Perforating operations: gun conveyance and procedures

Quick refresher

A gun is delivered on cable (a small gun through the tubing into a finished well, or a large gun into the casing before the tubing is run), on tubing, on coiled tubing, or on slickline with a stand-alone unit. A large gun gives better tunnels. A gun on tubing gives a long interval per run and a large underbalance, but work on tubing is longer and more expensive.
The underbalance is created before the shot. The pressure opposite the reservoir is the wellhead pressure plus the column of liquid above the reservoir. It is lowered with a lighter liquid, by lowering the level in the tubing, or with nitrogen.
The lower limit of the underbalance for oil-bearing sandstones is given by the field criterion (a rule from field experience) $\Delta p_{\min} \approx 3100/k^{0.37}$ psi. It is about 6 MPa at a permeability of 30 mD. Permeability shows how easily fluid flows through the rock, and mD (millidarcies) is its unit. Laboratory criteria call for 2–4 times more. The upper limit comes from the strength of the rock, the casing and the packer, and from the risk of throwing a gun up on a cable.
The depth of the gun is tied to the reference gamma ray log by which the interval was chosen. The casing collars, a short marker joint (a short piece of pipe in the string) and radioactive markers give reference points. The accuracy that can be reached is about 0.3 m.
For hydraulic fracturing, we perforate in short clusters. When the pumping is shared between clusters, few holes are made, and the pressure losses in them even out the rate. This is limited entry. Proppant (the grains that keep a fracture open) erodes the holes, and the effect weakens.
Perforating is blasting work on a well under pressure. It is done by specialised teams under an approved plan, and a gun that has not fired is treated as armed.

Key relationships

\Delta p_{\text{ub}} = \bar p_R - p_{\text{well}},\quad p_{\text{well}} = p_{wh} + 0.00981\,\rho h

underbalance in perforating (MPa, g/cm³, m)

\Delta p_{\min} \approx 3100/k^{0.37}

approximate field criterion for oil-bearing sandstones: psi, $k$ in mD (the data run from a few mD to hundreds of mD)

\Delta p_{\text{perf}} = \dfrac{\rho\,q^2}{2\,C_d^2\,n^2 A^2}

pressure loss in $n$ holes of area $A$ each (SI)

Common pitfalls

Treating an underbalance chosen by the criterion as a guarantee of clean tunnels. The criterion gives only a lower limit, and only for sandstones.
Perforating on cable with a large underbalance and no anchor. The pulse of inflow can throw the gun up and tangle the cable.
Placing the gun by the length of the cable, with no correlation to the gamma ray log and the collars.
Making tens of holes per cluster for hydraulic fracturing. The rate will not be evened out.
Mixing up perforating on tubing (the gun is run on the tubing) with perforating the tubing itself (a hole in the tubing for circulation).

After this lesson you can

compare delivery of perforating guns on cable through the tubing and into the casing, on tubing, on coiled tubing and on slickline, and choose a method for a given well
explain why we perforate underbalanced, estimate the lower limit of the underbalance with a field criterion, and check the upper limits set by the rock strength and the equipment
calculate the liquid level in the tubing and the volume of fluid to add to create a given underbalance, and the pressure difference across the packer (the seal) before the shot
correlate the depth of the gun with the depth of the well logs, using the gamma ray log (a record of the natural radioactivity of the rock), the casing collar locator (a tool that detects the joints of the casing) and markers
explain when oriented perforating, extreme-overbalance perforating and propellant gas generators are used
calculate the pressure loss in perforation holes, and explain how limited entry shares the pumping between clusters (groups of perforations) in hydraulic fracturing (opening cracks in the rock by pumping fluid at high pressure)

How the gun is delivered to the reservoir

A perforating plan is several linked decisions. Do we open the reservoir before the tubing string is run, or in a well that is already equipped? What do we run the gun on? Do we fire with the well pressure below the reservoir pressure (underbalanced) or above it (overbalanced, see overbalance)? What do we do with the gun after the shot? The answer to the first question largely decides the others. In an equipped well we can run only what will pass through the tubing or is run together with it. And an underbalance is easiest to create when the tubing string with its packer is already in place.

On cable through the tubing (through-tubing): A small gun is run on a logging cable (an electric cable) through a tubing string that has already been run and pressure tested, and it shoots into the casing below the end of the tubing. The well is closed by a lubricator (a pressure lock above the wellhead) and a blowout preventer (a set of valves that can close the well), and it can be under pressure. So we can perforate underbalanced and start the well at once. The price is small charges, short tunnels and a large clearance to the far wall (through-tubing guns).
On cable into the casing (casing gun): A large carrier gun is run into the casing before the tubing string: the largest charges, a high shot density, any phasing. But after perforating, the tubing still has to be run, so we usually shoot overbalanced, or kill the well afterwards (fill it with heavy fluid), and the tunnels end up under well fluid (why this is bad).
On tubing (tubing-conveyed perforating, TCP): The gun is screwed onto the lower end of the tubing, the drill pipe or a drill stem test string (a string for testing a reservoir) and run together with it. Often it is made part of the tubing string itself: the gun hangs below the packer, the string is hung at the wellhead, the packer is set, and the gun is fired underbalanced. Hundreds of metres of interval per run, large charges, and all the tunnels are opened at once. In Russian-language practice this is called “perforating on tubing”.
On coiled tubing: A continuous pipe from a reel goes into deviated and horizontal wells where a cable will not go by itself. It lets us work in a well under pressure, pump fluid, and assemble the gun from several sections.
On slickline: A gun with a stand-alone unit (a battery, a memory and an electronic firing circuit) is run on a thin wire with no conductor. The equipment is cheaper and simpler than a cable unit, but there is no link with the tool. The depth is found from the recorded casing collar locator and the pipe tally (the list of the measured lengths of the pipes), and the command to fire is given, for example, by a series of pressure pulses from the wellhead (Wireline operations).

