Well kill methods · MunaiHub

Quick refresher

A shut-in well with the string on the bottom is a U-shaped tube. In the pipe there is clean mud of known density, and in the annulus (the space between the string and the wall of the hole) there are mud and the light fluid of the influx. So we find the formation pressure from the pressure in the pipe, and the pressure in the annulus is higher if the influx is lighter than the mud.
The kill mud density depends only on the pressure in the pipe, the true vertical depth and the density of the current mud. The volume of the influx and the pressure in the annulus do not enter it.
The main principle is a constant bottomhole pressure. We keep the pump rate constant. We use the choke to hold the pipe pressure at its planned value, which goes from the initial circulating pressure (ICP) $p_{\text{SIDPP}} + p_{\text{SCR}}$ to the final circulating pressure (FCP) $p_{\text{SCR}}\,\rho_{\text{kill}}/\rho_m$ . Here SIDPP is the shut-in drill pipe pressure, and SCR is the pressure that the pump needs at the slow circulating rate chosen for killing.
Driller's method: first we circulate the influx out with the current mud, then we replace the mud with the heavy one. Wait and weight method: we pump the kill mud at once, lowering the pipe pressure step by step by a schedule. Its highest annulus pressure is usually lower, but we need time to make the mud heavier.
While gas is circulated out, the annulus pressure at the choke rises because the gas expands. This is as it should be. We must not lower it by opening the choke: the bottomhole pressure would fall, and a new influx would start.
If we cannot circulate, we manage the rising gas by the volumetric method, and in special cases we pump the fluid back into the formation.

Key relationships

p_p = p_{\text{SIDPP}} + 0.00981\,\rho_m\,h

formation pressure from the pipe pressure (MPa, g/cm³, m true vertical)

\rho_{\text{kill}} = \rho_m + \dfrac{p_{\text{SIDPP}}}{0.00981\,h}

kill mud density without a margin

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

initial circulating pressure (ICP)

p_{\text{FCP}} = p_{\text{SCR}}\,\dfrac{\rho_{\text{kill}}}{\rho_m}

final circulating pressure (FCP)

\rho_k = \rho_m - \dfrac{p_{\text{ann}} - p_{\text{SIDPP}}}{0.00981\,h_k}

estimate of the density of the influx fluid; here $p_{\text{ann}}$ is the annulus pressure at the wellhead of the shut-in well (the shut-in casing pressure) and $h_k$ is the height of the influx

Common pitfalls

Calculating the kill mud density from the annulus pressure, and not from the pipe pressure.
Changing the pump rate during killing without recalculating the pressures. The friction losses depend on the rate, so the planned pipe pressure schedule becomes meaningless.
Holding the annulus pressure at the choke constant while the gas rises up the hole. The bottomhole pressure falls, and a new influx starts.
Putting large “margins” into the kill mud density and into the choke pressure. They raise the pressure at the casing shoe (the bottom end of the casing) and may cause lost circulation (mud escaping into the rock).
Not recalculating the MAASP after the change to kill mud.

After this lesson you can

explain why the pressures in the drill pipe and in the annulus (the space between the pipe and the wall of the hole) differ after the well is shut in, and why the drill pipe pressure serves as a “gauge” of the bottomhole pressure
calculate the formation pressure and the kill mud density from the shut-in pressures (the pressures read on the closed well), and estimate the density of the fluid that came in
calculate the initial and final circulating pressure, the number of pump strokes to the bit (a stroke is one movement of the pump piston, and it pushes out a known volume of mud) and the schedule by which the drill pipe pressure is lowered
describe the driller's method and the wait and weight method, and compare them by the pressures in the annulus and at the shoe, by time and by complexity
explain the principle of the volumetric method and of bullheading, and name the cases in which they are used
name the limits that must not be exceeded during killing: the maximum allowable annular surface pressure (MAASP), the strength of the casing and the equipment, and the capacity of the mud-gas separator (the vessel that takes gas out of the returning mud)

The task of killing

When the signs of a kick have been confirmed, we shut in the well with the blowout preventer equipment (Well control: primary barrier and kick indicators). The influx stops, but its cause remains: the pressure of the mud column is lower than the formation pressure, and formation fluid takes up part of the hole. Killing does two jobs. It takes the fluid of the influx out of the well through the choke manifold (the set of pipes and adjustable valves through which the returns leave a shut-in well). And it fills the well with a mud of such a density that the column alone holds the formation again. That is, it restores primary control.

All of killing obeys one rule: the bottomhole pressure must stay constant and a little above the formation pressure. If it falls below, a new influx starts. If it rises too high, the pressure under the shoe of the last casing string may exceed the leak-off pressure. Then the mud goes into the formation, the level falls, the influx gets stronger, and a crossflow between formations is possible. So the methods of killing with circulation are called constant bottomhole pressure methods.

Methods of killing

Method: Driller's method
When it is used: the string is on the bottom; the kill mud is not ready, and we must start at once
The idea: two circulations: first we circulate the influx out with the current mud, then we replace the mud with kill mud

Method: Wait and weight method
When it is used: the string is on the bottom; the mud can be weighted up quickly
The idea: one circulation: we circulate the influx out at once with kill mud

Method: Volumetric method
When it is used: we cannot circulate: the string has been pulled, is not on the bottom, or is plugged
The idea: we let the gas rise and expand under control, bleeding off mud in portions

Method: Bullheading
When it is used: the influx cannot, or must not, be brought to the surface
The idea: we pump the fluid back into the formation

Method	When it is used	The idea
Driller's method	the string is on the bottom; the kill mud is not ready, and we must start at once	two circulations: first we circulate the influx out with the current mud, then we replace the mud with kill mud
Wait and weight method	the string is on the bottom; the mud can be weighted up quickly	one circulation: we circulate the influx out at once with kill mud
Volumetric method	we cannot circulate: the string has been pulled, is not on the bottom, or is plugged	we let the gas rise and expand under control, bleeding off mud in portions
Bullheading	the influx cannot, or must not, be brought to the surface	we pump the fluid back into the formation

The wait and weight method is also called the one-circulation method, or the “engineer's method”. The driller's method is called the two-circulation method. There is also an intermediate variant, in which the mud is weighted up gradually during circulation, but in drilling it is seldom used.

