Skin factor · MunaiHub

Quick refresher

Skin is a correction to the model of homogeneous radial flow. We treat the additional pressure drop $\Delta p_s$ as if it happened in an infinitely thin layer on the wall of the well. So it appears and disappears together with the flow rate.
$S > 0$ means that inflow is hindered (formation damage, which is harm to the rock near the well; partial penetration, where the well opens only part of the reservoir thickness; poor perforation). $S < 0$ means that inflow is eased (acid treatment, hydraulic fracture, deviated wellbore, which is a slanted well).
If Darcy's law holds, the skin does not depend on the flow rate. The pressure drop $\Delta p_s$ is proportional to the flow rate: double the flow rate and the losses on the skin double too.
In the Hawkins formula the reduction in permeability enters the skin linearly (in direct proportion), and the depth of the altered zone enters only through a logarithm. A treated zone of radius $r_s$ cannot give a skin below $-\ln(r_s/r_w)$ .
For most wells $\ln(r_e/r_w) - 3/4 \approx 7$ , so a skin of about +7 roughly halves the productivity. A skin of −3 or lower usually comes from a hydraulic fracture or a long deviated wellbore.
The measured skin is the sum of several components. An acid treatment can remove only the damage skin.

Key relationships

\Delta p_s = \dfrac{qB\mu}{2\pi kh}\,S

definition of the skin factor (consistent units)

S = \left(\dfrac{k}{k_s} - 1\right)\ln\dfrac{r_s}{r_w}

Hawkins formula for a zone of altered permeability

r_w' = r_w\,\e^{-S}

effective wellbore radius

\text{FE} = \dfrac{\ln(r_e/r_w) - 3/4}{\ln(r_e/r_w) - 3/4 + S}

flow efficiency (pseudo-steady-state flow)

\Delta p_s = 0.869\,m\,S

skin pressure drop from the slope $m$ of the semilog straight line of a well test

Common pitfalls

Confusing the skin factor (which has no units) with the skin pressure drop (in MPa). The same skin “costs” different pressure losses in wells with different flow rates and flow capacity $kh$ .
Planning an acid treatment from the total skin, without first separating out the components that acid does not remove.
Expecting a skin of −4 to −5 from an acid treatment of a shallow zone. Such values come from fractures, not from treating the near-wellbore zone.
Counting on a large gain in flow rate from a lower skin where the lift system, not the reservoir, limits the flow rate.

After this lesson you can

explain why a thin zone around the wellbore affects the flow rate so strongly, and name the causes of positive and negative skin
convert the skin factor into an additional pressure drop and back, in metric and oilfield units
calculate the skin of a zone of altered permeability with the Hawkins formula, and explain why the skin alone gives neither the depth nor the permeability of this zone
express the skin through the effective wellbore radius and the flow efficiency, and estimate how much flow rate a treatment can restore
break the measured skin down into components, and tell which of them can be removed

Why the near-wellbore zone decides

In radial flow all the fluid squeezes towards the wellbore through an ever smaller area. So the Darcy velocity (the speed of the flow through the rock) and the pressure gradient (how fast the pressure changes with distance) are greatest at the wall of the well. The pressure rises with distance following a logarithmic law. As the lesson on permeability shows, in a typical well the first few metres around the wellbore take more than half of the whole drawdown.

The main consequence is this: the properties of the rock in a narrow zone around the wellbore, the near-wellbore zone, affect the flow rate out of all proportion. Suppose the permeability in a ring half a metre thick has fallen several times. The pressure loss in this ring can then be greater than in the whole rest of the reservoir.

What changes the permeability around the wellbore

Process: Drilling and well killing (filling the well with heavy fluid to hold it under control)
What happens: mud particles plug the pores; the filtrate (the liquid part of the mud that soaks into the rock) makes clay aggregates swell and break up, and the loose particles lodge in the pore channels
Effect on inflow: impairment ( $S > 0$ )

Process: Cementing and perforating
What happens: cement filtrate penetrates the rock; the rock around the perforation tunnels (the holes shot through the casing) is crushed and compacted
Effect on inflow: impairment

Process: Production
What happens: fines (tiny particles) move towards the well, especially after water breakthrough; scale (mineral crust), wax and asphaltenes (heavy, sticky components of oil) are deposited; gas comes out of the oil at the wellbore when the pressure is below the bubble point pressure
Effect on inflow: impairment, often growing with time

Process: Water injection
What happens: particles carried in the water, and incompatibility of the injected water with the formation water (the two waters react and form deposits)
Effect on inflow: reduced injectivity (the well takes less water)

Process: Acid treatment
What happens: acid dissolves the contaminants and part of the rock around the wellbore
Effect on inflow: a positive skin gets smaller, sometimes $S < 0$

Process: Hydraulic fracturing
What happens: a fracture that carries fluid very easily extends tens of metres from the wellbore
Effect on inflow: strong improvement, $S$ as low as −4 to −6