Methods of delivering the gun

Method: Cable through the tubing
When: after the tubing is run
Gun: 35–54 mm
Underbalance: yes
Main limitation: small charges

Method: Cable into the casing
When: before the tubing is run
Gun: 86–127 mm
Underbalance: usually no
Main limitation: tunnels under the kill fluid

Method: Tubing or drill pipe
When: with the tubing or during a test
Gun: any
Underbalance: large
Main limitation: a misfire means pulling the pipe

Method: Coiled tubing
When: deviated wells, under pressure
Gun: in sections
Underbalance: yes
Main limitation: length of the sections, cost

Method: Slickline
When: simple jobs
Gun: small
Underbalance: yes
Main limitation: no link with the tool

Method	When	Gun	Underbalance	Main limitation
Cable through the tubing	after the tubing is run	35–54 mm	yes	small charges
Cable into the casing	before the tubing is run	86–127 mm	usually no	tunnels under the kill fluid
Tubing or drill pipe	with the tubing or during a test	any	large	a misfire means pulling the pipe
Coiled tubing	deviated wells, under pressure	in sections	yes	length of the sections, cost
Slickline	simple jobs	small	yes	no link with the tool

The sizes are approximate for a 177.8 mm casing and 73 mm tubing. The actual ones are set by the bore of the tubing string and the diameter of the casing.

Length per run. After the shot, a gun on cable is pulled up into the lubricator, the pipe above the wellhead that holds the well pressure while the gun is taken out (lubricator and blowout preventer). So the length of the gun is limited by the length of the lubricator and the strength of the cable: usually a few metres, rarely more than ten. A long interval is perforated in several runs from the bottom up, so that the next gun does not pass through debris and fresh tunnels and does not get stuck in them. If the interval is long and the lubricator is short, the gun is assembled in the well. First an anchor (a device that locks itself in the casing) is set, then the sections are placed on it one by one, with a firing head (the device that sets off the charges) on top. All of them are fired together, and then the sections are pulled one at a time or dropped down.

Several short intervals in one run are shot with a gun that has addressable switches (selective firing): the sections are fired one at a time, each by its own command, with the gun moved between the shots. Perforating in horizontal wells for multistage fracturing is done in the same way (see the section on fracturing).

On tubing, the gun fires on a signal from the firing head. The signal is given by a bar dropped into the tubing (mechanically), by the pressure in the tubing or in the annulus (hydraulically), or through a cable that is lowered into the tubing and connected to the head in the well. Hydraulic and mechanical heads do not need the restrictions on radio transmissions that apply to electrical firing (see the section on safety). What to choose, cable or tubing, is decided by the interval, the underbalance needed and the cost of a mistake:

On cable or on tubing: how they compare

Criterion: Interval per run
On cable: metres; a long one takes several runs
On tubing: hundreds of metres at once

Criterion: Underbalance
On cable: moderate; full only in the first run
On tubing: large, over the whole interval

Criterion: Charges in a hot well
On cable: hours
On tubing: a day or more

Criterion: If the gun did not fire
On cable: pulled out on the cable
On tubing: the tubing is pulled

Criterion: After the work
On cable: the hole below the tubing is free
On tubing: the gun is dropped into the sump or pulled out

Criterion: Cost
On cable: better for short intervals
On tubing: better for long ones

Criterion	On cable	On tubing
Interval per run	metres; a long one takes several runs	hundreds of metres at once
Underbalance	moderate; full only in the first run	large, over the whole interval
Charges in a hot well	hours	a day or more
If the gun did not fire	pulled out on the cable	the tubing is pulled
After the work	the hole below the tubing is free	the gun is dropped into the sump or pulled out
Cost	better for short intervals	better for long ones

A sump is a part of the hole drilled in advance below the interval. A gun left opposite the reservoir gets in the way of running survey tools below the end of the tubing.

Underbalance in perforating: how much, and how to create it

Why an underbalance cleans the tunnels is explained in the lesson the crushed zone and cleaning the tunnels: in the first fractions of a second after the shot, the reservoir gives the fresh tunnel a pulse of inflow, which carries out the debris and breaks up part of the crushed zone. What an uncleaned tunnel costs in flow rate is calculated in the lesson skin of the crushed zone. Two conclusions follow for the technology. The underbalance must exist at the moment of the shot, not appear later during production. And it is the same for the whole interval: if the reservoir is not uniform, weak and tight layers get the same underbalance.

Perforating on cable through the tubing gives the full underbalance only in the first run. After it, reservoir fluid comes into the well, and the pressure opposite the interval that is already open becomes equal to the reservoir pressure. The next intervals are perforated almost with no underbalance, unless the well is put on production between the runs, and this needs care, because the flow can catch the gun. A gun on tubing opens the whole interval at once, and the full underbalance goes to every tunnel.