Pressures after shutting in: the well as a U-tube

After the well is shut in, the pressures at the wellhead rise until the formation stops giving up fluid, and then they stabilise: in minutes for a permeable formation, longer for a tight one. We record three values: the shut-in drill pipe pressure (SIDPP, the gauge pressure in the drill pipe), the shut-in casing pressure (SICP, the gauge pressure in the annulus) and the pit gain, the rise of the volume of mud in the pits (the mud tanks at the rig), which equals the volume of the influx.

The drill string and the annulus are connected at the bit, so a shut-in well behaves like a U-tube (U-tube). The fluid of the influx is in the annulus, and in the pipe there is clean mud of known density. So we can find the bottomhole pressure from the pipe side: it equals the pressure at the top of the pipe plus the pressure of the mud column in it. While the well is shut in and the influx has stopped, the bottomhole pressure equals the formation pressure.

Formation pressure from the drill pipe pressure

p_p = p_{\text{SIDPP}} + \rho_m\,g\,h

where:

$p_p$ formation (pore) pressure of the formation that has kicked, Pa
$p_{\text{SIDPP}}$ gauge pressure in the drill pipe after shutting in and stabilisation (SIDPP), Pa
$\rho_m$ density of the mud in the drill pipe, kg/m³
$h$ true vertical depth of the formation that has kicked; with the bit on the bottom, the depth of the bottom, m
$g$ acceleration due to gravity, m/s²

Units: SI; the pressures are gauge pressures, as on the gauges

Holds when

the string is on the bottom, the influx is only in the annulus, and the pipe holds mud of one known density;
the pressures have stabilised, and the gas has not yet started to raise them by its rise. If both pressures keep rising at the same rate, this is the rise of the gas, and for the calculation we take the value from before this growth;
if there is a float valve in the string (a one-way valve), it does not pass pressure from below. We find the pressure under it by pumping a little mud into the pipe with care until the valve opens;
the pressures are gauge pressures. The mud column is also counted in gauge pressure, so atmospheric pressure does not enter the formula.

The gauge on the standpipe is the only instrument by which we can judge the bottomhole pressure: everything that is in the pipe is known. All the methods of killing with circulation rest on this. The pressure in the pipe is what the mud column lacked to hold the formation.

In other unit systems (2)

Metric units

p_p\,[\text{MPa}] = p_{\text{SIDPP}} + 0.00981\,\rho_m\,[\text{g/cm}^3]\;h\,[\text{m}]

pressures in MPa, density in g/cm³, depth in m.

0.00981 MPa is the pressure of a column of liquid of density 1 g/cm³ and height 1 m.

Oilfield units

p_p\,[\text{psi}] = p_{\text{SIDPP}} + 0.052\,\rho_m\,[\text{ppg}]\;h\,[\text{ft}]

pressures in psi, density in ppg, depth in feet.

0.052 psi/ft per ppg comes from the oilfield formula for hydrostatic pressure.

In the annulus above the influx there is the same mud, but at the bottom there is a column of light fluid of height $h_k$ . It weighs less than the mud that it displaced. So the pressure in the annulus at the wellhead is higher than in the pipe by this “shortfall” of hydrostatic pressure. From it we can estimate the density of the fluid of the influx.

Height and density of the influx from the shut-in pressures

h_k = \frac{V_k}{C_a}, \qquad \rho_k = \rho_m - \frac{p_{\text{ann}} - p_{\text{SIDPP}}}{g\,h_k}

where:

$h_k$ height of the column of the influx, true vertical, m
$V_k$ volume of the influx, the gain in the volume of mud in the pits, m³
$C_a$ capacity of the annulus opposite the influx (usually opposite the drill collars, the heavy pipes at the bottom of the string): volume per metre, m³/m
$\rho_k$ density of the fluid of the influx at bottomhole conditions, kg/m³
$p_{\text{ann}}$ gauge pressure in the annulus after shutting in (SICP), Pa
$p_{\text{SIDPP}},\ \rho_m,\ g$ pressure in the pipe, mud density, acceleration due to gravity, Pa, kg/m³, m/s²

Units: SI; in metric units $g\,h_k$ is replaced by $0.00981\,h_k$ (g/cm³, MPa, m)

Holds when

the influx fills the annulus at the bottom as one pocket and is not mixed with the mud;
the hole is vertical. In an inclined hole the length of the pocket along the hole is converted into a true vertical height;
the capacity of the annulus is known. In an open hole with washouts it is larger than the nominal one, and the pocket is in fact shorter than calculated;
if the volume of the influx is larger than the volume of the annulus opposite the drill collars, we calculate the height by sections with different capacity.

The larger the difference $p_{\text{ann}} - p_{\text{SIDPP}}$ at the same volume of the influx, the lighter the fluid. The estimate is rough, so when there is doubt we take the influx as gas. That is the most dangerous case.

Approximate density of the influx fluid at bottomhole conditions

Fluid: Gas
Density, g/cm³: 0.1–0.35
Gradient, kPa/m: 1.0–3.4

Fluid: Oil
Density, g/cm³: 0.6–0.9
Gradient, kPa/m: 5.9–8.8

Fluid: Formation water
Density, g/cm³: 1.0–1.2
Gradient, kPa/m: 9.8–11.8

Fluid	Density, g/cm³	Gradient, kPa/m
Gas	0.1–0.35	1.0–3.4
Oil	0.6–0.9	5.9–8.8
Formation water	1.0–1.2	9.8–11.8

The density of gas grows with pressure and depends on composition. Values in between may mean a mixture of gas and oil, or an influx mixed with mud. The values are approximate.

Worked exampleWhat the shut-in pressures tell us

Given (assumed data)

Depth of the bottom (vertical hole): 3350 m; the bit is on the bottom
Mud density $\rho_m$: 1.24 g/cm³
Pressures after stabilisation: 3.1 MPa in the pipe, 4.5 MPa in the annulus
Pit gain $V_k$: 2.1 m³
Annulus at the bottom: hole of 215.9 mm, 190 m of drill collars of 165.1 mm

Solution

Formation pressure: $p_p = 3.1 + 0.00981\cdot 1.24\cdot 3350 = 3.1 + 40.75 = 43.85$ MPa. The equivalent mud weight (the density of the mud that would give the same pressure) is $43.85/(0.00981\cdot 3350) = 1.334$ g/cm³.
Capacity of the annulus opposite the collars: $\frac{\pi}{4}(215.9^2 - 165.1^2)\cdot 10^{-3} = 15.20$ L/m. The height of the influx is $h_k = 2.1/0.01520 = 138$ m. The pocket fits opposite the collars, which are 190 m long.
Density of the influx: $\rho_k = 1.24 - \dfrac{4.5 - 3.1}{0.00981\cdot 138} = 0.21$ g/cm³.