Process	What happens	Effect on inflow
Drilling and well killing (filling the well with heavy fluid to hold it under control)	mud particles plug the pores; the filtrate (the liquid part of the mud that soaks into the rock) makes clay aggregates swell and break up, and the loose particles lodge in the pore channels	impairment ( $S > 0$ )
Cementing and perforating	cement filtrate penetrates the rock; the rock around the perforation tunnels (the holes shot through the casing) is crushed and compacted	impairment
Production	fines (tiny particles) move towards the well, especially after water breakthrough; scale (mineral crust), wax and asphaltenes (heavy, sticky components of oil) are deposited; gas comes out of the oil at the wellbore when the pressure is below the bubble point pressure	impairment, often growing with time
Water injection	particles carried in the water, and incompatibility of the injected water with the formation water (the two waters react and form deposits)	reduced injectivity (the well takes less water)
Acid treatment	acid dissolves the contaminants and part of the rock around the wellbore	a positive skin gets smaller, sometimes $S < 0$
Hydraulic fracturing	a fracture that carries fluid very easily extends tens of metres from the wellbore	strong improvement, $S$ as low as −4 to −6

This summary is qualitative. The lesson Formation damage and damage skin covers the mechanisms of damage and the ways to prevent it.

Exploration wells (wells drilled to find oil) are usually the most heavily damaged. Their reservoir pressure is poorly known, so engineers choose the density of the drilling fluid with a large margin. The pressure in the wellbore is then well above the reservoir pressure (a large overbalance), and the filtrate goes deeper into the formation. These wells are also more often drilled with water-based muds, which react more with clay minerals. In production wells the pressure is known, so the overbalance can be kept small and less harmful fluids can be chosen.

Skin factor and the skin pressure drop

To avoid describing the near-wellbore zone in every detail, we reduce its influence to a single number. Imagine that the whole change in permeability sits in an infinitely thin layer on the wall of the well. This layer is a “skin”, a film on the surface; that is where the name comes from. The reservoir beyond the layer is homogeneous. Across the layer itself the pressure drops abruptly by $\Delta p_s$ . This drop is the skin pressure drop.

The actual bottomhole flowing pressure of a working well, $p_{wf}$ , differs from the pressure $p_w$ that an ideal well would have at its wall at the same flow rate: $p_{wf} = p_w - \Delta p_s$ . The skin factor is this pressure drop counted in units of the typical pressure drop of radial flow, $qB\mu/(2\pi kh)$ :

Skin factor and the additional pressure drop

\Delta p_s = p_w - p_{wf} = \frac{qB\mu}{2\pi kh}\,S

where:

$\Delta p_s$ additional pressure drop in the near-wellbore zone; positive for damage, negative for improvement, Pa
$p_w$ pressure at the wall of an ideal well without skin at the same flow rate, Pa
$p_{wf}$ actual bottomhole flowing pressure of the working well, Pa
$S$ skin factor, —
$q$ flow rate at standard conditions; $qB$ is the flow rate at reservoir conditions, m³/s
$B$ formation volume factor of the fluid, m³/m³
$\mu$ fluid viscosity at reservoir conditions, Pa·s
$k,\ h$ permeability and net thickness of the reservoir beyond the near-wellbore zone, m², m

Units: SI (any consistent system of units)

Holds when

The zone of altered permeability is small compared with the drainage area, and the flow in it can be taken as steady-state at the current flow rate.
No fluid builds up in the thin zone, so $\Delta p_s$ follows the flow rate immediately and disappears when the well is shut in.
The flow is single-phase and obeys Darcy's law. If there are inertial losses, a term that grows with the flow rate is added to the skin.
The skin is always referred to the same $k$ and $h$ that describe the inflow in the reservoir.

The skin shows how many times the pressure loss in the near-wellbore zone is larger than the “unit” of radial flow, $qB\mu/(2\pi kh)$ . Since $\Delta p_s$ is proportional to $qB\mu$ , the ratio of the two does not depend on the flow rate or on the viscosity. It describes only the condition of the near-wellbore zone.

In other unit systems (2)

Metric oilfield units

\Delta p_s\,[\text{MPa}] = 1.866\,\frac{q\,[\text{m}^3/\text{d}]\;B\;\mu\,[\text{mPa·s}]}{k\,[\text{mD}]\;h\,[\text{m}]}\,S

$q$ in m³/d at standard conditions, $B$ in m³/m³, $\mu$ in mPa·s, $k$ in mD, $h$ in m, $\Delta p_s$ in MPa.

$1.866 = 1/(2\pi\cdot 0.0853)$ , where $0.0853$ is the constant of Darcy's law in these units. It comes from converting mD to m², MPa to Pa, mPa·s to Pa·s and seconds to days.

Oilfield units

\Delta p_s\,[\text{psi}] = 141.2\,\frac{q\,[\text{STB/d}]\;B\;\mu\,[\text{cP}]}{k\,[\text{mD}]\;h\,[\text{ft}]}\,S

$q$ in barrels of oil per day at standard conditions (STB/d), $B$ in rb/STB (reservoir barrels per stock-tank barrel), $\mu$ in cP, $k$ in mD, $h$ in ft, $\Delta p_s$ in psi.