Pressure opposite the reservoir before the shot, and the underbalance

p_{\text{well}} = p_{wh} + \rho\,g\,h, \qquad \Delta p_{\text{ub}} = \bar p_R - p_{\text{well}}

where:

$p_{\text{well}}$ well pressure opposite the perforated interval at the moment of the shot (gauge), Pa
$p_{wh}$ pressure at the wellhead in the pipes through which the pressure is passed to the interval (above the liquid), Pa
$\rho,\ h$ density of the liquid and the true vertical height of its column above the middle of the interval, kg/m³, m
$\bar p_R$ reservoir pressure at the depth of the interval (gauge), Pa
$\Delta p_{\text{ub}}$ underbalance; a negative value is an overbalance, Pa

Units: SI

Holds when

The liquid is at rest, and its density is constant over the height. If there are several liquids in the well, their columns are added.
Gas above the liquid level is hundreds of times lighter than the liquid, and its weight is ignored (at a high gas pressure it is included).
The reservoir pressure is the current one. In a depleted reservoir it is lower than the initial one, and the same column of liquid that earlier gave an underbalance may now give an overbalance.

The underbalance is controlled by three “knobs”: the wellhead pressure, the density of the liquid and the height of its column. We can increase it with a lighter liquid, by lowering the level in the tubing, or by pushing the liquid out with nitrogen.

In other unit systems (2)

Metric units

p_{\text{well}}\,[\text{MPa}] = p_{wh} + 0.00981\,\rho\,[\text{g/cm}^3]\;h\,[\text{m}]

pressures in MPa, density in g/cm³, height 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_{\text{well}}\,[\text{psi}] = p_{wh} + 0.052\,\rho\,[\text{ppg}]\;h\,[\text{ft}]

pressures in psi, density in ppg (pounds per gallon), height in feet.

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

How much is needed. Quantitative criteria appeared when people began to perforate on tubing with different underbalances and to compare the results. In a field study of the mid-1980s, wells perforated underbalanced were treated with acid. If the treatment did not increase the productivity, the tunnels were considered already clean. Later these data were summarised with a power-law relation, which for oil-bearing sandstones gives the lower limit of the underbalance:

Minimum underbalance for an oil-bearing sandstone (field criterion)

\Delta p_{\min} \approx \frac{3100}{k^{0.37}}

where:

$\Delta p_{\min}$ smallest static underbalance at which the tunnels were cleaned, psi
$k$ reservoir permeability, mD

Units: empirical: $\Delta p_{\min}$ in psi, $k$ in mD

Holds when

Oil-bearing sandstones, perforating on tubing with a static underbalance. For gas a different relation was found, and for carbonates the link with permeability does not work.
It is an approximate fit to scattered well data, with permeability mostly from a few to several hundred millidarcies. Different treatments of the same data give a coefficient of about 2900 to 3500 psi with an exponent of 0.36–0.37, and outside this range the formula is an extrapolation.
It is a lower limit based on an indirect sign (the response to acid), not a guarantee of clean tunnels.
Later laboratory criteria call for an underbalance 2–4 times larger.

The tighter the reservoir, the larger the underbalance needed: at 10 mD about 1300 psi (9 MPa), and at 100 mD about 560 psi (3.9 MPa). A tight reservoir gives the tunnel too weak a flow to break the crushed zone at a small underbalance.

In other unit systems (1)

Metric units

\Delta p_{\min}\,[\text{MPa}] \approx \frac{21.4}{k^{0.37}}

$\Delta p_{\min}$ in MPa, $k$ in mD.

$21.4 \approx 3100/145.04$ (there are 145.04 psi in 1 MPa).

Laboratory experiments of the 1990s (a shot into a rock sample squeezed by pressure, followed by pumping fluid through the tunnel) showed that clean tunnels need more, and later it became clear why. The crushed zone breaks when the stresses from the pressure difference exceed its strength. So the underbalance needed is set by the strength of the rock, and permeability is only an indirect sign of it. In sandstones, strength and permeability are linked, but in carbonates they are not. Besides, in the first milliseconds the pressure in the well swings, and a static underbalance created before the shot may for a short time turn into an overbalance. From this comes the idea of controlling the pulse itself: dynamic underbalance (advanced section).

Why more is not always better. The upper limit of the underbalance is set by:

the strength of the rock. In weak sandstones an excessive underbalance destroys the walls of the tunnels, sand comes into the well, and fine particles migrate in the pores and reduce the permeability (Sand production: types, prediction and cost of the problem);
the casing and the equipment. The pressure difference acts on the production casing below the packer, on the packer itself and on the tubing. If it is larger than the design value, the casing can be collapsed and the packer moved or damaged (Casing design, packers);
a gun on cable. The pulse of inflow can throw a light gun up and tangle and break the cable. On cable a smaller underbalance is used, or an anchor is set;
the reservoir itself. The underbalance cannot be larger than the reservoir pressure. In depleted reservoirs there is simply nothing to create it from.

How the underbalance is created. The well is filled with a liquid lighter than the one that balances the reservoir: oil, diesel fuel, or a fluid of lower density. The level in the tubing is lowered by taking liquid out with a swab (a tool that lifts liquid out of the tubing) or by pushing it out with nitrogen. In a gas well the wellhead pressure is released. Or the tubing is run empty and, after the packer is set, the calculated volume of liquid is added to it. Adding liquid is especially convenient in perforating on tubing: the volume of liquid sets the level, and the level sets the pressure opposite the reservoir.

