Hydraulic fracturing: purpose and well selection

Quick refresher

A fracture forms when the bottomhole pressure goes above the fracture pressure. It opens against the smallest principal stress (the smallest of the three stresses that squeeze the rock) and at ordinary depths it is vertical, with two symmetrical wings.
Proppant holds the fracture open. The ability of the fracture to carry fluid is described by the conductivity $k_f w$ : the permeability of the proppant pack multiplied by the width.
A fracture of high conductivity works like a well whose radius is about half of the fracture half-length: $r_w' \approx x_f/2$ . The equivalent skin $S_f = -\ln(r_w'/r_w)$ is usually from −4 to −6.
The dimensionless conductivity $F_{CD} = k_f w/(k x_f)$ compares how well the fracture carries fluid with how well the reservoir gives fluid up. At $F_{CD}$ of 10 and above, almost the whole length of the fracture is used. At a small $F_{CD}$ only the part near the wellbore works.
The lower the permeability of the reservoir, the larger the relative gain. In a tight reservoir the length of the fracture decides, and in a permeable one its conductivity.
A candidate has low permeability or damage, enough oil or gas left and enough pressure, and reliable barriers above and below, especially if water or gas is nearby. The well must be designed for fracturing pressures, and the lift system (the tubing, and the pump if there is one, that carries the fluid up the well) and the surface equipment must have spare capacity.

Key relationships

F_{CD} = \dfrac{k_f\,w}{k\,x_f}

dimensionless fracture conductivity

r_w' \approx \dfrac{x_f}{2},\quad S_f = -\ln\dfrac{r_w'}{r_w}

a fracture of high conductivity ( $F_{CD}$ of 10 and above)

\dfrac{q_2}{q_1} = \dfrac{X + S_1}{X + S_f},\quad X = \ln\dfrac{r_e}{r_w} - \dfrac34

the folds of increase (FOI): how many times the rate grows at the same drawdown (the pressure difference that pushes fluid into the well)

Common pitfalls

Expecting the same effect from the same fracture in reservoirs of different permeability.
Designing a long, narrow fracture for a permeable reservoir. It will not have enough conductivity.
Forgetting about barriers. A fracture that has grown into a water-bearing or gas-bearing layer can ruin the well.
Fracturing a well whose casing, cement and wellhead are not designed for its pressures.
Taking the equivalent skin as constant. The conductivity of the fracture falls when the load on the proppant grows, when proppant is carried out of the fracture, and when the pack gets clogged.

After this lesson you can

explain how a hydraulic fracture forms, why it is usually vertical, and what proppant does
describe a fracture by its half-length, height, width and conductivity, and explain the meaning of the dimensionless fracture conductivity
calculate the equivalent skin (a number for the extra resistance to flow near the well; it is below zero when a fracture helps the flow) and the effective wellbore radius of a well with a fracture, and estimate the folds of increase (FOI) of the rate, that is, how many times the rate grows
explain why the relative gain from fracturing is larger in low-permeability reservoirs, and why in permeable ones the conductivity of the fracture matters more than its length
select candidate wells and choose between an acid treatment and hydraulic fracturing
list the stages of the job, the kinds of fracturing and the main operating risks

How a fracture forms and what it gives

If fluid is pumped into the reservoir faster than the reservoir can take it, the pressure at the bottom of the well rises. When it goes above the fracture pressure, the rock splits. For the fracture to open and keep growing, the pressure of the fluid in it must stay above the stress that squeezes its walls. This is the smallest of the principal stresses in the rock (Fracture gradient and leak-off testing). So the fracture opens against the smallest stress and grows perpendicular to it.

At ordinary depths the weight of the overlying rocks is larger than the horizontal stresses, and the smallest one turns out to be the minimum horizontal stress. So the fracture is vertical, with two wings that spread symmetrically from the wellbore in the direction of the largest horizontal stress. All the fractures of one field are therefore oriented almost the same way, and this is taken into account when production and injection wells are placed (Rock mechanics for hydraulic fracturing).

The fracturing fluid is made viscous. This gives the fracture its width, and the fluid holds the proppant (sand or ceramic granules) in suspension. When pumping stops, the fluid leaks off into the reservoir, the pressure falls, and the walls of the fracture close onto the proppant. What is left is a narrow but very permeable channel. The viscosity of the fluid is then broken down with special additives (breakers), so that the fluid flows out of the fracture during clean-up.