$141.2 = 1/(2\pi\cdot 1.127\cdot10^{-3})$ .

When the near-wellbore zone is improved, $\Delta p_s < 0$ : the bottomhole pressure is higher than that of an ideal well at the same flow rate. A negative skin does not mean “negative permeability”. It is only a way of saying that the well works better than an ideal one. As a rule we do not calculate the skin in advance but measure it. Finding the skin is one of the main tasks of well testing.

Zone of altered permeability: the Hawkins formula

An infinitely thin layer is a convenient simplification. In reality the altered zone has a finite radius $r_s$ and its own permeability $k_s$ . If the zone is small compared with the drainage area, we can treat the flow through it as steady-state at the current flow rate. Compare two losses: the pressure loss in a zone of permeability $k_s$ , and the loss that would occur if the zone had the permeability of the reservoir. They differ by exactly $\Delta p_s$ . This gives the Hawkins formula:

Skin of a zone of altered permeability (Hawkins formula)

S = \left(\frac{k}{k_s} - 1\right)\ln\frac{r_s}{r_w}

where:

$k$ permeability of the reservoir, mD
$k_s$ permeability of the altered zone, mD
$r_s$ radius of the altered zone (from the well axis), m
$r_w$ well radius, m

Units: any consistent units: only the ratios $k/k_s$ and $r_s/r_w$ enter

Holds when

The altered zone is a cylinder around the wellbore with uniform permeability $k_s$ , and $r_s \ll r_e$ .
The well penetrates the whole thickness of the reservoir, and the flow in the zone is radial.
The flow is single-phase and obeys Darcy's law.

With damage ( $k_s < k$ ) the skin is positive. It grows in proportion to $k/k_s$ , but only logarithmically with the radius of the zone. With improvement ( $k_s > k$ ) the skin is negative, but it has a lower limit. Even when $k_s \to \infty$ , it does not fall below $-\ln(r_s/r_w)$ . This is as if the wellbore had been enlarged to radius $r_s$ .

CalculatedCalculated pressure around the well for the reservoir of the examples below. The flow rate is the same, 60 m³/d, and the pressure at the boundary of the drainage area is 20 MPa. Three cases are shown: without skin, with a damaged zone of radius 0.5 m, and with a treated zone of radius 1.2 m. The distance scale is logarithmic, so in a homogeneous reservoir the profile is a straight line. At the wall of the well, the difference between the bottomhole pressure and the pressure in the ideal case (no skin) is

\Delta p_s

The inverse problem (finding the cause from the result) has no single answer. A well test gives one number, $S$ , but there are two unknowns, $k_s$ and $r_s$ . For $r_w$ = 0.1 m, a skin of +5 fits both a two-fold reduction of permeability in a zone of radius about 15 m and a six-fold reduction in a zone of radius 0.27 m. We estimate the depth of the zone from other data: from resistivity tools with different depths of investigation, from the volume of reagent injected, or from laboratory tests on core (rock samples from the well).

We can calculate directly with the Hawkins formula when both quantities are known. One example is consolidating loose sandstone with resin (gluing the grains together). We measure the reduction in permeability on core, and we estimate the radius of the treated zone from the volume of fluid injected. Another example is gas coming out of the oil near a well when the bottomhole pressure is below the bubble point pressure. In the zone with free gas the permeability to oil falls to $k\,k_{ro}$ . Here $k_{ro}$ is the relative permeability to oil at that gas saturation (how well oil flows when gas takes up part of the pores). The boundary of the zone lies where the pressure equals the bubble point pressure. This is exactly why people try to keep the reservoir pressure above the bubble point pressure.

Worked exampleSkin of the invaded zone and its price in flow rate

Given (assumed data)

Reservoir permeability $k$: 60 mD
Invaded zone (the zone that the mud filtrate has soaked into): radius $r_s$ and permeability $k_s$: 0.5 m and 10 mD
Well radius $r_w$ (216 mm bit): 0.108 m
Radius of the drainage area $r_e$: 250 m
Thickness $h$ , oil viscosity $\mu$ , formation volume factor $B$: 15 m; 2.0 mPa·s; 1.15 m³/m³
Drawdown $\bar p - p_{wf}$: 4.0 MPa