Worked examplePerforating on tubing below a packer: how much to add to the tubing

Given (assumed data)

Well: reservoir at 2000 m true vertical depth, reservoir pressure 21.6 MPa, permeability 30 mD, oil-bearing sandstone
Assembly: a gun on 73 mm tubing (62 mm inside) below a packer at 1950 m in a 177.8 mm casing; the tubing is connected with the space below the packer through a perforated sub (a short pipe with holes) above the gun; below the packer and in the annulus there is brine (salt water) of 1.05 g/cm³
Decision: the tubing is run empty (the holes of the sub are closed during the run), and after the packer is set it is opened to the space below the packer and filled with brine; the tubing pressure at the wellhead is atmospheric
Limits: by the stability of the rock the underbalance is not more than 12 MPa; an underbalance of 8.0 MPa is chosen

Solution

Lower limit by the field criterion: $30^{0.37} = 3.52$ , $\Delta p_{\min} = 3100/3.52 = 881$ psi, or $881/145.04 = 6.07$ MPa. The chosen 8.0 MPa is above this limit and below the limit set by the rock, 12 MPa.
The pressure opposite the reservoir before the shot is $21.6 - 8.0 = 13.6$ MPa. It must be created by a column of brine of height $h = 13.6/(0.00981\cdot1.05) = 1320$ m. So the level in the tubing is at a depth of $2000 - 1320 = 680$ m.
The capacity of the tubing is 3.02 L/m. Below the packer the casing is already full, so only the tubing from the packer up to the level is filled: $(1950 - 680)\cdot 3.02 = 3835$ L, about 3.84 m³.
For comparison, with the tubing full of brine the underbalance would be only $21.6 - 0.00981\cdot1.05\cdot2000 = 1.00$ MPa, and with the tubing empty down to the packer it would be 21.1 MPa, which is more than the limit set by the rock.
Pressure difference across the packer before the shot: in the annulus at 1950 m, $0.00981\cdot1.05\cdot1950 = 20.09$ MPa, and below the packer, $0.00981\cdot1.05\cdot(1950 - 680) = 13.08$ MPa. The packer holds about 7.0 MPa from above.

Answer: About 3.84 m³ of brine is added to the empty tubing, up to a level of 680 m. The underbalance at the moment of the shot is 8.0 MPa, against a lower limit by the criterion of 6.07 MPa.

What it means. The margin above the criterion is small, and that is normal. The criterion gives a lower limit from old field data, and the later laboratory criteria would need 12–24 MPa, which is at the limit of the stability of the rock and above the reservoir pressure. So the underbalance is chosen as a compromise between cleaning the tunnels and the stability of the rock, and the result is checked by a well test after start-up. The calculation is static: the pressure swings of the first milliseconds, and the dynamic underbalance from the filling of the gun carrier, are not included. After the shot, the inflow raises the level in the tubing, and the well is brought to steady production through a choke. The pressure difference across the packer (7.0 MPa from above) and across the casing below the packer is checked against their data sheets. The data in this example are assumed for illustration.

CalculatedPressure against depth before the shot in the example. In the tubing above the level at 680 m the pressure is atmospheric, and below it there is a column of brine of 1.05 g/cm³. In the annulus above the packer there is brine up to the wellhead. Opposite the reservoir at 2000 m, the well pressure is 8 MPa below the reservoir pressure. At the packer, the annulus above it presses on it 7 MPa harder than the space below.

Overbalanced perforating remains usual for large guns on cable run into the casing before the tubing, and also before hydraulic fracturing and acid treatment, which will pass through the tunnels under pressure anyway. Its harm is reduced. We perforate in a clean filtered liquid with no solids. We limit the loss of liquid into the reservoir with thickened or bridging pills (small batches of fluid) that are removed afterwards. And we put the well on production as early as possible (Formation damage and damage skin).

Correlating the gun depth

The perforating interval is chosen from the open-hole logs, which show the oil-bearing part of the reservoir, the shale barriers and the contacts (the boundaries between oil, water and gas). So the gun must be placed at the depth of these logs, not by the length of the cable or the pipe. A difference of one metre in a reservoir a few metres thick can open water under the oil or gas above it.

The length of the cable run in gives the depth only roughly. In the well the cable heats up and lengthens, friction in a deviated hole and tight spots change its stretch, and the measuring wheel slips (why the depth counter is wrong). The length of a string of pipes also changes with weight and temperature. So the depth is checked on the spot by features that can be seen even through the casing.

Gamma ray log (GR): The natural radioactivity of rocks can be seen through the casing too, although weakened (Gamma ray log and natural gamma ray spectrometry). A GR sensor is placed above the gun, and a short section is recorded. Its peaks are compared with the reference GR log of the open hole, and a correction to the depth on the cable is found.
Casing collar locator (CCL): A magnet and a coil. Opposite a collar of the casing (the coupling that joins two pipes) there is more metal, the magnetic flux changes, and when the tool moves a pulse appears in the coil. Collars repeat at the length of a pipe, about 10–13 m. From their pattern and the pipe tally recorded when the casing was run, the position of the tool is found.
Marker joint (a short pipe): A shortened pipe placed in the casing in advance above the productive reservoir. Two close collars on the CCL record cannot be mixed up with any others.
Radioactive marker: A small source in a casing collar or in the pipes above a gun on tubing. Its depth is found with a GR tool, and the gun on tubing is positioned from the known distance from the marker to the top charge.