Bypassing damage. The flow enters the fracture far from the wellbore and bypasses a damaged near-wellbore zone of any kind. For this it is enough to know that damage exists (lesson on formation damage).
A different geometry of inflow. Instead of converging on a wellbore of 10 cm radius, the fluid flows to two planes tens of metres long. The area of filtration is huge, the velocities are low, and the same drawdown gives a much larger rate.
A link to what the wellbore did not open. A fracture can connect to the well layers that are separated by thin shale beds (layers of clay-rich rock), and natural fractures.

Half-length, height, width and conductivity

SchematicA hydraulic fracture in plan view and in section. At the top is the view from above: two wings of half-length

x_f

are opened against the smallest horizontal stress, and the width is shown greatly magnified. At the bottom is a section along the plane of the fracture: the created fracture goes a little way into the shale barriers, and the part held by proppant is shorter and lower. The diagram is not to scale.

Half-length $x_f$: The distance from the wellbore to the end of one wing of the fracture. What matters is the propped half-length: the created fracture is longer, but its unpropped part closes when the pressure is released.
Height $h_f$: The size of the fracture in the vertical direction. It is limited by layers with a higher stress, usually shales. If the barriers are weak, the fracture grows into the neighbouring layers.
Width $w$: The opening of the propped fracture: usually millimetres, and with special technology up to a centimetre or two.
Conductivity $k_f w$: The permeability of the proppant pack, $k_f$ , multiplied by the width. It is measured in mD·m (in English-language literature, mD·ft). Without load, the permeability of a proppant pack is hundreds of darcies. Under the closure pressure (the stress that squeezes the fracture shut) and with gel residues it is several times lower.

Conductivity alone is not enough to judge a fracture. It must be large compared with the reservoir. The reservoir gives fluid to the fracture along its whole length, and the fracture must carry all this flow to the wellbore. The ratio of the two abilities is the dimensionless fracture conductivity.

Dimensionless fracture conductivity

F_{CD} = \frac{k_f\,w}{k\,x_f}

where:

$F_{CD}$ dimensionless fracture conductivity (also written $C_{fD}$ in the literature), —
$k_f$ permeability of the proppant pack in the fracture at reservoir conditions, mD
$w$ width of the propped fracture, m
$k$ permeability of the reservoir, mD
$x_f$ propped half-length of the fracture, m

Units: any consistent units: $k_f$ and $k$ in the same units, and $w$ and $x_f$ in the same units too

Holds when

A vertical fracture over the whole thickness of the reservoir, with two equal wings.
The conductivity of the fracture and the permeability of the reservoir are the same along the length.
Single-phase flow that follows Darcy's law. Inertial losses and multiphase flow in the fracture reduce its effective conductivity.

The numerator is the ability of the fracture to carry fluid along itself to the wellbore. The denominator is the ability of the reservoir to give fluid to the fracture along its length. At a large $F_{CD}$ the pressure hardly falls along the fracture, and its whole length works. At a small one the fracture “cannot keep up” with the inflow: the pressure falls along it, and the far parts hardly work.

Several things lower the conductivity of a propped fracture: the closure pressure (crushing of grains and pressing them into the walls), polymer residues of the fracturing fluid, fine rock particles that clog the pack, proppant carried into the well, and inertial losses and multiphase flow in the fracture itself. Sand is cheaper but fits only moderate loads. At large depths and loads, strong ceramic proppant is used. The choice of proppant and of the size of the fracture is covered in the lesson Fracture design: size and conductivity.

Equivalent skin and the folds of increase of the rate

Far from the well, the flow does not “see” the details of the fracture. A well with a fracture behaves like an ordinary well of a larger radius. This effective wellbore radius and the negative skin that corresponds to it let us calculate the inflow to a well with a fracture by the usual formulas of radial flow. For a fracture of high conductivity the effective wellbore radius equals half of the half-length.

