2 — Kick height.** Check whether the kick fits within the drill collar annulus: $$V_\text{dc annulus} = 500 \times 0.01069 = 5.35 \text{ bbl}$$ The kick is 10 bbl, which exceeds 5.35 bbl. Therefore, 5.35 bbl fills the drill collar annulus (500 ft), and the remaining 4.65 bbl occupies the drill pipe annulus: $$H_\text{in dp} = \frac{4.65}{0.01943} = 239 \text{ ft}$$ Total kick height: $$H_\text{kick} = 500 + 239 = 739 \text{ ft}$$ **Step 3 — Kick density.** Converting mud weight to psi/ft: $0.52$ psi/ft (since $10 \times 0.052 = 0.52$). $$\rho_\text{kick} = \rho_\text{mud} - \frac{\text{SICP} - \text{SIDPP}}{H_\text{kick}} = 0.52 - \frac{500 - 300}{739} = 0.52 - 0.271 = 0.249 \text{ psi/ft}$$ Converting to ppg: $0.249 / 0.052 = 4.8$ ppg. **Step 4 — Kick fluid identification.** Typical kick fluid densities: | Fluid type | Density (ppg) | Gradient (psi/ft) | |------------|--------------|-------------------| | Gas | 1–4 | 0.05–0.20 | | Oil/gas mixture | 4–6 | 0.20–0.31 | | Crude oil | 6–7 | 0.31–0.36 | | Brine / formation water | 8.3–9.0 | 0.43–0.47 | At 4.8 ppg (0.249 psi/ft), this kick is a **mixture of oil and gas** — too dense to be pure gas, but too light to be crude oil. It may also represent oil with dissolved gas that has not yet reached its bubble point. ```{admonition} Implication for Kill Operations :class: warning A gas/oil mixture kick will expand as it rises during a kill circulation. The gas component will come out of solution as pressure decreases (reaching the bubble point), increasing the effective gas volume above what was observed at the kick depth. Monitor casing pressure carefully during the kill and be prepared to open the choke more than expected as the gas phase expands near surface. ``` **Step 5 — Kill mud weight.** Using TVD ≈ 10,000 ft (assumed for this example): $$\rho_\text{kill} = 10.0 + \frac{300}{0.052 \times 10000} = 10.0 + 0.577 = 10.58 \approx 10.6 \text{ ppg}$$ ```{figure} ../figures/ch10/fig_kick_identification_notes.png :name: fig-kick-identification-notes :width: 75% :align: center Instructor's worked notes for this kick identification problem: annular capacities convert the 10 bbl pit gain to a 739.7 ft kick height, and the SICP–SIDPP difference yields a kick gradient of 0.249 psi/ft — a mix of oil and gas (from PETE 355 lecture notes). ``` --- ## 10.6 Common Errors and How to Detect Them Understanding what *should* happen during a kill operation allows the driller to recognize when something has gone wrong. **Drill pipe pressure higher than expected:** Suggests BHP is too high (over-balanced), which can cause lost circulation. The choke should be opened slightly to reduce surface pressure. **Drill pipe pressure lower than expected:** Suggests BHP is too low (under-balanced), meaning more formation fluid may be entering. The choke must be closed slightly. If SIDPP also begins to rise, additional influx is occurring. **Casing pressure rising faster than expected during gas circulation:** Gas is expanding more rapidly than anticipated, possibly indicating the gas column is taller than estimated or the mud weight has been over-stated. Open the choke to maintain drill pipe pressure. **Drill pipe pressure not decreasing as expected during kill mud displacement:** Could indicate a washout (hole in drill string allowing bypass flow), or that the pump rate has not reached kill rate. Verify pump speed and recalculate. **Casing pressure not decreasing after kill mud at bit (FCP reached):** Could indicate gas in the annulus that has not yet reached the choke, or a secondary influx. Continue circulating and monitoring. --- ## 10.7 Practice Problems **Problem 10.1** — A well is shut in with the following data: mud weight 11.0 ppg, TVD 10,500 ft, SIDPP 500 psi, SICP 750 psi, pit gain 18 bbl, SCR pressure 550 psi at 25 spm. The drill string holds 120 bbl total, with 450 ft of drill collars and 9,050 ft of drill pipe in the annulus (annular capacity 0.0270 bbl/ft opposite collars, 0.0520 