Solution

Hawkins skin: $S = \left(\dfrac{60}{10} - 1\right)\ln\dfrac{0.5}{0.108} = 5\cdot 1.532 = 7.66$ .
Logarithmic term of the ideal well in pseudo-steady-state flow: $X = \ln\dfrac{250}{0.108} - \dfrac34 = 6.997$ .
Productivity indices from the metric formula with the constant 0.536 (see the section on productivity). Without damage: $J_{\text{ideal}} = \dfrac{0.536\cdot 60\cdot 15}{2.0\cdot 1.15\cdot 6.997} = 30.0$ . With damage: $J = \dfrac{0.536\cdot 60\cdot 15}{2.0\cdot 1.15\cdot(6.997 + 7.66)} = 14.3$ m³/(d·MPa).
Flow rate at a drawdown of 4.0 MPa: $q = 14.3\cdot 4.0 = 57$ m³/d instead of $120$ m³/d. Flow efficiency: $\text{FE} = \dfrac{6.997}{6.997 + 7.66} = 0.48$ .
Skin pressure drop: $\Delta p_s = 4.0\cdot\dfrac{7.66}{6.997 + 7.66} = 2.09$ MPa. So 52% of the drawdown is used up in a ring about 0.4 m thick.
Effective wellbore radius: $r_w' = 0.108\cdot\e^{-7.66}$ m $= 0.051$ mm.

Answer: The skin of the invaded zone is about 7.66. The well produces 57 m³/d, that is, about 48% of the flow rate of an undamaged well at the same drawdown.

What it means. A ring of rock less than half a metre thick takes more than half of the drawdown. If the reservoir limits the flow rate, and not the lift system, removing the damage (for example by an acid treatment) can roughly double the flow rate. An effective wellbore radius of hundredths of a millimetre shows clearly that the well works like a very narrow hole. The data in this example are assumed for illustration.

Effective wellbore radius

We can show the skin as a picture of a different well. In the inflow formula, replace the sum $\ln(r_e/r_w) + S$ by $\ln(r_e/r_w')$ . The result is a well without skin, but with a different radius: the effective wellbore radius:

Effective wellbore radius

r_w' = r_w\,\e^{-S}

where:

$r_w'$ effective radius: the radius of an ideal well without skin that has the same bottomhole pressure at the same flow rate, m
$r_w$ actual wellbore radius, m
$S$ skin factor, —

Units: any units of length (the same for $r_w$ and $r_w'$ )

Holds when

The skin does not change with time and does not depend on the flow rate.
The zone that the effective radius replaces is small compared with the drainage area ( $r_w' \ll r_e$ ).

A positive skin “squeezes” the well: at $S = +5$ it works like a wellbore almost 150 times smaller than the real one. A negative skin “widens” it: at $S = -3$ the radius is, so to speak, 20 times larger.

Skin in numbers: a well of radius 0.1 m, a drainage area of radius 300 m

Skin $S$: −5
Effective radius $r_w'$: 14.8 m
Flow efficiency $\text{FE}$: 3.22
Typical cause: long hydraulic fracture

Skin $S$: −3
Effective radius $r_w'$: 2.0 m
Flow efficiency $\text{FE}$: 1.70
Typical cause: short fracture, strongly deviated wellbore

Skin $S$: −1
Effective radius $r_w'$: 0.27 m
Flow efficiency $\text{FE}$: 1.16
Typical cause: successful acid treatment

Skin $S$: 0
Effective radius $r_w'$: 0.1 m
Flow efficiency $\text{FE}$: 1.00
Typical cause: ideal well

Skin $S$: +2
Effective radius $r_w'$: 13.5 mm
Flow efficiency $\text{FE}$: 0.78
Typical cause: mild damage, suboptimal perforation

Skin $S$: +5
Effective radius $r_w'$: 0.67 mm
Flow efficiency $\text{FE}$: 0.59
Typical cause: noticeable damage

Skin $S$: +10
Effective radius $r_w'$: 0.0045 mm
Flow efficiency $\text{FE}$: 0.42
Typical cause: severe damage

Skin $S$: +20
Effective radius $r_w'$: $2\cdot10^{-7}$ mm
Flow efficiency $\text{FE}$: 0.27
Typical cause: very severe damage or several causes at once

Skin $S$	Effective radius $r_w'$	Flow efficiency $\text{FE}$	Typical cause
−5	14.8 m	3.22	long hydraulic fracture
−3	2.0 m	1.70	short fracture, strongly deviated wellbore
−1	0.27 m	1.16	successful acid treatment
0	0.1 m	1.00	ideal well
+2	13.5 mm	0.78	mild damage, suboptimal perforation
+5	0.67 mm	0.59	noticeable damage
+10	0.0045 mm	0.42	severe damage
+20	$2\cdot10^{-7}$ mm	0.27	very severe damage or several causes at once

$\text{FE} = X/(X + S)$ with $X = \ln(300/0.1) - 3/4 = 7.26$ (see the next section). The causes are typical, not the only possible ones.

The effective radius also helps us to estimate the negative skin of a fracture. Take a vertical fracture of high conductivity (it carries fluid very easily) with a half-length $x_f$ (the distance from the wellbore to the tip of the fracture on one side). Its effective radius is close to $x_f/2$ . To the flow far from the fracture, it looks like a wellbore of very large diameter.