Equivalent skin of a fracture of high conductivity

S_f = -\ln\frac{r_w'}{r_w},\qquad r_w' \approx \frac{x_f}{2}

where:

$S_f$ equivalent skin of a well with a fracture, —
$r_w'$ effective wellbore radius: the radius of a well with no fracture and no skin that has the same productivity, m
$r_w$ radius of the wellbore, m
$x_f$ propped half-length of the fracture, m

Units: any units of length, the same for all the radii

Holds when

The fracture has high conductivity: $F_{CD}$ is 10 and above. At a lower conductivity the effective wellbore radius is smaller (the next section).
The fracture is small compared with the drainage area (the part of the reservoir that feeds the well): the half-length is much smaller than $r_e$ .
Pseudo-steady-state flow (the pressure falls at the same pace everywhere in the drainage area). In the first months, while the flow to the fracture is linear, productivity is higher.
The fracture bypasses the damage, so the damage skin is not included in the sum.

A fracture with a half-length of 50 m acts like a wellbore of radius about 25 m. At $r_w$ = 0.108 m this is a skin of $-\ln(25/0.108) \approx -5.4$ . The equivalent skin grows in size only logarithmically: a fracture twice as long adds only $-\ln 2 \approx -0.7$ to it.

Folds of increase (FOI) of the rate after fracturing

\frac{q_2}{q_1} = \frac{X + S_1}{X + S_f},\qquad X = \ln\frac{r_e}{r_w} - \frac34

where:

$q_1,\ q_2$ rate before and after fracturing at the same drawdown, m³/d
$S_1$ skin before the treatment, including the damage skin that the fracture bypasses, —
$S_f$ equivalent skin of the well with a fracture, —
$X$ logarithmic term of an ideal well in pseudo-steady-state flow, —

Units: dimensionless; the logarithm is natural

Holds when

The average reservoir pressure and the drawdown are the same. The lift system and the surface equipment pass the increased rate.
Pseudo-steady-state flow in a circular drainage area.

In English-language literature this quantity is called the folds of increase (FOI): the number of times by which the rate grows. With a long fracture the denominator $X + S_f$ becomes small. This is why the FOI is 3–6 and more, even for undamaged wells, where a treatment of the near-wellbore zone gives almost nothing.

Worked exampleEquivalent skin of a fracture and the gain in rate

Given (assumed data)

Reservoir: $k = 1$ mD, $h = 15$ m
Oil in the reservoir: $\mu = 0.8$ mPa·s, $B = 1.3$ m³/m³
Well: $r_w = 0.108$ m, $r_e = 400$ m, drawdown 10 MPa, skin before the treatment +3
A fracture over the whole thickness of the reservoir: $x_f = 60$ m, $k_f w = 900$ mD·m

Solution

Dimensionless conductivity: $F_{CD} = \dfrac{900}{1\cdot 60} = 15$ . This is a fracture of high conductivity, and $r_w' \approx x_f/2 = 30$ m.
Equivalent skin: $S_f = -\ln\dfrac{30}{0.108} = -5.63$ .
The logarithmic term: $X = \ln\dfrac{400}{0.108} - 0.75 = 7.467$ .
Rate before fracturing: $q_1 = \dfrac{0.536\cdot 1\cdot 15\cdot 10}{0.8\cdot 1.3\cdot(7.467 + 3)} = 7.38$ m³/d.
After: $X + S_f = 1.840$ , $q_2 = 42.0$ m³/d, and the FOI is $\dfrac{7.467 + 3}{1.840} = 5.69$ .
A refinement for finite conductivity: at $F_{CD} = 15$ , the effective wellbore radius from the correlation (see the next section) is $0.46\,x_f = 27.4$ m, the skin is $-5.54$ , the FOI is 5.4, and the rate is 40.0 m³/d.

Answer: The fracture gives an equivalent skin of about −5.54…−5.63 and raises the rate from 7.38 to about 40.0 m³/d. That is 5.4 times, or 32.6 m³/d more (205 bbl/d).

What it means. Part of the gain came from bypassing the damage: for an undamaged well the FOI would be 3.9. The estimate $r_w' = x_f/2$ is an upper one. At $F_{CD} = 15$ it overstates the rate by only 5%. A half-length of 60 m at $r_e$ = 400 m is still a “small” fracture. For fractures comparable with the size of the drainage area, the effective wellbore radius is replaced by solutions for the particular shape of the area. The data in this example are assumed for illustration.

Length or conductivity: the role of reservoir permeability

At a small dimensionless conductivity the fracture itself becomes the bottleneck. The reservoir gives it more than it can carry, and the effective wellbore radius comes out smaller than half of the half-length. The dependence of $r_w'/x_f$ on $F_{CD}$ comes from the solution of the problem of inflow to a fracture of finite conductivity. A convenient approximation of it is given in the advanced block below.