bbl/ft opposite pipe). (a) Calculate kill mud weight. (b) Calculate ICP and FCP. (c) Determine kick height and kick density. (d) If the casing shoe is at 7,500 ft TVD with LOT EMW = 15.0 ppg, calculate MAASP. ```{dropdown} Solution **(a) Kill mud weight:** $$\rho_\text{kill} = 11.0 + \frac{500}{0.052 \times 10500} = 11.0 + 0.916 = 11.9 \text{ ppg (round to 12.0 ppg)}$$ **(b) ICP and FCP:** $$\text{ICP} = 500 + 550 = 1050 \text{ psi}$$ $$\text{FCP} = \frac{12.0}{11.0} \times 550 = 600 \text{ psi}$$ **(c) Kick height and density:** Collar annulus volume: $450 \times 0.0270 = 12.15$ bbl Remaining in pipe annulus: $18 - 12.15 = 5.85$ bbl Height in pipe annulus: $5.85 / 0.0520 = 112.5$ ft Total kick height: $450 + 112.5 = 562.5$ ft $$\rho_\text{kick} = 11.0 - \frac{750 - 500}{0.052 \times 562.5} = 11.0 - \frac{250}{29.25} = 11.0 - 8.55 = 2.45 \text{ ppg}$$ 2.45 ppg indicates a **gas kick**. **(d) MAASP:** $$\text{MAASP} = (15.0 - 11.0) \times 0.052 \times 7500 = 4.0 \times 0.052 \times 7500 = 1560 \text{ psi}$$ Current SICP (750 psi) is well below MAASP (1560 psi). ✓ ``` **Problem 10.2** — Using the data from Problem 9.1 and pump output of 0.095 bbl/stroke, construct the full choke pressure schedule for the Wait-and-Weight Method at 10% drill string displacement intervals. ```{dropdown} Solution $$N_\text{ds} = 120 \text{ bbl} / 0.095 \text{ bbl/stroke} = 1263 \text{ strokes}$$ ICP = 1050 psi, FCP = 600 psi. Pressure drop = 450 psi over 1263 strokes. Pressure change per 10% interval: $450 / 10 = 45 \text{ psi}$ | Strokes | % displaced | Target DP pressure (psi) | |---------|------------|--------------------------| | 0 | 0% | 1050 | | 126 | 10% | 1005 | | 253 | 20% | 960 | | 379 | 30% | 915 | | 505 | 40% | 870 | | 632 | 50% | 825 | | 758 | 60% | 780 | | 884 | 70% | 735 | | 1011 | 80% | 690 | | 1137 | 90% | 645 | | 1263 | 100% | 600 | After 1263 strokes, maintain drill pipe pressure at 600 psi (FCP) until kill mud appears at the choke. ``` **Problem 10.3** — A well is shut in with SIDPP = 300 psi, SICP = 480 psi, mud weight = 9.6 ppg, TVD = 8,800 ft. The casing shoe is at 6,000 ft with LOT EMW = 12.8 ppg. (a) Calculate kill mud weight and MAASP. (b) Is SICP below MAASP? Is there margin available for the kill operation? (c) If SCR pressure is 420 psi, what are ICP and FCP? (d) What is the pressure margin between ICP and MAASP? ```{dropdown} Solution **(a):** $$\rho_\text{kill} = 9.6 + \frac{300}{0.052 \times 8800} = 9.6 + 0.656 = 10.26 \text{ ppg (use 10.3 ppg)}$$ $$\text{MAASP} = (12.8 - 9.6) \times 0.052 \times 6000 = 3.2 \times 0.052 \times 6000 = 998 \text{ psi}$$ **(b):** SICP = 480 psi < MAASP = 998 psi. ✓ Yes, there is 518 psi of margin. **(c):** $$\text{ICP} = 300 + 420 = 720 \text{ psi}$$ $$\text{FCP} = \frac{10.3}{9.6} \times 420 = 451 \text{ psi}$$ **(d):** The ICP of 720 psi is at the standpipe. MAASP of 998 psi is a casing pressure limit. These are not directly comparable during dynamic circulation (annular friction also contributes to casing pressure). However, the 278 psi gap between SICP (480 psi) and MAASP (998 psi) provides comfortable margin for gas expansion during the kill. ``` **Problem 10.4** — During a Driller's Method first circulation, the drill pipe pressure (held at ICP) suddenly drops by 200 psi. What are the two most likely causes, and what action should the driller take in each case? ```{dropdown} Solution Likely causes: 1. **Drill string washout** — a hole (washout) has developed in the drill string body or at a connection. Flow bypasses the bit nozzles through the hole in the pipe, reducing the total pressure drop through the drill string. The pump is now pushing against less resistance, so standpipe pressure drops. Consequence: BHP also drops (less pump energy reaching the bit and annulus), so the well is underbalanced and additional influx may enter. Do NOT close the choke to restore drill pipe pressure — this would increase annular pressure but not restore BHP because the pump is no longer effectively pressurizing the annulus. Action: shut the pump down, close the well in, and investigate. The choke pressure gauge and drill pipe gauge will both stabilize; if SIDPP has risen from its original value, additional influx has entered. 