Worked exampleWhat a treatment can give: acid or a fracture

Given (assumed data)

Wellbore radius $r_w$ and drainage radius $r_e$: 0.108 m and 250 m
Acid treatment: radius of the zone $r_s$: 1.2 m, permeability in the zone 5 times the reservoir permeability
Hydraulic fracturing: half-length of the high-conductivity fracture $x_f$: 40 m

Solution

Acid treatment, by the Hawkins formula: $S = \left(\dfrac15 - 1\right)\ln\dfrac{1.2}{0.108} = -0.8\cdot 2.408 = -1.93$ .
The limit for such a zone (infinitely high permeability in it): $S_{\min} = -\ln\dfrac{1.2}{0.108} = -2.41$ .
Fracture: $r_w' \approx x_f/2 = 20$ m, so $S = -\ln\dfrac{r_w'}{r_w} = -\ln\dfrac{20}{0.108} = -5.22$ .
Flow efficiency: $\text{FE} = X/(X + S)$ , with $X = \ln\dfrac{250}{0.108} - \dfrac34 = 6.997$ . After the acid treatment it is $\dfrac{6.997}{6.997 - 1.93} = 1.38$ . After fracturing it is $\dfrac{6.997}{6.997 - 5.22} = 3.9$ .

Answer: An acid treatment of a shallow zone gives a skin of about −1.93 (it cannot go lower than −2.41 with any acid) and a productivity 1.38 times that of an ideal well. A fracture of half-length 40 m gives a skin of about −5.22 and a productivity roughly 3.9 times that of an ideal well.

What it means. Treating the near-wellbore zone cures damage, but it hardly makes the well better than an ideal one. Its ceiling is set by the radius of the treated zone. Only a fracture that reaches far beyond the near-wellbore zone gives a strongly negative skin. The estimate $r_w' \approx x_f/2$ applies to a high-conductivity fracture that is short compared with the drainage area. For fractures of lower conductivity the effective radius is smaller. The data in this example are assumed for illustration.

Skin, productivity and flow efficiency

Skin enters every radial inflow formula in the same way: it is added to the logarithmic term of the ideal well. Two cases are shown below. The first is steady-state flow with a constant pressure $p_e$ at the boundary. The second is pseudo-steady-state flow in a closed area, where the pressure falls at the same rate everywhere (Pseudo-steady-state flow and the shape factor). We get:

Radial inflow with skin

\begin{aligned} p_e - p_{wf} &= \frac{qB\mu}{2\pi kh}\left(\ln\frac{r_e}{r_w} + S\right)\\ \bar p - p_{wf} &= \frac{qB\mu}{2\pi kh}\left(\ln\frac{r_e}{r_w} - \frac34 + S\right)\end{aligned}

where:

$p_e$ pressure at the outer boundary in steady-state flow, Pa
$\bar p$ average pressure in the drainage area in pseudo-steady-state flow, Pa
$p_{wf}$ bottomhole flowing pressure of the working well, Pa
$r_e,\ r_w$ radius of the drainage area and radius of the well, m
$q,\ B,\ \mu,\ k,\ h,\ S$ flow rate at standard conditions, formation volume factor, viscosity, permeability, thickness, skin factor, m³/s, m³/m³, Pa·s, m², m, —

Units: SI (any consistent system of units)

Holds when

A homogeneous reservoir, a circular drainage area with the well at the centre.
The flow is single-phase and obeys Darcy's law. The well penetrates the whole thickness of the reservoir. Otherwise a component for imperfect penetration (the well opens only part of the layer) enters the skin.
The second formula is for the pseudo-steady-state regime, when the pressure disturbance has already reached the boundaries of the closed area.

The resistance of the system “reservoir + near-wellbore zone” has two parts, one after the other: the reservoir (the logarithmic term) and the near-wellbore zone ( $S$ ). For typical wells the logarithmic term is about 7–8. So a skin of the same size already halves the flow rate.

Productivity index with skin (pseudo-steady-state flow)

J = \frac{q}{\bar p - p_{wf}} = \frac{2\pi kh}{B\mu\left(\ln\dfrac{r_e}{r_w} - \dfrac34 + S\right)}

where:

$J$ productivity index with respect to the average reservoir pressure, m³/(s·Pa)
$q,\ \bar p,\ p_{wf}$ flow rate at standard conditions, average reservoir pressure and bottomhole flowing pressure, m³/s, Pa
$k,\ h,\ B,\ \mu,\ r_e,\ r_w,\ S$ as in the inflow formula above, m², m, m³/m³, Pa·s, m, m, —

Units: SI

Holds when

Pseudo-steady-state flow; in other regimes the logarithmic term changes, and the skin enters in the same way.

The productivity is directly proportional to the flow capacity $kh$ and inversely proportional to the viscosity. The skin, $r_e$ and $r_w$ stand side by side in the denominator. The radii sit under a logarithm, but the skin does not. That is why the skin, unlike the radii, can change the productivity several times over.