How a gun on cable is positioned

1
Calculation
From the reference log and the interval, find the depths of the top and bottom charges, and from the assembly, the distances from the GR and CCL sensors to the top charge.
2
Check record
Lower the assembly below the interval and, pulling it up, record GR and CCL through the interval and above it.
3
Correction
Compare the GR peaks and the collars with the reference ones, and calculate how much the depth on the cable differs from the depth of the reference log.
4
Positioning
Pull the gun to the calculated depth, allowing for the correction, and, if there is time, repeat a short record to check the collar opposite the sensor.
5
Shot and check
After the shot, record the real depth and the signs that the gun fired, and enter the real interval in the well file.

A gun on tubing is also correlated by GR. A tool on cable is lowered inside the tubing, the radioactive marker above the gun is found, and the string is adjusted, by adding or removing short pup joints (short pieces of pipe), before the packer is set. On slickline, where there is no link with the tool, the CCL records into memory, and a pressing device at each collar briefly increases the tension of the wire, which can be seen at the surface. The depth is counted from the pipe tally. With all the methods, the accuracy that can be reached is about 0.3 m.

Oriented perforating, extreme overbalance and propellant gas generators

Oriented perforating. Usually the direction of the shots is set by the phasing, and the gun itself can turn any way. Sometimes the direction matters, and the gun is turned in the well by an off-centre weight that hangs to the low side, by a magnetic device, or by a gyroscope:

a small gun in a wide casing is pressed against the wall and shoots into the near wall (0° phasing);
for hydraulic fracturing the tunnels are directed along the future fracture, along the largest horizontal stress, so that the fracture does not have to bend near the wellbore (orientation of the fracture);
in a well with two tubing strings, the upper reservoir is perforated with the charges turned away from the neighbouring string, which is found by its magnetic field;
in horizontal wells in weak sandstones the tunnels are directed up and down, along the largest stress, which is usually vertical. Around such a tunnel the two smaller stresses act, and its walls are more stable (Sand production: types, prediction and cost of the problem).

Extreme-overbalance perforating solves the same problem from the other side: the debris is not pulled out of the tunnels by inflow but pushed deep into the reservoir. For this, the pressure in the tubing above the interval is raised above the fracture pressure of the reservoir, with compressed nitrogen above a small column of liquid. After the shot, the expanding gas drives the liquid into the tunnels, the rock at their ends splits, and the debris goes into short fractures. When the pressure falls below the closure pressure (the pressure at which a fracture closes), the fractures close, the debris stays far from the wellbore, and the tunnels are connected to the reservoir. The method is used when an underbalance cannot be created or does not help, and as a preparation before hydraulic fracturing. The price is a high wellhead pressure and a large volume of compressed gas at the surface.

Propellant gas generators give a similar effect with no compressed gas at the surface: the source of pressure is run into the well. This is a solid fuel that does not detonate in microseconds like an explosive but burns in milliseconds. Instead of a shock wave we get a pulse of high-pressure gas, and it opens short fractures in the near-wellbore zone. In Russian-language practice this is called gas-dynamic fracturing of the formation. The propellant is placed on the gun, so that the fractures start right from the fresh tunnels, or is run as a separate device.

Perforating for fracturing: clusters and limited entry

Perforating for hydraulic fracturing has different tasks from perforating for natural inflow. The tunnel can be short, because the fracture will go beyond the damaged zone anyway. But the hole must pass proppant (big-hole charges), the tunnels must point along the future fracture, and the interval must be short, so that the fracture starts at the chosen place and not in several places at once. The pressure losses in the holes are part of the pumping pressure (pumping pressure).

In horizontal wells, fracturing is done in stages. On each stage, several short clusters are perforated (sections a fraction of a metre long with a few holes), and liquid is pumped into all of them at once. In a cased hole, a plug-and-gun assembly (a plug with a gun made of addressable sections) is run on cable for this. In the horizontal section it is carried by the flow of the pumped liquid. The plug shuts off the stage that is already treated, the sections are fired one at a time at the places of the clusters, the assembly is pulled out, and the fracturing is done. Another way is sleeves in the liner (a pipe string hung at the bottom of the casing), opened by dropped balls, with no perforating (Horizontal wells). The distance between clusters is chosen so that the fractures do not hinder each other by their stresses (each opened fracture squeezes the rock around it, the “stress shadow”), but also do not leave untreated rock between them.

The clusters of one stage work in parallel, and their closure pressures are different. If there are many holes, the liquid goes mainly where the rock opens more easily, and the clusters with a larger closure pressure get little or nothing. Limited entry evens out the rate: few holes are made, so that the pressure loss in them at the design rate becomes larger than the difference between the closure pressures. Then the rate of a cluster depends mainly on the number of its holes, not on the rock behind them.

Pressure loss in the perforation holes

\Delta p_{\text{perf}} = \frac{\rho\,q^2}{2\,C_d^2\,n^2 A^2}, \qquad A = \frac{\pi d^2}{4}

where:

$\Delta p_{\text{perf}}$ pressure loss as the liquid passes from the casing into the reservoir through the holes, Pa
$q$ flow rate of liquid through these holes, m³/s
$\rho$ density of the liquid (of the mixture, if it carries proppant), kg/m³
$n,\ d$ number of open holes and their diameter, —, m
$C_d$ discharge coefficient: about 0.6 for new holes with sharp edges, and it grows to about 0.9 when proppant rounds the edges, —

Units: SI

Holds when

The flow is like flow through a short nozzle: pressure turns into jet speed, and friction along the length of the tunnel is ignored.
The rate is divided equally between the holes.
Erosion of the holes by proppant increases both $C_d$ and $d$ , and the losses fall several times.