2. **Pump malfunction / loss of a pump cylinder** — if a valve or liner fails in the pump, pump output and pump pressure both drop. This is not a well control problem per se, but it looks identical to a washout from the pressure gauge perspective. Action: verify pump speed and stroke count; switch to a backup pump if available; shut in and investigate before restarting. In both cases: stop pumps, shut in, compare new SIDPP to the value recorded at the start of the kill. If SIDPP is unchanged, the issue is a pump or string problem, not a formation pressure change. If SIDPP has increased, additional influx has occurred and the kill sheet must be recalculated. ``` **Problem 10.5** — A well control operation using the Wait-and-Weight Method is underway. At 60% of drill string displacement (stroke count = 0.6 × N_ds), the driller observes that drill pipe pressure is 150 psi higher than the schedule. List three possible causes and describe the appropriate response. ```{dropdown} Solution At 60% displacement, the scheduled drill pipe pressure should be ICP − 0.6(ICP − FCP). An observed pressure 150 psi above this target indicates that either the hydrostatic in the drill string is rising slower than expected (the kill mud is not as heavy as assumed) or friction has increased. Possible causes: 1. **Kill mud is lighter than specified.** If the mud engineer inadvertently mixed kill mud below the target density, the hydrostatic benefit of displacing original mud is less than calculated. The schedule predicts a larger hydrostatic gain per stroke than is actually occurring, so higher surface pressure is needed to maintain BHP. Action: check kill mud weight at the pits; if light, recalculate the schedule based on the actual mud weight. 2. **Pump speed (strokes per minute) is higher than the kill rate.** Higher pump speed increases friction losses throughout the circulating system. Since ICP and FCP were calculated at the slow pump rate, any increase in pump speed raises the actual circulating pressure above the schedule. Action: verify pump stroke counter against the slow pump rate used to calculate SCR; reduce pump speed to the correct kill rate. 3. **Additional influx is entering the well.** If the well is continuing to take in formation fluid (formation pressure higher than initially estimated), BHP is below formation pressure. The constant-BHP principle means the driller must apply more surface pressure than scheduled to maintain balance. Action: shut in and re-read SIDPP. If SIDPP has increased from its original shut-in value, the formation pressure is higher than assumed and the kill mud weight must be recalculated using the new SIDPP. In all cases: open the choke slightly to reduce drill pipe pressure to the schedule target while simultaneously diagnosing the root cause. Do not continue the kill operation with an undiagnosed pressure deviation. ``` --- ## 10.8 Looking Ahead: Advanced Well Control Topics The methods in this chapter assume a simple vertical well geometry, a clean single-fluid kick, and ideal circulating behavior. Real wells and real kicks introduce additional complexities that require more advanced treatment. **Gas migration calculations.** The basic analysis assumes the kick stays at the bottom of the well until circulation begins. In a shut-in well, gas migrates upward due to buoyancy and its volume changes as pressure changes. Tracking the gas position and pressure during migration requires applying the real gas law ($PV = ZnRT$) iteratively as the gas moves from high-pressure depth to lower-pressure depth. The Z-factor accounts for non-ideal behavior and is a function of pressure, temperature, and gas composition. In practice, migration calculations are performed by well control software using real-time pressure data. **Graphical kill sheet methods.