Answer: The formation pressure is 43.85 MPa (an equivalent mud weight of 1.334 g/cm³). In the annulus at the bottom there is a pocket about 138 m high with a density of 0.21 g/cm³: this is gas.

What it means. The mud column of 1.24 g/cm³ lacked exactly 3.1 MPa, and this is what the pipe shows. The influx is gas, so while it is circulated out, the annulus pressure at the choke will grow as the gas expands. The lesson's other examples use the same well. The data in this example are assumed for illustration.

Kill mud

Kill mud must balance the formation pressure with its column when the wellhead is open. We set the pressure of its column equal to the formation pressure, and we get a formula that contains only the pipe pressure, the depth and the density of the current mud.

Kill mud density

\rho_{\text{kill}} = \rho_m + \frac{p_{\text{SIDPP}}}{g\,h}

where:

$\rho_{\text{kill}}$ kill mud density: the density at which its column balances the formation pressure, kg/m³
$\rho_m$ density of the current mud, kg/m³
$p_{\text{SIDPP}}$ gauge pressure in the drill pipe after shutting in (SIDPP), Pa
$h$ true vertical depth of the formation that has kicked, m

Units: SI

Holds when

the same as for the calculation of the formation pressure from the pipe pressure;
a margin above balance, if it is needed, is set separately: by the mud density or by the choke pressure;
$h$ is the true vertical depth. The length of an inclined hole does not enter the formula.

Neither the gain in volume nor the pressure in the annulus affects the kill mud density: they characterise the influx, not the formation.

In other unit systems (2)

Metric units

\rho_{\text{kill}}\,[\text{g/cm}^3] = \rho_m + \frac{p_{\text{SIDPP}}\,[\text{MPa}]}{0.00981\; h\,[\text{m}]}

densities in g/cm³, pressure in MPa, depth in m.

Oilfield units

\rho_{\text{kill}}\,[\text{ppg}] = \rho_m + \frac{p_{\text{SIDPP}}\,[\text{psi}]}{0.052\; h\,[\text{ft}]}

densities in ppg, pressure in psi, depth in feet.

On the rig the mud density is adjusted in steps of 0.01 g/cm³ (about 0.1 ppg), so we round the calculated value up. An extra margin, for example for swabbing during a later pull, is set by the drilling programme (the drilling plan), but every margin raises the pressure on the whole open part of the hole. Before we make the mud heavier, we check that the rock under the shoe will withstand the new mud. In this check we count the equivalent circulating density (ECD, the density that the mud effectively has while it circulates). We also recalculate the maximum allowable annular surface pressure (MAASP). It gets smaller when the mud is made heavier.

Worked exampleKill mud density and the new MAASP

Given (assumed data)

Shut-in data: from the previous example: 3350 m, mud 1.24 g/cm³, pipe pressure 3.1 MPa
Shoe of the 244.5 mm casing: 2450 m true vertical
Leak-off pressure under the shoe from the test: an equivalent mud weight of 1.68 g/cm³

Solution

Kill mud density: $\rho_{\text{kill}} = 1.24 + \dfrac{3.1}{0.00981\cdot 3350} = 1.24 + 0.0943 = 1.3343$ g/cm³. We round up to 1.34 g/cm³. The margin above balance is $0.00981\cdot(1.34 - 1.3343)\cdot 3350 = 0.19$ MPa.
Check in oilfield units: the mud is $1.24\cdot 8.345 = 10.35$ ppg, the pressure is $3.1\cdot 145.04 = 450$ psi, and the depth is $3350/0.3048 = 10{,}991$ ft. $\rho_{\text{kill}} = 10.35 + 450/(0.052\cdot 10{,}991) = 11.13$ ppg, which is 1.334 g/cm³.
MAASP with the current mud: $0.00981\cdot(1.68 - 1.24)\cdot 2450 = 10.6$ MPa. With the kill mud: $0.00981\cdot(1.68 - 1.34)\cdot 2450 = 8.2$ MPa.

Answer: We need kill mud of 1.34 g/cm³ (11.2 ppg). The MAASP will fall from 10.6 to 8.2 MPa.

What it means. The pressure in the annulus after shutting in (4.5 MPa) is far from the MAASP, and the margin under the shoe after killing is 0.34 g/cm³. The window is wide, and the influx can be circulated out in the usual way. Rounding up gave only a small margin, 0.19 MPa. If a larger one is needed, it is set separately, while the pressure at the shoe is checked. The metric and the oilfield calculations agree to within the rounding of the constants. The data in this example are assumed for illustration.

We calculate how much weighting material (barite, a heavy mineral powder) we need in the same way as for ordinary weighting of mud (weighting up the mud). But we do it for the whole active volume: the inner volume of the string, the annulus and the mud in the pits. This much barite must be on the rig. Before pumping starts, we make the mud in the pits heavier. This is the “waiting” of the wait and weight method. We make the mud that returns from the well heavier as the killing goes on.

Circulation at constant bottomhole pressure

While the well is shut in, the bottomhole pressure is created by the mud column in the pipe and the pressure at the top of the pipe. Now the pump sends the mud down the string, and the mud with the fluid leaves the annulus through the choke. From the annulus side, the bottomhole pressure is then the sum of the pressure of the column in the annulus, the friction losses in the annulus and the pressure that the choke creates (the gauge of the annulus shows it). The choke is the main tool. By closing it a little we raise the pressure in the whole well, and by opening it a little we lower it.

We cannot see the bottomhole pressure, but we can hold it by the pressure in the pipe. At a constant pump rate the friction losses in the string and in the bit nozzles are constant, and the column in the pipe is known. If the pressure on the standpipe equals the calculated one, then the pressure at the bottom is the one that we need. So we kill at a constant reduced pump rate, and we use the choke to hold the pipe pressure at its planned value.

We choose the rate for killing several times lower than the drilling rate. Then the friction losses, which add to the pressure at the shoe, are smaller. The operator has time to follow the changes of the pressure. The gas that comes to the surface has time to separate in the mud-gas separator (a vessel that takes gas out of the mud). The standpipe pressure at this rate is the slow circulating rate pressure $p_{\text{SCR}}$ (SCR). We measure it beforehand, while drilling, for each pump at one or two reduced rates, and we repeat it after the properties of the mud change and after the well is deepened considerably.