The loss grows as the square of the rate, and is inversely proportional to the square of the number of holes and to the fourth power of their diameter: half as many holes means four times the loss. The same formula describes the pressure drop across the nozzles of a drill bit (Circulating pressure losses).

In other unit systems (2)

Metric units

\Delta p_{\text{perf}}\,[\text{MPa}] = 2.25\cdot10^{5}\,\frac{\rho\,[\text{g/cm}^3]\;q^2\,[\text{m}^3/\text{min}]}{C_d^2\,n^2\,d^4\,[\text{mm}]}

density in g/cm³, flow rate in m³/min, diameter in mm.

$2.25\cdot10^{5} \approx 8\cdot10^{9}/(3600\,\pi^2)$ : the SI formula $8\rho q^2/(\pi^2 C_d^2 n^2 d^4)$ with the conversions g/cm³ → kg/m³, m³/min → m³/s, mm → m and Pa → MPa.

Oilfield units

\Delta p_{\text{perf}}\,[\text{psi}] = 0.2376\,\frac{\rho\,[\text{ppg}]\;q^2\,[\text{bbl/min}]}{C_d^2\,n^2\,d^4\,[\text{in}]}

density in ppg, flow rate in barrels per minute, diameter in inches.

0.2376 comes from the same unit conversion (ppg → kg/m³, bbl/min → m³/s, inches → m, Pa → psi). Handbooks give values that differ in the third digit because of rounding.

Worked exampleLimited entry: 20 holes per cluster or 5

Given (assumed data)

Stage: four clusters, closure pressures 40.0, 40.5, 41.0 and 42.0 MPa
Pumping: 9 m³/min of liquid of 1050 kg/m³
Holes: diameter 10 mm, $C_d$ = 0.6; after erosion, 11 mm and 0.85
Simplifications: friction in the casing between the clusters, the net pressure (the pressure that holds a fracture open above the closure pressure) and the bending of the fracture path near the wellbore (tortuosity) are ignored

Solution

20 holes per cluster (80 per stage). With equal division, $9/60/80 = 0.001875$ m³/s goes through each hole, the speed is $0.001875/(7.854\cdot10^{-5}) = 23.87$ m/s, and the loss is $1050\cdot23.87^2/(2\cdot0.6^2)$ Pa $= 0.83$ MPa, which is less than the 2 MPa difference between the closure pressures.
So the cluster with the highest closure pressure hardly opens: the shares of the rate are 39 / 34 / 27 / 0.2%, and the bottomhole pressure is 42.0 MPa.
5 holes per cluster (20 per stage): the speed is four times larger and the loss 16 times larger, 13.3 MPa with equal division. The shares are 26 / 25 / 25 / 24%, and the bottomhole pressure is 54.2 MPa, which is 12.2 MPa higher.
After the holes are eroded, the loss with equal division is multiplied by $(0.6/0.85)^2(10/11)^4 = 0.34$ and falls to 4.5 MPa, and the shares drift apart: 27 / 26 / 25 / 22%.

Answer: With five holes per cluster, all four clusters get 24–26% of the rate each. With twenty, the cluster with the largest closure pressure gets 0.2%.

What it means. Limited entry buys evenness with pressure: the bottomhole pressure grew by 12.2 MPa, and with it the wellhead pressure and the power of the pumps, and all of this must stay within the strength of the casing and the equipment. The effect is temporary: proppant rounds and widens the holes, and by the end of the stage the evening-out weakens. The friction in the casing that we ignored adds rate to the clusters nearest the heel (the start of the horizontal section), and the bending of the fracture path near the wellbore differs from cluster to cluster. In reality the distribution is worse than the calculation, and it is checked with downhole sensors and records. The data in this example are assumed for illustration.

CalculatedCalculated share of the rate of each of the four clusters of the example against the number of holes in a cluster (10 mm each,

C_d

= 0.6, 9 m³/min per stage). With 4–6 holes the clusters get almost equal shares. With 20 or more, the cluster with a closure pressure of 42 MPa practically does not open.

Safety: what the rules are built on

Perforating combines two hazards: explosives and a well under pressure. The specific requirements are set by the industrial safety rules for blasting work, by the work plan and by the manufacturers' instructions. In international practice they are brought together in the recommended practice API RP 67. Below are the principles on which they are built.

Specialists and a plan. Storage, transport, arming of the guns, running and firing are done by a perforating and blasting service that is authorised for blasting work, under an approved plan. During the work a danger zone is set up around the wellhead and the arming place, and everyone who does not take part in the work is moved out of it.
Stray current. An electrical initiating device (the part that sets off the charge) can fire from stray currents, induced voltage or radio emission. So while such a gun is connected and is near the surface, radio transmitters, welding and other sources of current are restricted, and the equipment, the casing and the cable are checked for dangerous voltage between them. Mechanical and hydraulic initiation does not need these restrictions, but it has its own measures against firing at the wrong depth.
A well under pressure. After the first shot the reservoir is connected with the well. A gun on cable is pulled out through a lubricator with a blowout preventer (wellhead equipment), the tubing string for perforating on tubing is pressure tested before the shot, and the work plan provides for how to close and kill the well (Well control: primary barrier and kick indicators).
A misfire is an armed gun. If there was no shot, or not all the charges fired, the gun is treated as loaded. It is pulled out and disarmed by a special procedure, and there may still be pressure in its carrier.
The gun must not be thrown up. The underbalance in perforating on cable is limited and, when needed, an anchor is set. A strong flow can throw the gun upward and tangle and break the cable.
Gas and hydrogen sulfide. On gas wells and wells that contain hydrogen sulfide, gas detectors and protective equipment are used, because reservoir fluid can reach the surface.