Effective wellbore radius of a fracture of finite conductivity

$F_{CD}$: 0.3
$r_w'/x_f$: 0.08
What it means: only the part of the fracture near the wellbore works

$F_{CD}$: 1
$r_w'/x_f$: 0.19
What it means: the conductivity strongly limits the gain

$F_{CD}$: 3
$r_w'/x_f$: 0.33
What it means: the limit is noticeable

$F_{CD}$: 10
$r_w'/x_f$: 0.44
What it means: almost the limiting radius

$F_{CD}$: 30
$r_w'/x_f$: 0.48
What it means: practically infinite conductivity

$F_{CD}$: 100
$r_w'/x_f$: 0.49
What it means: the limit $x_f/2$

$F_{CD}$	$r_w'/x_f$	What it means
0.3	0.08	only the part of the fracture near the wellbore works
1	0.19	the conductivity strongly limits the gain
3	0.33	the limit is noticeable
10	0.44	almost the limiting radius
30	0.48	practically infinite conductivity
100	0.49	the limit $x_f/2$

The values are calculated from the approximation in the advanced block. Its error is a few per cent.

This gives the main conclusion about choosing a fracture. For a given fracture, $F_{CD}$ is inversely proportional to the permeability of the reservoir. In a tight reservoir even a modest conductivity gives a large $F_{CD}$ . The fracture is almost ideal, and the gain is set by its length. In a permeable reservoir the same fracture carries poorly. The gain is smaller, and the conductivity decides. So in tight reservoirs we aim for long fractures, and in permeable ones for short, wide ones.

CalculatedThe folds of increase (FOI) of the rate of an undamaged well (

S_1 = 0

) after fracturing, against the permeability of the reservoir. The fracture has a half-length of 50 m and a conductivity of 500 mD·m (solid line) or 2000 mD·m (dashed line);

r_w

= 0.108 m,

r_e

= 400 m. A, B and C are the reservoirs of 0.5, 5 and 50 mD from the example below.

More detail:Effective wellbore radius of a fracture of finite conductivity

A widely used chart that links the effective wellbore radius of a fracture of finite conductivity with $F_{CD}$ was published in 1981 by H. Cinco-Ley and F. Samaniego. The limiting result $r_w' = x_f/2$ for a fracture of infinite conductivity was obtained as early as 1961 by M. Prats. For calculations it is convenient to replace the chart with an approximation:

Effective wellbore radius of a fracture of finite conductivity (approximation)

\ln\frac{x_f}{r_w'} = \frac{1.65 - 0.328\,u + 0.116\,u^2}{1 + 0.180\,u + 0.064\,u^2 + 0.005\,u^3},\qquad u = \ln F_{CD}

where:

$x_f$ propped half-length of the fracture, m
$r_w'$ effective wellbore radius of a well with a fracture, m
$u$ natural logarithm of the dimensionless conductivity, —
$F_{CD}$ dimensionless fracture conductivity, —

Units: dimensionless; the logarithms are natural

Holds when

A vertical fracture over the whole thickness of the reservoir, the well at the centre of the drainage area, and a fracture that is small compared with the area.
The approximation fits the chart with an error of a few per cent in the practically important range, from about 0.3 to hundreds. At a lower conductivity it overstates $r_w'$ (at $F_{CD} = 0.1$ by about 12%, in more detail in the lesson Inflow to a hydraulically fractured well). At large $F_{CD}$ the right-hand side approaches $\ln 2$ , that is, $r_w'$ approaches $x_f/2$ .

The equivalent skin is expressed through the same quantity: $S_f = \ln(x_f/r_w') - \ln(x_f/r_w)$ . At infinite conductivity the right-hand side equals $\ln 2 \approx 0.69$ . Its excess over this value is the price paid for finite conductivity. For example, at $F_{CD} = 1$ the right-hand side equals 1.65, and $r_w' \approx 0.19\,x_f$ .