Initial and final circulating pressure

p_{\text{ICP}} = p_{\text{SIDPP}} + p_{\text{SCR}}, \qquad p_{\text{FCP}} = p_{\text{SCR}}\,\frac{\rho_{\text{kill}}}{\rho_m}

where:

$p_{\text{ICP}}$ initial circulating pressure (ICP): the standpipe pressure at the kill rate while the pipe holds the current mud, MPa
$p_{\text{FCP}}$ final circulating pressure (FCP): the standpipe pressure when the pipe is full of kill mud, MPa
$p_{\text{SIDPP}}$ pressure in the pipe after shutting in (SIDPP), MPa
$p_{\text{SCR}}$ circulating pressure with the current mud at the reduced rate (SCR), MPa
$\rho_{\text{kill}},\ \rho_m$ densities of the kill mud and of the current mud, g/cm³

Units: any identical units of pressure; the densities in identical units

Holds when

the pump rate is constant and equal to the rate at which $p_{\text{SCR}}$ was measured;
when the mud is changed, the friction losses change in proportion to the density. This is an approximation for turbulent flow in the pipe and in the bit nozzles. The viscosity of the kill mud is close to the original;
$p_{\text{SCR}}$ includes the losses in the whole system, including the annulus. During killing the losses in the annulus add to the bottomhole pressure as a small margin (the derivation is in the advanced section);
with a subsea wellhead (a wellhead on the sea floor), friction losses in the long choke line (the pipe that carries the returns from the blowout preventer to the choke) are added to the pressures. That is a separate calculation.

At the start the standpipe pressure is higher than the usual circulating pressure by the SIDPP: this keeps the bottomhole pressure equal to the formation pressure. When the string is full of kill mud, its own column balances the formation, the SIDPP “disappears”, and the friction grows a little because of the higher density.

When the pump is started, friction losses appear in the string that were not there before, and in that short time the gas in the annulus hardly moves. So, while we bring the pump up to the kill rate, we use the choke to hold the pressure in the annulus at the wellhead constant, equal to the shut-in casing pressure (SICP). Then we compare the steady standpipe pressure with the calculated $p_{\text{ICP}}$ . A change of the choke position does not reach the gauge on the standpipe at once, but after a few seconds: this is the time that the pressure wave takes to run down the annulus and up the string. So we work the choke in small steps and wait.

The schedule of the pipe pressure

In the wait and weight method we pump the kill mud at once. While it fills the string, the column in the pipe gets heavier, and the standpipe pressure must fall from $p_{\text{ICP}}$ to $p_{\text{FCP}}$ . In a vertical well with a string of one internal diameter the hydrostatic pressure grows in proportion to the volume pumped, so we lower the pressure along a straight line against the number of pump strokes. The strokes to the bit equal the inner volume of the string divided by the pump output per stroke (the volume of mud that one stroke of the pump piston delivers).

Schedule of the pipe pressure while kill mud is pumped

p(N) = p_{\text{ICP}} - \left(p_{\text{ICP}} - p_{\text{FCP}}\right)\frac{N}{N_{\text{bit}}}, \qquad N_{\text{bit}} = \frac{V_{\text{string}}}{V_{\text{stk}}}

where:

$p(N)$ planned standpipe pressure after $N$ pump strokes, MPa
$N$ number of pump strokes from the start of pumping the kill mud, —
$N_{\text{bit}}$ strokes to the bit (in the lesson Rig circulating and rotary systems it is $Z_{\text{bit}}$ ), —
$V_{\text{string}}$ inner volume of the drill string, m³
$V_{\text{stk}}$ output of the pump in one stroke, with the volumetric efficiency counted (only the part of the piston volume that is really delivered), m³

Units: pressures in any identical units, volumes in identical units

Holds when

the well is vertical, and the string has one internal diameter. A short section of heavy pipes at the bottom hardly changes the schedule (see the example below). For a string of long sections and for an inclined well, we build the schedule by sections (see the advanced section);
the formula holds for $N \le N_{\text{bit}}$ . After that we hold the pressure equal to $p_{\text{FCP}}$ until the kill mud comes out at the surface;
the volume of the surface lines from the pump to the string is small, and for simplicity it is not counted.

If the standpipe pressure is above the schedule, the bottomhole pressure is greater than needed, and we open the choke a little. If it is below, we close it a little. The choke makes up for everything that happens in the annulus, including the expansion of the gas.

CalculatedThe standpipe pressure during killing for the lesson's well. In the wait and weight method it falls along a straight line from 5.5 to 2.59 MPa in 1854 strokes, while the kill mud fills the string, and then it stays constant. In the first circulation of the driller's method the standpipe pressure is held constant at 5.5 MPa.

Worked exampleThe kill sheet: pressures, strokes, time and barite

Given (assumed data)

Muds and pipe pressure: 1.24 g/cm³, kill mud 1.34 g/cm³; 3.1 MPa
Slow circulating rate pressure $p_{\text{SCR}}$: 2.4 MPa at 30 strokes per minute
Pump output per stroke: 16.2 L
Drill string: 3160 m of 127 mm pipe with an internal diameter of 108.6 mm and 190 m of drill collars with an internal diameter of 71.4 mm
Annulus: 215.9 mm hole below the shoe at 2450 m; above it, casing with an internal diameter of 222.4 mm
Mud in the pits; barite: 40 m³; 4.2 g/cm³

Solution

Pressures: $p_{\text{ICP}} = 3.1 + 2.4 = 5.5$ MPa; $p_{\text{FCP}} = 2.4\cdot 1.34/1.24 = 2.59$ MPa.
The capacity of the pipe is 9.26 L/m, and of the collars 4.00 L/m. The inner volume of the string: $3160\cdot 0.00926 + 190\cdot 0.00400 = 30.0$ m³. The strokes to the bit: $30.0/0.0162 = 1854$ , which is 62 min at 30 strokes per minute.
The schedule: we lower the standpipe pressure by $(5.5 - 2.59)\cdot 100/1854 = 0.157$ MPa for every 100 strokes: after 500 strokes 4.72 MPa, after 1000 strokes 3.93 MPa, after 1500 strokes 3.15 MPa. From stroke 1854 on, we hold 2.59 MPa.
A check of the straight line: the string has two sections, and strictly the schedule is built by sections. By the end of the drill pipe ( $3160\cdot 0.00926/0.0162 = 1807$ strokes) the kill mud has filled 3160 m out of 3350, and the pressure should be $5.5 - (5.5 - 2.59)\cdot 3160/3350 = 2.76$ MPa. The straight line gives 2.67 MPa, which is 0.09 MPa less. This is less than the margin of 0.19 MPa from rounding the density up, so for such a string the straight line is acceptable.
The annulus: 19.9 m³ in the open hole and 64.1 m³ in the casing, 84.0 m³ in all, which is another 173 min. The strokes for a full circulation are 7041, which is about 3.9 h.
The active volume is $30.0 + 84.0 + 40 = 154$ m³. The barite needed to make the mud heavier, from 1.24 to 1.34 g/cm³, is $154\cdot\dfrac{1.34 - 1.24}{4.2 - 1.34} = 5.39$ m³, or 22.6 t.