Terms and symbols

Perforating on cable, on tubing (TCP), on coiled tubing, on slickline: Methods of delivering the gun. On cable, it is through the tubing or into the casing before the tubing is run.
Underbalanced perforating and overbalanced perforating: Perforating with the well pressure below or above the reservoir pressure at the moment of the shot.
Firing head: The device that sets off a gun on tubing: from a dropped bar, from pressure, or through a cable.
Casing collar locator: A magnetic tool that marks the collars of the casing. Together with GR it is used for depth correlation.
Oriented perforating: Perforating with a set direction of the tunnels: to the wall, along the fracture, away from a neighbouring string, up and down.
Extreme overbalance and propellant gas generator: Ways of splitting the rock at the tunnels with gas under pressure: compressed nitrogen, or the products of burning of a fuel.
Limited entry: A small number of holes, whose pressure losses even out the pumping between clusters.

Common mistakes and misconceptions

Wrong

“The larger the underbalance, the cleaner the tunnels, so we take the maximum.”

In fact

The upper limit of the underbalance is set by the strength of the rock (sand, fine particles), by the casing and the packer, and on cable by the risk of throwing the gun up. It is chosen between the lower limit by the criterion and these upper limits.

Wrong

“The length of the cable is the depth of the gun.”

In fact

In the well the cable heats up, its stretch changes with friction and tight spots, and the wheel slips. The depth is tied to the reference GR log by the GR peaks, the collars and the markers.

Wrong

“For fracturing we make more holes, so there is less pressure loss.”

In fact

When the pumping is shared between clusters, small losses leave the whole distribution to the rock: the liquid goes into the clusters with a lower closure pressure. Limited entry deliberately makes the losses larger than the difference between the closure pressures.

Wrong

“Perforating on tubing is always better than on cable.”

In fact

For long intervals and a large underbalance, yes. But a short interval in a well that is already completed is faster and cheaper to shoot on cable through the tubing. On tubing the charges are heated for longer, and a misfire costs pulling the string.

Wrong

“The gun did not fire, so it is safe.”

In fact

A gun that has not fired, or has fired in part, is treated as loaded. It is pulled out and disarmed by a special procedure, and there may still be pressure in the carrier.

In depth: advanced detail

The first second after the shot: static and dynamic underbalance

Records of fast pressure gauges showed that the pressure in the well in the first tens of milliseconds after the shot is not constant at all. First the gases of the explosion and the swelling of the carrier raise it. Then the well fluid rushes into the empty carrier of the gun, where before the shot the pressure was atmospheric, and the pressure at the tunnels falls sharply. While it swings, well fluid can for a moment enter the tunnels even at a static underbalance. And conversely, a short fall of pressure can clean the tunnels at a static balance.

Dynamic underbalance is based on this. The volume of empty spaces in the gun and in the chambers is chosen so that at the needed moment, right after the tunnels are pierced, the pressure at them falls by the calculated amount. In milliseconds each tunnel has time to give only its own small volume of fluid, and neighbouring tunnels do not take the flow from each other. The total volume of inflow is small, so there is less risk of sand production and of the gun getting stuck. When the general inflow is established, the fluid chooses the most conductive tunnels, and the plugged ones stay almost with no flow.

This also gives the modern view of the criteria: cleaning depends not so much on the static underbalance as on the largest pressure difference in the first milliseconds and on the strength of the crushed zone. The field criterion of this lesson remains a useful lower limit for sandstones, but the calculation for a particular perforating job is done with programs that model the dynamics of the well for the chosen gun and well.

Where the formula for the loss in the holes comes from

The liquid in the casing moves slowly, and in a hole it speeds up to a speed $v$ . By the Bernoulli equation, $\rho v^2/2$ goes into this speeding up, and the real losses at the entrance and the contraction of the jet are taken into account by the discharge coefficient: $\Delta p = \rho v^2/(2C_d^2)$ . Through $n$ holes of area $A$ the flow rate is $q = n A v$ , so $\Delta p_{\text{perf}} = \rho q^2/(2C_d^2 n^2 A^2)$ . With $A = \pi d^2/4$ this becomes $8\rho q^2/(\pi^2 C_d^2 n^2 d^4)$ , which is where the fourth power of the diameter comes from.

Why the loss falls with erosion: proppant first rounds the sharp edges, $C_d$ grows from 0.6 to about 0.9, and this alone reduces the loss by more than half. Then it widens the hole, and the loss falls further as the fourth power of the diameter. So in limited entry, a calculation for new holes gives an upper limit of the loss, and by the end of the stage the loss is several times smaller. The change of pressure when the rate is lowered in steps at the end of pumping lets us estimate how many holes really work, because the loss in the holes is proportional to the square of the rate.