Worked exampleThe same fracture in reservoirs of different permeability

Given (assumed data)

Fracture: $x_f = 50$ m, $k_f w = 500$ mD·m
Reservoirs: $k$ = 0.5, 5 and 50 mD; skin 0 before the treatment
Well: $r_w = 0.108$ m, $r_e = 400$ m

Solution

$F_{CD} = \dfrac{500}{k\cdot 50}$ : 20, 2 and 0.2 for 0.5, 5 and 50 mD.
From the approximation, $r_w'/x_f$ = 0.47, 0.28 and 0.055, that is, $r_w'$ = 23.4, 13.9 and 2.76 m.
The equivalent skin $S_f = -\ln(r_w'/0.108)$ is −5.38, −4.86 and −3.24. The FOI $X/(X + S_f)$ at $X = 7.467$ is 3.57, 2.86 and 1.77.
In the 50 mD reservoir, the same volume of proppant can be placed differently. The volume is proportional to $x_f w$ . So, for the same permeability of the pack, the product $x_f\,k_f w = 25{,}000$ mD·m² stays constant. Take $F_{CD} = 1.6$ . Then $k_f w = 80\,x_f$ and $x_f = \sqrt{25{,}000/80} = 17.7$ m, $k_f w = 1414$ mD·m. This fracture is 2.8 times shorter and the same number of times wider.
For it $r_w'/x_f = 0.25$ , $r_w' = 4.4$ m, $S_f = -3.71$ , and the FOI is 1.99 instead of 1.77.

Answer: The same fracture raises the rate 3.57 times in the 0.5 mD reservoir and only 1.77 times in the 50 mD reservoir. In the permeable reservoir it pays to place the same proppant in a short, wide fracture, with an FOI of 1.99.

What it means. In the tight reservoir the fracture is almost ideal, and the length decides the gain. In the permeable reservoir the fracture cannot carry what the reservoir gives, and the conductivity decides the gain. For a given amount of proppant, and a fracture that is small compared with the drainage area, the best result comes at $F_{CD}$ of about 1.6. Trying different lengths in this example gives the same optimum. The design of the size of a fracture is based on this (Fracture design: size and conductivity). The data in this example are assumed for illustration.

Which wells suit fracturing

The main sign of a candidate is low permeability. In oil reservoirs fracturing is usually used at permeabilities from fractions of a millidarcy to a few tens of millidarcies. In gas reservoirs it is used at permeabilities 10 to 100 times lower (one or two orders of magnitude), down to microdarcies, because gas has a low viscosity, and a profitable gas rate can be reached in much tighter rocks. In permeable reservoirs short, wide fractures are used, to bypass deep damage, and in weak sandstones together with a gravel pack (a sand filter built in the well) against sand production (Fracturing fluids and tip-screenout fracturing, Sand control methods).

Remaining oil or gas and pressure. A fracture speeds up production, so the drainage area must still hold something to produce, and the reservoir pressure must last for the whole period (or artificial lift must be planned).
Barriers and contacts. Above and below the reservoir we need layers with a higher stress that will stop the growth of the fracture in height. If a water-bearing layer or a gas cap (a layer of free gas above the oil) lies a few metres away without a reliable barrier, the fracture can open a path for water or gas.
Water cut. A well with a high water cut will most often give more water after fracturing, not more oil.
Well design. The casing, the cement, the wellhead (the “Christmas tree”) and the tubing must withstand the fracturing pressure. Good cement is needed so that the fracture does not run up the outside of the casing. A well that was not designed for fracturing often cannot be treated.
Gathering system and lift system. The rate can grow several times, and the lift system, the flowline (the surface pipe that carries the production to the plant) and the processing plant must be able to take it.
People and equipment. Fracturing is much more complex than an acid treatment, and the pumping has to be adjusted on site. So experienced specialists and a reliable fleet of pumping units are needed. The first jobs in a new area end in a premature stop more often than usual, until the technology is adjusted to the local rocks.

Acid or fracturing

1
How permeable is the reservoir?
If the permeability is low, only a fracture will give a noticeable gain. Removing damage in a tight reservoir adds little, while a fracture changes the geometry of the inflow itself.
2
Is there damage?
If the reservoir is permeable and undamaged, an acid treatment will give almost nothing, except in a carbonate, where wormholes give a skin of −2…−3. A fracture will give a gain here too, but a smaller one than in a tight reservoir, and only at a high conductivity. Whether the gain will pay for the costs and risks is decided by a calculation and by economics.
3
What do we know about the damage?
Shallow damage of a known type that acid can dissolve is cheaper to remove with an acid treatment. Deep damage, damage that does not dissolve, or damage we do not understand is bypassed with a short fracture. For that, it is enough to know that damage exists.
4
What do economics and risks say?
We compare the gain and the costs of both options, the experience of neighbouring wells, how close water and gas are, and the condition of the casing and cement.