In other unit systems (2)

Metric oilfield units

J\,[\text{m}^3/(\text{d}\cdot\text{MPa})] = \frac{0.536\,k\,h}{\mu\,B\left(\ln\dfrac{r_e}{r_w} - 0.75 + S\right)}

$k$ in mD, $h$ in m, $\mu$ in mPa·s, $B$ in m³/m³; the flow rate is at standard conditions.

$0.536 = 2\pi\cdot 0.0853$ .

Oilfield units

J\,[\text{STB/(d·psi)}] = \frac{7.08\cdot10^{-3}\,k\,h}{\mu\,B\left(\ln\dfrac{r_e}{r_w} - 0.75 + S\right)}

$k$ in mD, $h$ in ft, $\mu$ in cP, $B$ in rb/STB.

$7.08\cdot10^{-3} = 2\pi\cdot 1.127\cdot10^{-3}$ .

The skin is an absolute measure. To decide “treat or not”, a relative measure is handier. This is the flow efficiency (FE; also called the productivity ratio): the actual productivity divided by the productivity of the same well without skin:

Flow efficiency

\begin{aligned}\text{FE} &= \frac{J}{J_{S=0}} = \frac{\ln\dfrac{r_e}{r_w} - \dfrac34}{\ln\dfrac{r_e}{r_w} - \dfrac34 + S}\\ &= \frac{\bar p - p_{wf} - \Delta p_s}{\bar p - p_{wf}}\end{aligned}

where:

$\text{FE}$ flow efficiency, —
$J,\ J_{S=0}$ actual productivity and productivity of the same well without skin, m³/(d·MPa)
$\Delta p_s$ skin pressure drop at the current flow rate, MPa
$\bar p - p_{wf}$ actual drawdown, MPa
$r_e,\ r_w,\ S$ radius of the drainage area, radius of the well, skin factor, m, m, —

Units: dimensionless; pressures in any identical units

Holds when

Pseudo-steady-state flow; both productivities refer to the same drainage area.
$\bar p$ is the average pressure in the drainage area. For a new well we use instead the extrapolated pressure from the build-up curve (the pressure found by extending the build-up curve to an infinitely long shut-in).

FE < 1 means that the well is damaged. FE > 1 means that it works better than an ideal well (after a treatment or hydraulic fracturing). The reciprocal $1/\text{FE}$ is called the damage ratio. It is the factor by which the flow rate grows at the same drawdown if we remove the skin completely. The second line follows from the definition: without skin, the same flow rate would need a drawdown smaller by $\Delta p_s$ .

What the measured skin is made of

A well test measures the total effect of everything that makes a real well differ from the ideal model, which is a vertical wellbore that penetrates the whole of a homogeneous reservoir. So the measured skin is the sum of several components:

Components of the measured skin

S = S_d + S_{\text{geom}} + S_{\text{compl}} + S_{\text{op}}

where:

$S$ measured (total) skin factor of the well, —
$S_d$ damage skin: a change in the permeability of the near-wellbore zone, —
$S_{\text{geom}}$ geometry of penetration: only part of the thickness is open, a deviated wellbore, a well displaced towards the boundary of the drainage area, —
$S_{\text{compl}}$ completion: the number, length and placement of the perforation tunnels, the crushed zone around them, a gravel pack (a filter of gravel placed around the well screen), —
$S_{\text{op}}$ operating effects: inertial losses that grow with the flow rate, and two-phase flow near the wellbore, —

Units: dimensionless quantities

Holds when

Simple addition is only an approximation, because the components affect one another. If only part of the thickness $h_w$ is open, the damage skin, counted over the whole thickness $h$ , grows by roughly a factor of $h/h_w$ . Shallow damage that the perforation tunnels pass right through hardly hinders the inflow.

An acid treatment or re-perforation removes only part of the skin. The components that come from the geometry of penetration change only if the well is built differently. They are also called pseudo-skins.

Components of skin and what can be done about them

Component: Damage $S_d$
Causes: drilling and cementing fluids, fines, scale, wax, asphaltenes
Sign: +
Can a treatment remove it?: yes: acid treatment, hydraulic fracturing that bypasses the zone

Component: Partial penetration, off-centre well
Causes: the flow converges on a short interval or on the edge of the area
Sign: +
Can a treatment remove it?: no: needs additional perforation or a different well design

Component: Deviated wellbore
Causes: inside the reservoir the wellbore is longer than a vertical well's
Sign: −
Can a treatment remove it?: —

Component: Perforation, gravel pack
Causes: few tunnels or short tunnels; a crushed zone around them; resistance of the pack
Sign: usually +; dense, deep perforation can give −
Can a treatment remove it?: partly: re-perforation

Component: Inertial losses
Causes: high velocities in gas wells and high-rate wells
Sign: +, grows with the flow rate
Can a treatment remove it?: no, but they are reduced by a larger inflow area (a fracture, more perforations)

Component: Two-phase flow near the wellbore
Causes: gas comes out of the oil below the bubble point pressure; in gas condensate wells, liquid condensate drops out of the gas near the wellbore
Sign: +, depends on the bottomhole pressure
Can a treatment remove it?: by maintaining the bottomhole and reservoir pressure