Answer:

p_{\text{ICP}}

= 5.5 MPa,

p_{\text{FCP}}

= 2.59 MPa. The kill mud will reach the bit in 62 min, the whole circulation will take about 3.9 h, and about 22.6 t of barite is needed to make the mud heavier.

What it means. The whole active volume of 154 m³ needs more than 20 t of barite. We make the mud in the pits heavier before pumping starts, and all that time the well stays shut in: this is the “waiting” of the method. We make the mud that returns from the well heavier as circulation goes on. In the driller's method we can start the first circulation at once, holding 5.5 MPa on the standpipe to the end of the circulation, and we pump the kill mud in the second circulation, when it is ready. The data in this example are assumed for illustration.

The driller's method and the wait and weight method

Both methods maintain the same bottomhole pressure, and they differ in when the kill mud goes into the well. It is convenient to describe them in stages. The exact order of actions and the permitted deviations are set by the procedures of the company.

Driller's method (two circulations)

1
First circulation
We bring the pump up to the kill rate while holding the annulus pressure at the choke constant, at the value of the shut-in casing pressure. Then we use the choke to hold the standpipe pressure equal to $p_{\text{ICP}}$ until the influx has left the well. With a gas influx the annulus pressure at the choke rises. It reaches its highest value when the gas approaches the wellhead, and it falls when the gas leaves through the choke.
2
Check
When the influx has been washed out, the annulus is full of the original mud, and the annulus pressure at the choke becomes equal to the original SIDPP. If at this moment we stop the pump and shut in the well, both pressures must equal the SIDPP.
3
Second circulation
We pump the kill mud. While it fills the string, nothing changes in the annulus, so we use the choke to hold the annulus pressure at the wellhead constant, and the standpipe pressure falls by itself to $p_{\text{FCP}}$ . Then we hold $p_{\text{FCP}}$ on the standpipe until the kill mud comes out at the surface. The annulus pressure falls to zero.
4
Result
We stop the pump. If the pressures in the pipe and in the annulus are zero and there is no flow, the well has been killed.

Wait and weight method (one circulation)

1
Waiting
While the kill mud is being prepared, the well is shut in. If gas rises and the pressures grow, we manage them by the volumetric method (see the next section).
2
Pumping into the string
We bring the pump up to the kill rate at a constant annulus pressure at the wellhead. Then we use the choke to lower the standpipe pressure by the schedule from $p_{\text{ICP}}$ to $p_{\text{FCP}}$ .
3
Circulating out
When the kill mud has left the bit, we hold $p_{\text{FCP}}$ on the standpipe. The gas rises and expands, and behind it rises the heavy mud, which lowers the pressure in the annulus.
4
Result
When the kill mud has come out at the surface, the choke is fully open, and the annulus pressure is zero. After the pump is stopped, we check the well for flow.

CalculatedThe pressure in the annulus at the wellhead while the gas pocket of the lesson's example is circulated out, calculated by the single-pocket model (see the advanced section). Up to 30 m³, while the kill mud fills the string, the curves coincide. Then, in the wait and weight method, the heavy mud rises up the annulus, and by the time the gas reaches the wellhead the pressure is 1 MPa lower: 7.1 MPa against 8.1 MPa.

The shape of the curves comes from two effects. As the gas rises, it expands and pushes mud out of the annulus. The column in the annulus gets lighter, and the pressure at the wellhead rises, most of all in the last hundreds of metres, where the pressure is low. The second effect is geometry: when the pocket passes from the narrow annulus opposite the drill collars into the wider one opposite the drill pipe, its height gets smaller, and the pressure in the annulus falls for a while. In the wait and weight method there is a third effect: the heavy mud that rises behind the gas lowers the pressure in the annulus.

Worked examplePressure in the annulus and at the shoe while gas is circulated out

Given (assumed data)

Well, influx and muds: from the examples above
Model: the gas is a single pocket, it moves with the mud and does not dissolve; the gas is ideal, and the temperature is constant; friction in the annulus is not counted; the bottomhole pressure equals the formation pressure

Solution

At the start of circulation the pressure in the annulus is 4.5 MPa. When the whole pocket has passed from the annulus opposite the collars into the wider one (after 2.9 m³), the pressure in the annulus falls to 4.05 MPa.
The top of the gas passes the shoe after 17 m³, while the kill mud leaves the bit only after 30 m³. So the highest pressure at the shoe is the same in both methods: 34.3 MPa (an equivalent mud weight of 1.43 g/cm³). It occurs right at the start, while the gas is at the bottom. The leak-off pressure is 40.4 MPa.
Driller's method: the gas reaches the wellhead after 73 m³. The pressure in the annulus at this moment is the highest, 8.1 MPa, and the volume of the gas is 11 m³.
Wait and weight method: by the time the gas arrives (after 71.5 m³), a column of kill mud has risen up the annulus, and the pressure in the annulus is 7.1 MPa, which is 1.0 MPa less.

Answer: The highest pressure in the annulus is 8.1 MPa in the driller's method and 7.1 MPa in the wait and weight method. The pressure at the shoe does not exceed 34.3 MPa, against a limit of 40.4 MPa.

What it means. The wait and weight method lowered the highest pressure in the annulus, but not the highest pressure at the shoe. The inner volume of the string (30 m³) is larger than the volume of the annulus in the open hole (20 m³), and the gas passes the shoe before the kill mud leaves the bit. Real gas also rises relative to the mud and partly dissolves, and the pocket is stretched, so the real pressures differ from the model ones. The model shows the nature of the process and the order of the quantities. The data in this example are assumed for illustration.