How a fracturing job is done

Stages of the job

1
Preparation
Collecting data on the stresses and the properties of the rocks, checking the casing and cement, and pressure-testing the equipment. Often a calibration injection (mini-frac) is run, from which we find the closure pressure of the fracture and the leak-off of fluid into the reservoir.
2
Pad
A batch of fracturing fluid without proppant. It opens the fracture, creates a width that is enough for the grains, and partly leaks off into the reservoir.
3
Proppant stage
The carrier fluid with a gradually growing concentration of proppant. The last, most loaded batches stay near the wellbore, where the greatest conductivity is needed.
4
Displacement (flush)
The proppant is pushed with clean fluid to the interval of perforation, and no further, so as not to leave the fracture near the wellbore without proppant.
5
Closure
The well is shut in. The fluid leaks off into the reservoir, the fracture closes onto the proppant, and the breaker destroys the gel.
6
Clean-up and evaluation
The spent fracturing fluid is brought to the surface, and then the well is put on production. The rate and the well test are compared with the design.

A fracturing fleet works on the surface. It includes tanks with the base fluid (often a potassium chloride solution, and at sea, seawater) and a blender (a mixer) where the thickener, the crosslinker (a chemical that makes the gel stronger), the breaker and the proppant are added to the fluid. It also has proppant hoppers with conveyors, and several high-pressure pumping units that work in parallel, with spare units. The pumps are joined to the well by a manifold (a pipe junction). A control station is the place from which the pressure, the rate and the proppant concentration are watched. The job must run without stops: the failure of a pump in the middle of pumping can ruin it.

The well is under heavy loads. The wellhead is protected with a special device that shuts it off from the high pressure. The pressure inside the tubing tries to burst it, so a back pressure (a pressure that pushes the other way) is held in the annulus (the space between the tubing and the casing), and a way of releasing pressure is provided in case a pipe bursts. Cold fluid cools the pipes, they shorten, and the loads on the packer (the seal in the annulus) and the threads grow. All this is built into the design of the well in advance.

What can go wrong: a screen-out, where the proppant blocks the fracture or the near-wellbore zone, the pressure rises sharply, and pumping is stopped before time; growth of the fracture in height beyond the reservoir; settling of proppant because the viscosity is too low, so that the propped part of the fracture is shorter than the created one; damage to the pack by gel residues; and proppant carried into the well during clean-up.

Kinds of fracturing

Kind: Propped fracturing
Where it is used: sandstones and carbonates of low and medium permeability
What holds the conductivity: the proppant pack

Kind: A short, wide fracture, including with a gravel pack
Where it is used: permeable reservoirs with deep damage, weak sandstones
What holds the conductivity: a dense proppant pack near the wellbore

Kind: Acid fracturing
Where it is used: strong, heterogeneous carbonates
What holds the conductivity: acid dissolves the walls unevenly, and the ridges stop them from closing

Kind: Multistage fracturing
Where it is used: horizontal wells in low-permeability and shale formations
What holds the conductivity: several fractures along the wellbore, each with proppant

Kind	Where it is used	What holds the conductivity
Propped fracturing	sandstones and carbonates of low and medium permeability	the proppant pack
A short, wide fracture, including with a gravel pack	permeable reservoirs with deep damage, weak sandstones	a dense proppant pack near the wellbore
Acid fracturing	strong, heterogeneous carbonates	acid dissolves the walls unevenly, and the ridges stop them from closing
Multistage fracturing	horizontal wells in low-permeability and shale formations	several fractures along the wellbore, each with proppant

Acid fracturing does not work in sandstones: acid hardly dissolves their walls, and a fracture without proppant closes.

The size of the fracture is chosen by economics. As the length grows, the gain in production grows more and more slowly (the equivalent skin grows in size only logarithmically), while the volume of fluid and proppant, and with it the cost, grow faster and faster. So there is a length at which the NPV (net present value) of the job is the largest (Net present value (NPV), Fracture design: size and conductivity). As after an acid treatment, a large part of the gain is faster production, not new reserves.