** The pressure vs. stroke count schedule developed in this chapter (ICP to FCP for W&W; constant ICP for Driller's Method first circulation) forms the basis of graphical monitoring charts used in the field. The driller plots actual drill pipe pressure against stroke count in real time and compares it to the schedule. Deviations above or below the schedule line indicate specific problems (Section 10.7) and trigger defined responses. **Kill sheet example — pressure vs. depth plot.** In addition to the stroke schedule, engineers plot pressure vs. depth to visualize the kick location and the circulating pressure profile in both the drill string and annulus. This shows how the U-tube pressure balance shifts as the kick rises, helps identify if the gas kick will approach the shoe fracture gradient, and guides choke adjustments. Worked examples of pressure vs. depth plots are developed in the senior-level course. **Horizontal and extended-reach well control.** Section 10.7.1 introduced the complications of horizontal wells. The calculation differences include: using TVD (not MD) for all hydrostatic calculations; using MD for stroke counts; accounting for kick stratification in the horizontal section; and recognizing that the shoe is not at the bottom of the well — it is typically at the heel of the horizontal turn, and the kick must be circulated past a much larger horizontal annular volume before it reaches the shoe. **Deepwater well control.** The narrow drilling window of deepwater formations means that ICP, SICP, and the maximum casing pressure during a gas kick may all approach MAASP simultaneously. Kill operations require much tighter choke management, and MPD is commonly used to maintain ECD within the narrow window during both normal drilling and kill operations. **Underground blowouts.** When the gas kick exceeds the shoe fracture gradient, the kick fluid diverts into the formation at the shoe rather than continuing to surface. This underground blowout scenario requires different pressure modeling — the well may appear to "self-kill" as surface pressures drop, but the kick is flowing from one formation into another underground, which can destabilize the shallow formation and lead to surface heave or uncontrolled gas seeps at the surface. **Managed pressure drilling (MPD).** MPD applies a controlled back-pressure to the annulus at all times using a rotating control device (RCD) and an adjustable choke. This allows the operator to hold ECD nearly constant throughout drilling and connections, and to detect kicks within a few barrels. MPD effectively converts the entire drilling operation into a continuously managed well control scenario, eliminating the distinction between "normal drilling" and "kill mode." --- ## Chapter Summary All well control kill methods rest on the constant bottomhole pressure principle: maintain BHP, formation pore pressure throughout the kill by adjusting choke pressure as the fluid column composition changes. Three equations define the pressure framework for any kill operation: $$\rho_\text{kill} = \rho_\text{mud} + \frac{\text{SIDPP}}{0.052 \times \text{TVD}}$$ $$\text{ICP} = \text{SIDPP} + \text{SCR}$$ $$\text{FCP} = \frac{\rho_\text{kill}}{\rho_\text{mud}} \times \text{SCR}$$ The choke pressure schedule for the Wait-and-Weight Method is a linear decrease from ICP to FCP over the number of strokes required to fill the drill string. After FCP is reached (kill mud at bit), drill pipe pressure holds constant while kill mud fills the annulus and the well is killed. The Driller's Method holds drill pipe pressure at ICP throughout the first circulation (kick removal) and applies the same linear ICP-to-FCP decrease during the second circulation (kill mud displacement). MAASP is a hard constraint throughout: if any calculated pressure exceeds MAASP, the standard kill method must be modified.