Component	Causes	Sign	Can a treatment remove it?
Damage $S_d$	drilling and cementing fluids, fines, scale, wax, asphaltenes	+	yes: acid treatment, hydraulic fracturing that bypasses the zone
Partial penetration, off-centre well	the flow converges on a short interval or on the edge of the area	+	no: needs additional perforation or a different well design
Deviated wellbore	inside the reservoir the wellbore is longer than a vertical well's	−	—
Perforation, gravel pack	few tunnels or short tunnels; a crushed zone around them; resistance of the pack	usually +; dense, deep perforation can give −	partly: re-perforation
Inertial losses	high velocities in gas wells and high-rate wells	+, grows with the flow rate	no, but they are reduced by a larger inflow area (a fracture, more perforations)
Two-phase flow near the wellbore	gas comes out of the oil below the bubble point pressure; in gas condensate wells, liquid condensate drops out of the gas near the wellbore	+, depends on the bottomhole pressure	by maintaining the bottomhole and reservoir pressure

Here is a practical rule. Before you plan a treatment, subtract from the measured skin the estimated components for imperfect penetration (Partial penetration and well deviation) and for perforation (Shaped-charge perforating). Then separate the skin that grows with the flow rate, using tests at several rates (Inflow at high rates: non-Darcy flow). A candidate for treatment is a well with a large damage skin. In Russian-language literature, these components of imperfection are traditionally expressed as coefficients of additional flow resistance, one for the degree and one for the character of penetration of the reservoir. In meaning, these are the same pseudo-skins.

The skin is not constant. After drilling and completion it usually decreases, because the well cleans itself of filtrate and particles. During production it can grow. The causes are fines moving towards the well after water breakthrough, scale deposits, and gas coming out of the oil at the wellbore. So we measure the skin again from time to time, from new tests.

How skin is determined in practice

We cannot measure skin on core or from a log (a record of measurements made down the well). It shows up only in the performance of the well. We find it from well tests: from the pressure drawdown curve after the well starts to flow (Pressure drawdown analysis), or from the pressure build-up curve after the well is shut in (Pressure build-up analysis).

The logic is the same in both cases. The slope of the straight section on the semilog plot (a plot with a logarithmic time axis) gives the flow capacity $kh$ . The position of this line relative to the bottomhole flowing pressure of the working well gives the skin. Let $m$ be the slope of the line per decimal logarithmic cycle (one tenfold step in time). Then $qB\mu/(2\pi kh) = 2m/\ln 10 \approx 0.869\,m$ , and the skin pressure drop comes straight from the test result:

Skin pressure drop from test results

\Delta p_s = 0.869\,m\,S

where:

$m$ slope of the semilog straight line per decimal logarithmic cycle (absolute value), MPa/cycle
$S$ skin factor from the same test, —
$\Delta p_s$ skin pressure drop at the flow rate of the test, MPa

Units: any pressure units (the same as for $m$ )

Holds when

We get $m$ and $S$ from one test, on a section of radial flow. $\Delta p_s$ refers to the flow rate of that test.

The formula turns the skin, which has no units, into something easy to grasp: how many megapascals of the drawdown go to the near-wellbore zone. The constant is $0.869 = 2/\ln 10$ .

Worked exampleSkin pressure drop and treatment potential from test data

Given (assumed data)

Slope of the semilog straight line $m$: 0.45 MPa per cycle
Skin factor from the test $S$: +6.0
Average reservoir pressure $\bar p$ and bottomhole flowing pressure $p_{wf}$: 21.0 and 15.5 MPa
Oil flow rate: 85 m³/d

Solution

Skin pressure drop: $\Delta p_s = 0.869\cdot 0.45\cdot 6.0 = 2.35$ MPa.
Drawdown: $\bar p - p_{wf} = 21.0 - 15.5 = 5.5$ MPa. Without skin, $5.5 - 2.35 = 3.15$ MPa would be enough for the same flow rate.
Flow efficiency: $\text{FE} = \dfrac{5.5 - 2.35}{5.5} = 0.57$ .
If we remove the whole skin and keep the bottomhole flowing pressure at 15.5 MPa, the flow rate grows by a factor of about $1/\text{FE} = 1.74$ , to 148 m³/d.

Answer: About 2.35 MPa is lost on the skin, which is 43% of the drawdown. FE ≈ 0.57, and the potential flow rate without skin is about 148 m³/d.

What it means. This is an upper estimate. It assumes that the whole skin is damage that can be removed, and that the lift system can lift the extra liquid. Before planning a treatment, we break the skin down into components. The data in this example are assumed for illustration.