Terms and symbols

Hydraulic fracturing (frac): Creating a fracture in the reservoir by pumping fluid at a pressure above the fracture pressure, and holding it open with proppant.
Proppant: Sand or ceramic granules that hold the fracture open.
Fracture half-length $x_f$: The distance from the wellbore to the end of one wing of the propped fracture.
Fracture conductivity $k_f w$: The permeability of the proppant pack multiplied by the width of the fracture.
Dimensionless conductivity $F_{CD}$: The ratio of the conductivity of the fracture to the product of the permeability of the reservoir and the half-length.
Equivalent skin of a fracture $S_f$: The negative skin with which a well with a fracture works like an ordinary well.
Pad and flush: A batch of fluid without proppant at the start of pumping, and a batch of clean fluid at the end that brings the proppant to the perforations.
Screen-out: A premature stop of pumping because the proppant has blocked the fracture or the near-wellbore zone.
Acid fracturing: Fracturing of carbonates with acid and no proppant: the conductivity is created by unevenly etched walls.

Common mistakes and misconceptions

Wrong

“The longer the fracture, the better, always.”

In fact

In a permeable reservoir a long fracture of ordinary conductivity works only with its part near the wellbore, because its $F_{CD}$ is small. Also, the equivalent skin grows with length only logarithmically, and the cost grows faster. The length is chosen together with the conductivity, and by economics.

Wrong

“Fracturing gives the same effect in any reservoir.”

In fact

The lower the permeability, the larger the relative gain. In the example of the lesson the same fracture raised the rate 3.6 times in the 0.5 mD reservoir and only 1.8 times in the 50 mD reservoir.

Wrong

“The height of the fracture equals the thickness of the reservoir.”

In fact

The height is set by the contrasts of stress between the layers. If the barriers are weak, the fracture grows into the neighbouring layers, including water-bearing ones.

Wrong

“The skin after fracturing does not change.”

In fact

The conductivity of a fracture falls when the load on the proppant grows as the reservoir is depleted, when grains are crushed and pressed into the walls, when proppant is carried out of the fracture, and when the pack is clogged by fine particles. The equivalent skin grows with time.

Wrong

“Nothing can be done against damage that acid does not dissolve.”

In fact

A fracture bypasses damage of any kind: the flow enters it beyond the damaged zone. For fracturing it is enough to know that damage exists.

In depth: advanced detail

Why a fracture is usually vertical

A fracture opens against the smallest of the three principal stresses. The vertical stress comes from the weight of the overlying rocks, and it grows with depth by about 22–25 kPa per metre. The horizontal stresses in most sedimentary basins are smaller than it. So at depths of more than a few hundred metres, fractures are vertical. At shallow depths, and in areas of strong horizontal compression, the vertical stress can be the smallest. Then the fracture is horizontal and grows along the bedding (the flat layers of the rock).

A vertical fracture is elongated in the direction of the largest horizontal stress. A horizontal well drilled along the direction of the smallest stress is crossed by transverse fractures (at right angles to the well), and this is how multistage fracturing works. Along the largest stress, one longitudinal fracture forms along the wellbore. Stresses and the closure pressure are covered in more detail in the lesson Rock mechanics for hydraulic fracturing, and horizontal wells in the lesson Horizontal wells.

The first months after fracturing

The formulas with the effective wellbore radius describe the steady picture, when the pressure disturbance (the change in pressure that spreads out from the well) has covered the whole drainage area. Right after start-up the fluid flows to the plane of the fracture along almost parallel lines. This is the linear flow regime, and at finite conductivity it is at first bilinear, with flow both in the reservoir and along the fracture. During this time the rate is higher than the formula gives, and it falls quickly. The FOI of the rate is at first larger than the calculated one, and it gradually comes closer to it.

In reservoirs with a permeability of a fraction of a millidarcy and lower, the transient period (the time before the pressure disturbance reaches the edge of the drainage area) lasts months and years. So the production of wells with fractures in tight reservoirs is forecast with transient-flow models, and when such wells are tested we look for the typical signs of linear and bilinear flow (Well testing: purposes and types of test, Inflow to a hydraulically fractured well).