Comparison of the methods

Feature: Start of circulating out
Driller's method: at once after shutting in
Wait and weight method: after the mud in the pits has been made heavier

Feature: Circulations
Driller's method: two
Wait and weight method: one, shorter in all

Feature: What is held on the standpipe
Driller's method: a constant pressure
Wait and weight method: a pressure by the schedule to the bit, then a constant one

Feature: Highest pressure in the annulus
Driller's method: higher
Wait and weight method: lower, if the kill mud enters the annulus before the gas reaches the wellhead

Feature: Pressure at the shoe
Driller's method: set by the gas pocket while it is below the shoe
Wait and weight method: lower only if the kill mud leaves the bit before the gas passes the shoe

Feature: Gas while we wait
Driller's method: there is no waiting
Wait and weight method: it rises; the pressures are managed by the volumetric method

Feature	Driller's method	Wait and weight method
Start of circulating out	at once after shutting in	after the mud in the pits has been made heavier
Circulations	two	one, shorter in all
What is held on the standpipe	a constant pressure	a pressure by the schedule to the bit, then a constant one
Highest pressure in the annulus	higher	lower, if the kill mud enters the annulus before the gas reaches the wellhead
Pressure at the shoe	set by the gas pocket while it is below the shoe	lower only if the kill mud leaves the bit before the gas passes the shoe
Gas while we wait	there is no waiting	it rises; the pressures are managed by the volumetric method

The driller's method is simpler: fewer calculations are needed, and we can start it at once. The wait and weight method is shorter and usually gives a lower pressure at the wellhead, but it needs time to make the mud heavier and a schedule calculated in advance. We decide in advance which method to use, in the emergency response plan and in the procedures of the company.

When we cannot circulate: the volumetric method and bullheading

The methods with circulation need the string to be on the bottom and to allow pumping through it. Suppose the kick happened while the tools were being pulled, and the string is far from the bottom or out of the hole. Or the string or the nozzles are plugged. Or the pump cannot be started, and the gas in the shut-in well rises. Then we manage it without circulation (gas in a shut-in well). If we can, we run the string to the bottom while the well is under pressure, through the closed preventer, and we bleed off the mud that the string displaces. This is called stripping. Then we can kill in the usual way.

The volumetric method is based on a simple balance. If we bleed off a volume of mud $\Delta V$ from the annulus, the column in the annulus gets shorter, and the bottomhole pressure falls by the weight of this column. To keep the pressure at the bottom unchanged, the pressure at the wellhead must rise by exactly the same amount. The rising gas does this, if we let it expand in portions. First we let the annulus pressure at the wellhead rise above its shut-in value by a margin and a working step. Then, holding it constant, we bleed off the volume of mud that corresponds to the working step, close the choke and wait until the pressure rises by one more step. We go on like this until the gas comes to the wellhead. After that we replace the gas with mud: we pump a small portion of mud into the annulus, let it fall through the gas, and bleed off gas, lowering the wellhead pressure by the hydrostatic pressure of the portion that we pumped in.

Loss of hydrostatic pressure when mud is bled off from the annulus

\Delta p = \rho_m\,g\,\frac{\Delta V}{C_a}

where:

$\Delta p$ fall of the pressure of the column in the annulus, which must be made up by the wellhead pressure, Pa
$\Delta V$ volume of mud bled off, m³
$C_a$ capacity of the annulus (or of the open hole without a string) where the gas is, m³/m
$\rho_m,\ g$ mud density, acceleration due to gravity, kg/m³, m/s²

Units: SI; in metric units $\Delta p\,[\text{MPa}] = 0.00981\,\rho_m\,\Delta V/C_a$ (g/cm³, m³, m³/m)

Holds when

mud is bled off in small portions, and its volume is measured accurately, for example in the trip tank;
the hole is vertical, and the capacity of the section with gas is known;
the gas does not dissolve in the mud. In oil-based muds a large part of the gas is dissolved, and the method needs corrections.

This is the “price” of every cubic metre that we bleed off: by this much we must raise the wellhead pressure, so that the bottomhole pressure does not fall below the formation pressure.

Worked exampleHow much mud to bleed off in one step

Given (assumed data)

Well: the tools have been pulled, and gas rises in casing with an internal diameter of 222.4 mm
Mud: 1.24 g/cm³
Working pressure step: 0.35 MPa

Solution

Capacity of the casing: $\frac{\pi}{4}\cdot 222.4^2\cdot 10^{-3} = 38.85$ L/m.
Every cubic metre bled off lowers the pressure of the column by $0.00981\cdot 1.24/0.03885 = 0.313$ MPa.
The volume for a working step: $\Delta V = 0.35\cdot 0.03885/(0.00981\cdot 1.24) = 1.12$ m³.

Answer: At each step we first let the annulus pressure rise by 0.35 MPa, and then at a constant pressure we bleed off about 1.12 m³ of mud.

What it means. The 1.12 m³ that we bled off lowered the hydrostatic pressure in the annulus by 0.35 MPa, while the wellhead pressure had just risen by the same 0.35 MPa. So the bottomhole pressure stayed no lower than the formation pressure, with the margin that was put in at the start. If we bleed off more than we should, the bottomhole pressure will fall, and a new influx will start. If we do not bleed off at all, the rising gas will raise the pressure until the rock under the shoe ruptures. The data in this example are assumed for illustration.

Bullheading is pumping into a shut-in well so that the fluid of the influx is pushed back into the formation. We resort to it in three cases. The influx cannot or must not be brought to the surface (gas with hydrogen sulfide, a poisonous gas, as in a number of fields of the Pre-Caspian Basin). Or the influx is too large to be circulated out safely. Or there is no string in the well. The pumping pressure must exceed the formation pressure, but it must not exceed what the casing and the equipment permit. The weakest rock opens most easily, often under the shoe, so the fluid may go somewhere other than the formation it came from. Gas also rises to meet the pumped fluid, so the pump rate must be high enough. We plan bullheading with special care.

Limits during killing

During killing the pressures in the well must stay within limits that are set in advance:

the pressure at the shoe: below the leak-off pressure from the test under the shoe. At the wellhead it corresponds to the MAASP (Fracture gradient and leak-off testing);
the pressure at the wellhead: below what the casing permits (its internal yield pressure, the pressure inside the pipe at which the wall begins to yield, with a margin; see Casing: purpose, types, properties and standards), the casing head (the fitting at the top of the casing), the blowout preventer equipment and the choke manifold. The smallest of these values applies (Blowout prevention equipment);
the flow of gas at the surface: not more than the mud-gas separator can separate. When gas approaches the wellhead, we lower the pump rate if necessary, by the procedure;
hydrogen sulfide: if it is possible, we send the gas to the flare (a stack where gas is burned safely), the personnel use protective equipment, and we choose the method knowing that it is dangerous to bring such gas to the surface.