Connections to other topics

Shaped-charge perforating — charges, guns, phasing, the crushed zone, and why an underbalance cleans the tunnels.
Effect of completion on inflow — the skin of the perforations and of the crushed zone: what a clean tunnel gives in flow rate.
Wireline operations — cable and slickline, the lubricator, the blowout preventer, weights, and the tension calculations when a gun is run.
Completion string equipment — the packer, the nipples and the circulation valves of the assembly for perforating on tubing.
Sand production: types, prediction and cost of the problem — rock strength and the critical drawdown, which set the upper limit of the underbalance in perforating.
Gamma ray log and natural gamma ray spectrometry — the gamma ray log by which the gun is correlated.
Rock mechanics for hydraulic fracturing — stresses, the orientation of the fracture, and the pumping pressure.
Hydraulic fracturing: purpose and well selection — why hydraulic fracturing is needed, and how wells are chosen.
Well control: primary barrier and kick indicators — barriers and well control: after the first shot the well is under pressure.

Check yourself

1
The well is completed: the 73 mm tubing string with a packer has been pressure tested, and the wellhead is installed. We need to add a 3 m interval above the reservoir that is already producing, quickly and cheaply. Which delivery method suits best?
1. A.A gun on drill pipe
2. B.A small gun on cable through the tubing, with a lubricator
3. C.A 114 mm carrier gun on cable
4. D.A gun on tubing, pulling the tubing string
Show the answer
Correct answer: B. A small gun on cable through the tubing, with a lubricator
A large gun will not pass through the tubing, and work on tubing would need pulling the tubing string and killing the well. A small gun on cable passes through the tubing, the well stays under the control of the lubricator and the blowout preventer, and we can shoot underbalanced. The price is shorter tunnels.
2
An oil-bearing sandstone with a permeability of 50 mD at 2500 m, reservoir pressure 25.0 MPa. The tubing is full of oil of 0.85 g/cm³ up to the wellhead, and the wellhead pressure is atmospheric. Is the underbalance enough by the field criterion? If not, by how many metres must the level be lowered?
Show the answer
The pressure opposite the reservoir is $0.00981\cdot0.85\cdot2500 = 20.85$ MPa, so the underbalance is $25.0 - 20.85 = 4.15$ MPa. The criterion: $50^{0.37} = 4.25$ , $3100/4.25 \approx 729$ psi $\approx 5.03$ MPa. About 0.88 MPa is missing. The pressure opposite the reservoir must be no more than $25.0 - 5.03 = 19.97$ MPa. This is a column of oil of $19.97/(0.00981\cdot0.85) \approx 2395$ m, so the level must be lowered by about 105 m. This gives only the lower limit. With a margin, the level is lowered further, checking the limit set by the strength of the rock and the equipment.
3
A long interval is perforated on cable in three runs. Which one comes first?
1. A.The top one, because it is nearer the wellhead
2. B.The order does not matter
3. C.The middle one
4. D.The bottom one
Show the answer
Correct answer: D. The bottom one
The bottom one: otherwise the next gun would pass the fresh tunnels and debris and might get stuck. The underbalance matters too: after the first shot the well is connected to the reservoir, and only the first run gets the full underbalance.
4
On the reference GR log, a shale peak is at 1987.4 m. On the check record, the same peak is seen at 1988.1 m on the cable. The top charge is 3.6 m below the GR sensor, and the interval on the reference log starts at 1995.0 m. At what depth on the cable should the GR sensor be placed?
Show the answer
The cable reads 0.7 m more than the reference depth. The sensor must stand at $1995.0 - 3.6 = 1991.4$ m on the reference log, which is $1991.4 + 0.7 = 1992.1$ m on the cable. Check: the top charge is then at 1995.7 m on the cable, which is 1995.0 m on the reference log.
5
A fracturing stage of four clusters was perforated with 30 holes per cluster. The closure pressures of the clusters differ by 2 MPa. What is most likely to happen?
1. A.The rate will be divided equally, because there are enough holes
2. B.The liquid will go into the cluster with the largest closure pressure
3. C.The pumping pressure will grow 16 times
4. D.The liquid will go mainly into the clusters with a lower closure pressure, and the one with the highest closure pressure may not open
Show the answer
Correct answer: D. The liquid will go mainly into the clusters with a lower closure pressure, and the one with the highest closure pressure may not open
With 30 holes the losses in them are fractions of a megapascal, less than the difference between the closure pressures. The rock sets the distribution: in the calculation of the lesson, already at 20 holes the cluster with a closure pressure of 42 MPa gets about 0.2% of the rate. Limited entry needs fewer holes, so that the losses exceed this difference.
6
A gun on cable has been pulled out, and the signs show that not all the charges fired. How should it be handled?
1. A.Disconnect the cable and leave it on the catwalk
2. B.As a spent gun: since it fired, it is safe
3. C.As an armed gun: the charges that did not fire and the initiating devices are dangerous, and there may be pressure in the carrier. The blasting service disarms it by a special procedure
4. D.Run it in again and fire at the same depth
Show the answer
Correct answer: C. As an armed gun: the charges that did not fire and the initiating devices are dangerous, and there may be pressure in the carrier. The blasting service disarms it by a special procedure
A gun that has fired in part is still loaded, and there may still be pressure in its carrier. Only specialists handle it, by the procedure set by the rules for blasting work. Until then, the danger zone around it is kept.

Updated: 16 October 2026