Connections to other topics

Formation damage and damage skin — damage to the near-wellbore zone and why a fracture bypasses it.
Skin factor — the effective wellbore radius and the negative skin.
Acid treatments: principle, economics and candidate selection — when an acid treatment is enough instead of a fracture.
Fracture gradient and leak-off testing — the fracture pressure and the smallest stress in the rock.
Rock mechanics for hydraulic fracturing — stresses in the reservoir, the closure pressure, and the height and orientation of a fracture.
Inflow to a hydraulically fractured well — inflow to a well with a fracture, and the folds of increase (FOI) of productivity in detail.
Fracture design: size and conductivity — proppant, conductivity, and the optimum size of a fracture.
Nodal analysis of the production system — whether the lift system will pass the increased rate.

Check yourself

1
The same fracture ( $x_f$ = 50 m, $k_f w$ = 500 mD·m) is created in undamaged reservoirs of 0.5, 5 and 50 mD. Where will the relative gain in rate be the largest?
1. A.The same everywhere: the fracture is the same
2. B.In the 0.5 mD reservoir
3. C.In the 50 mD reservoir
4. D.In the 5 mD reservoir
Show the answer
Correct answer: B. In the 0.5 mD reservoir
$F_{CD} = k_f w/(k x_f)$ equals 20, 2 and 0.2. In the tight reservoir the fracture is almost ideal ( $r_w' \approx 0.47\,x_f$ ), and in the permeable one only its part near the wellbore works ( $r_w' \approx 0.06\,x_f$ ). The FOI values are about 3.6, 2.9 and 1.8. The absolute gain in the permeable reservoir may be larger, but the relative gain is smaller.
2
A fracture of high conductivity with a half-length of 40 m is created in a well of radius 0.1 m; $X = \ln(r_e/r_w) - 3/4 = 7.2$ . Find the equivalent skin and the folds of increase (FOI) of the rate, if the skin before the treatment was 0, and if it was +4.
Show the answer
$r_w' \approx 20$ m, and $S_f = -\ln(20/0.1) = -\ln 200 \approx -5.3$ . With an initial skin of 0 the FOI is $7.2/(7.2 - 5.3) \approx 3.8$ . With a skin of +4 it is $11.2/1.9 \approx 5.9$ , because the fracture also bypasses the damage.
3
How will the dimensionless conductivity of a fracture change if the same fracture is created in a reservoir with 10 times higher permeability?
1. A.It will fall 10 times
2. B.It will not change: it depends only on the proppant
3. C.It will grow 10 times
4. D.It will fall $\sqrt{10}$ times
Show the answer
Correct answer: A. It will fall 10 times
The permeability of the reservoir stands in the denominator of $F_{CD} = k_f w/(k x_f)$ . The reservoir gives ten times more to the fracture, while the fracture carries the same amount, so it is 10 times “worse” relative to the reservoir.
4
Which well is the worst candidate for fracturing?
1. A.A 300 mD reservoir with deep damage of unknown nature
2. B.An oil reservoir of 2 mD with damage, enough oil and pressure, and thick shales above and below
3. C.A 0.1 mD gas reservoir with reliable barriers
4. D.A 3 mD reservoir with a water-bearing layer 4 m below it and no shale barrier
Show the answer
Correct answer: D. A 3 mD reservoir with a water-bearing layer 4 m below it and no shale barrier
Without a barrier the fracture will almost certainly grow into the water-bearing layer, and the well will start to produce water. The others are normal candidates: low permeability in the first and third cases, and in the fourth, deep damage of unknown nature is sensibly bypassed with a short, wide fracture.
5
Why is a fracture in sandstone held open with proppant, while in a carbonate acid alone is sometimes enough?
Show the answer
Hydrochloric acid dissolves carbonate rock, and it does so unevenly. In a strong, heterogeneous rock, ridges remain on the fracture walls. When the pressure is released, they stop the walls from closing, and the etched channels carry fluid. Acid hardly dissolves sandstone, and a fracture without proppant closes.
6
For a 50 mD reservoir, a fracture with a half-length of 150 m and a conductivity of 300 mD·m is proposed. What is wrong with this design?
Show the answer
$F_{CD} = 300/(50\cdot 150) = 0.04$ . The fracture carries incomparably worse than the reservoir gives fluid to it, and only a small part of it near the wellbore works. Most of the length and of the proppant is wasted. A permeable reservoir needs a short, wide fracture with $F_{CD}$ of the order of one. And if the only task is to bypass shallow damage, an acid treatment may be enough.

Updated: 1 October 2026