How large an influx may be, so that all these limits are held, is estimated beforehand through the kick tolerance. The earlier a kick is noticed, the smaller the pocket and the lower the pressures during killing (early detection).

Terms and symbols

SIDPP, $p_{\text{SIDPP}}$: The gauge pressure in the drill pipe after the well is shut in and the pressures have stabilised. From it we find the formation pressure and the kill mud density.
SICP, $p_{\text{ann}}$: The shut-in casing pressure: the gauge pressure in the annulus after shutting in. It is greater than the SIDPP if the influx is lighter than the mud. The same symbol $p_{\text{ann}}$ also stands for the annulus pressure at the choke while we circulate.
Kill mud, $\rho_{\text{kill}}$: A mud whose column balances the formation pressure.
Slow circulating rate pressure (SCR), $p_{\text{SCR}}$: The standpipe pressure when the current mud circulates at the kill rate. It is measured beforehand.
ICP and FCP: The initial ( $p_{\text{SIDPP}} + p_{\text{SCR}}$ ) and final ( $p_{\text{SCR}}\,\rho_{\text{kill}}/\rho_m$ ) circulating pressure during killing.
Choke: An adjustable valve at the outlet of the annulus that restricts the flow. It sets the pressure in the annulus, and through it the bottomhole pressure.
Driller's method: Two circulations: circulating out the influx with the current mud, and then replacing the mud with kill mud.
Wait and weight method: One circulation with kill mud, with a schedule of the fall of the pipe pressure.
Volumetric method: Managing rising gas without circulation: we let the gas expand and bleed off mud in portions.
Bullheading: Pumping in which the fluid of the influx is pushed back into the formation.

Common mistakes and misconceptions

Wrong

“The kill mud density must be calculated from the annulus pressure: it is higher, so it is safer.”

In fact

The annulus pressure includes the effect of the light fluid of the influx, and it tells us about the influx, not about the formation. We calculate the formation pressure and the kill mud density from the pipe pressure.

Wrong

“The annulus pressure is rising: we must open the choke a little.”

In fact

While gas is circulated out, a rise of the annulus pressure at the choke is expected: the gas expands. We adjust the choke by the standpipe pressure. Lowering the annulus pressure “by hand” lowers the bottomhole pressure and causes a new influx.

Wrong

“We may change the pump rate during killing if we keep the standpipe pressure the same.”

In fact

The friction losses depend on the rate, and at another rate the same standpipe pressure corresponds to another bottomhole pressure. We keep the rate constant. If we do have to change it, we do it by the procedure, usually at a constant annulus pressure, and we set a new planned standpipe pressure.

Wrong

“The wait and weight method always lowers the pressure under the shoe.”

In fact

Only if the kill mud leaves the bit before the top of the gas passes the shoe. For that, the inner volume of the string must be smaller than the volume of the annulus in the open hole (more exactly, that volume less the volume of the gas pocket). The method usually lowers the annulus pressure at the wellhead.

Wrong

“The pipe pressure after shutting in is zero, so there was no influx.”

In fact

If the annulus pressure is above zero, there is a light fluid in the annulus, and the mud density is high enough: the influx may have come in during swabbing. We do not need to make the mud heavier: we circulate the influx out with the current mud. But first we make sure that the zero pressure is not caused by a closed float valve in the string.

In depth: advanced detail

Where the formulas for the initial and final pressure come from

We divide the circulating pressure at the reduced rate into two parts: the losses in the surface lines, the string and the bit nozzles, $\Delta p_{\text{str}}$ , and the losses in the annulus, $\Delta p_{\text{ann}}$ , so that $p_{\text{SCR}} = \Delta p_{\text{str}} + \Delta p_{\text{ann}}$ . When we circulate through the choke, the bottomhole pressure from the pipe side equals $p_{\text{SPP}} + \rho_m g h - \Delta p_{\text{str}}$ , where $p_{\text{SPP}}$ is the standpipe pressure. If we hold $p_{\text{SPP}} = p_{\text{SIDPP}} + p_{\text{SCR}}$ , the bottomhole pressure equals $p_{\text{SIDPP}} + \rho_m g h + \Delta p_{\text{ann}} = p_p + \Delta p_{\text{ann}}$ : the formation pressure plus the losses in the annulus at a small rate, which is a small margin.

When the string is full of kill mud, the losses in it at the same rate are about $\rho_{\text{kill}}/\rho_m$ times greater, and the column in the pipe equals $\rho_{\text{kill}} g h = p_p$ . The standpipe pressure $p_{\text{SPP}} = p_{\text{SCR}}\,\rho_{\text{kill}}/\rho_m$ gives at the bottom $p_p$ plus about the same losses in the annulus. The proportionality of the losses to the density is an approximation: in turbulent flow they grow a little more slowly than the density, and the viscosity of the mud may change after it is made heavier. So we compare the actual standpipe pressure, when the kill mud has reached the bit, with the calculated one, and when the difference is noticeable, we act by the procedure.

The pressure schedule in an inclined well and in a string of several sections

The straight line of the schedule rests on two assumptions: the hydrostatic pressure in the pipe grows in proportion to the pumped volume, and the friction losses do too. In an inclined well the first is untrue: the volume is counted along the hole, and the hydrostatic pressure by the true vertical depth. In the vertical section every metre of kill mud adds a full metre of vertical height, in the build section (where the hole curves away from the vertical) less, and in the horizontal section nothing. So the standpipe pressure that is really needed falls faster than the straight line at the start of pumping, and more slowly at the end.

If we keep to the straight line, the standpipe pressure in the middle of pumping will be higher than needed, and the bottomhole pressure will exceed the formation pressure, which is an extra load on the shoe. So for inclined and horizontal wells we calculate the pressure at characteristic points (at the kick-off point, where the hole starts to leave the vertical, at the end of the build section, at the bit) and join them with straight segments. We do the same if the string consists of sections with different inner diameters: we count the strokes to the end of each section separately.

How the curve of the annulus pressure was calculated

The single-pocket model treats the gas as one volume that moves up with the mud. After a volume $V$ has been pumped, the bottom of the pocket is where the volume of the annulus, counted from the bottom, equals $V$ (everything pumped has passed through the bit and lies in the annulus under the gas). The pressure in the pocket equals the bottomhole pressure less the weight of the columns under it: the original mud, and, in the wait and weight method, after the first $V_{\text{string}}$ cubic metres, the kill mud as well.

Single gas pocket model at constant bottomhole pressure

V_g = V_k\,\frac{p_p + p_a}{p_g + p_a}, \qquad p_{\text{ann}} = p_p - g\sum_j \rho_j\,h_j

where:

$V_g$ volume of the gas pocket at the current depth, m³
$V_k$ initial volume of the influx at the bottom, m³
$p_g$ gauge pressure in the pocket: the bottomhole pressure minus the weight of the columns under it, Pa
$p_a$ atmospheric pressure, about 0.101 MPa (Boyle's law needs absolute pressures), Pa
$p_{\text{ann}}$ pressure in the annulus at the wellhead, at the choke, while we circulate, Pa
$\rho_j,\ h_j$ density and true vertical height of each column in the annulus: kill mud, original mud, gas, mud above the gas, kg/m³, m
$p_p$ formation pressure, equal to the bottomhole pressure that is held, Pa

Units: SI; the pressures are gauge pressures, except for the sum $p + p_a$ in Boyle's law

Holds when

the gas is ideal, and the temperature and the gas deviation factor are constant (Ideal and real gas: the gas deviation factor (Z));
the gas moves with the mud, does not rise relative to it, does not dissolve and is not stretched along the hole;
the mass of the gas is constant, so its density is inversely proportional to its volume;
friction losses in the annulus and in the choke line are not counted. The bottomhole pressure is held exactly equal to the formation pressure.

We find the height of the pocket from its volume and from the capacity of the annulus in the sections where it is. We find the pressure at the shoe in the same way as at the wellhead, subtracting from the bottomhole pressure the weight of the columns between the shoe and the bottom. Real gas is stretched into a long zone of gas-cut mud, and this lowers the pressure peaks. Here the model gives an estimate from above. But gas also rises faster than the mud and arrives at the wellhead earlier. In the wait and weight method the heavy mud has risen less by that moment than in the model, and the gain in wellhead pressure is smaller.

Connections to other topics

Well control: primary barrier and kick indicators — causes and signs of kicks, the behaviour of gas in the hole and the U-tube principle.
Fracture gradient and leak-off testing — the test under the shoe, the MAASP and the kick tolerance.
Pore pressure and overburden pressure — hydrostatics, equivalent mud weight and the choice of the mud density.
Drilling fluids: functions and properties — weighting up the mud with barite and control of the density.
Blowout prevention equipment — blowout preventers, the choke and kill manifolds, the mud-gas separator.
Casing: purpose, types, properties and standards — the strength of casing against internal pressure.
Circulating pressure losses — where friction losses come from and why they depend on the rate.
Ideal and real gas: the gas deviation factor (Z) — expansion of a real gas, with a correction for the gas deviation factor.

Check yourself

1
The well has been shut in after a kick: the pressure in the pipe is 2.0 MPa and in the annulus 3.2 MPa. From which pressure do we calculate the kill mud density?
1. A.From the pipe pressure
2. B.From the annulus pressure: it is higher
3. C.From their sum
4. D.From the mean of the two
Show the answer
Correct answer: A. From the pipe pressure
In the pipe there is only mud of known density, so the pressure in the pipe plus the column in it equals the formation pressure. The annulus pressure includes the effect of the light fluid of the influx, and it depends on its volume, not on the formation.
2
The true vertical depth is 2800 m, the mud is 1.18 g/cm³, the pipe pressure after shutting in is 2.3 MPa, and the slow circulating rate pressure is 2.0 MPa. Find the kill mud density and the initial and final circulating pressures.
Show the answer
$\rho_{\text{kill}} = 1.18 + 2.3/(0.00981\cdot 2800) = 1.18 + 0.0837 = 1.2637$ g/cm³, which we round up to 1.27 g/cm³. $p_{\text{ICP}} = 2.3 + 2.0 = 4.3$ MPa; $p_{\text{FCP}} = 2.0\cdot 1.27/1.18 \approx 2.15$ MPa.
3
In the first circulation of the driller's method the standpipe pressure is held at the planned value, and the annulus pressure at the choke rises. What does this mean?
1. A.A new influx has started: we must raise the pump rate
2. B.The choke is faulty
3. C.We must open the choke and return the annulus pressure to the SICP
4. D.The gas is rising and expanding: this is as it should be while the standpipe pressure equals the plan
Show the answer
Correct answer: D. The gas is rising and expanding: this is as it should be while the standpipe pressure equals the plan
The gas pushes mud out of the annulus, the column gets lighter, and to keep the bottomhole pressure the same, the pressure at the choke rises. While the standpipe pressure is on the plan, the bottomhole pressure is constant. If we opened the choke to lower the annulus pressure, we would lower the bottomhole pressure too.
4
After the well is shut in, the pressure in the pipe is zero, and in the annulus 0.8 MPa. What does this say, and do we need to make the mud heavier?
Show the answer
The column of mud in the pipe balances the formation, so the mud density is high enough. The annulus pressure says that there is a light fluid in it, for example an influx “sucked in” while the tools were pulled. We do not need to make the mud heavier: we circulate the influx out with the current mud at a constant bottomhole pressure, and we find the cause. First we check whether a closed float valve is holding the pressure in the pipe.
5
When does the wait and weight method lower the pressure at the shoe compared with the driller's method?
1. A.Only with an oil influx
2. B.Never
3. C.Always
4. D.If the kill mud leaves the bit before the top of the gas passes the shoe
Show the answer
Correct answer: D. If the kill mud leaves the bit before the top of the gas passes the shoe
The pressure at the shoe depends on what lies between it and the bottom. Until the kill mud has left the bit, the annulus holds the same columns as in the driller's method. If the inner volume of the string is larger than the volume of the annulus in the open hole, the gas passes the shoe earlier, and there is no gain at the shoe. Only the lower pressure at the wellhead remains.
6
Why do we let the annulus pressure rise in the volumetric method, but bleed off mud in strictly measured portions?
Show the answer
Every volume $\Delta V$ that we bleed off lowers the hydrostatic pressure in the annulus by $\rho_m g\,\Delta V/C_a$ . For the bottomhole pressure not to fall below the formation pressure, the wellhead pressure must rise by the same amount. The rising, expanding gas creates it. If we bleed off more, a new influx will start. If we do not bleed off at all, the gas will raise the pressure until the rock under the shoe ruptures.

Updated: 19 October 2026