Terms and symbols

Near-wellbore zone: The part of the reservoir around the wellbore, usually up to a few metres. Drilling, completion, production or treatment has altered its properties.
Skin factor $S$: A number, without units, for the additional resistance to inflow in the near-wellbore zone. $S > 0$ means impairment, and $S < 0$ means improvement.
Skin pressure drop $\Delta p_s$: The part of the drawdown that is used up in the near-wellbore zone, in excess of the losses in a homogeneous reservoir. It is proportional to the flow rate.
Effective wellbore radius $r_w'$: The radius of an ideal well without skin that has the same productivity: $r_w' = r_w\e^{-S}$ .
Flow efficiency (FE): The ratio of the actual productivity to the productivity of the same well without skin.
Pseudo-skin: The component of skin that comes not from a change in permeability but from the geometry of the flow: partial penetration, wellbore deviation, perforation.

Common mistakes and misconceptions

Wrong

“A skin of +10 means that the permeability at the well is 10 times lower than that of the reservoir.”

In fact

The skin combines the degree and the depth of the alteration. For $r_w$ = 0.1 m, a skin of 10 fits both a five-fold reduction of permeability in a zone of radius about 1.2 m and a twenty-fold reduction in a zone of about 0.17 m. The skin alone cannot tell these cases apart.

Wrong

“A negative skin is physically impossible — it is an interpretation error.”

In fact

A negative skin means that inflow is easier than in an ideal well. It happens after an acid treatment or hydraulic fracturing, and in a deviated wellbore. For wells with a hydraulic fracture, a skin of −3 to −6 is quite common.

Wrong

“The skin is large, so an acid treatment is needed.”

In fact

First break the skin down into components: acid cannot remove partial penetration, perforation or inertial losses. Also check whether the lift system limits the flow rate.

Wrong

“The skin is a constant characteristic of the well.”

In fact

The skin changes. It decreases as the well cleans up after completion. It grows when fines move towards the well, when scale is deposited, and when gas comes out of the oil at the wellbore. In gas wells the measured skin also grows with the flow rate.

In depth: advanced detail

Derivation of the Hawkins formula and of the effective radius

In the zone $r_w < r < r_s$ the flow is steady-state. By Darcy's law for radial flow, the pressure drop in it is $\dfrac{qB\mu}{2\pi k_s h}\ln\dfrac{r_s}{r_w}$ . If the permeability of the zone were that of the reservoir, the drop would be $\dfrac{qB\mu}{2\pi k h}\ln\dfrac{r_s}{r_w}$ . The additional pressure drop is the difference between the two:

$\Delta p_s = \dfrac{qB\mu}{2\pi h}\left(\dfrac{1}{k_s} - \dfrac{1}{k}\right)\ln\dfrac{r_s}{r_w} = \dfrac{qB\mu}{2\pi k h}\left(\dfrac{k}{k_s} - 1\right)\ln\dfrac{r_s}{r_w}.$ Dividing by $qB\mu/(2\pi kh)$ , we get the Hawkins formula. Beyond the zone the pressure is the same as in a homogeneous reservoir, because the same flow $q$ passes through every circle.

The effective radius follows from the identity $\ln\dfrac{r_e}{r_w} + S = \ln\dfrac{r_e}{r_w\,\e^{-S}}$ : a well with skin behaves like an ideal well of radius $r_w\e^{-S}$ .

Estimating the depth of filtrate invasion

When we drill with overbalance (the pressure in the well is higher than the reservoir pressure), the mud filtrate goes into the formation and forms an invaded zone. At first it goes in quickly, until a mudcake (a layer of mud solids) forms on the wall of the well. Then, while the mud circulates, the filtrate goes in at an almost constant rate, because the erosion of the cake balances its growth. After circulation stops, the cake thickens, and the inflow of filtrate gradually slows. Suppose the filtrate pushes the moveable oil ahead of it like a piston. Then the radius of the invaded zone follows from a material balance:

Radius of the filtrate invaded zone

r_{inv} = \sqrt{r_w^2 + \frac{Q_l}{\pi\,\phi\,(1 - S_{or} - S_{wc})}}

where:

$r_{inv}$ radius of the invaded zone, m
$Q_l$ total volume of filtrate that has entered, per unit length of wellbore, m³/m
$r_w$ well radius, m
$\phi$ porosity, fraction
$S_{or}$ residual oil saturation in the flushed zone (the zone where the filtrate has pushed the oil away), fraction
$S_{wc}$ connate (irreducible) water saturation, fraction

Units: SI (m, m³/m)

Holds when

Piston-like displacement; the reservoir is uniform over its thickness.
Usually $r_{inv}$ is much larger than $r_w$ , and the term $r_w^2$ can be left out.

For example, 0.05 m³ of filtrate per metre of wellbore, with $\phi$ = 0.2 and $1 - S_{or} - S_{wc} = 0.5$ , gives $r_{inv} = \sqrt{0.108^2 + 0.05/(\pi\cdot0.2\cdot0.5)} \approx 0.41$ m. This is an upper estimate of the radius of the damaged zone, because the permeability is not reduced in the whole flushed zone. Resistivity tools with different depths of investigation give an independent estimate.

Connections to other topics

Rock permeability — Darcy's law and radial flow, on which the concept of skin is built.
Pressure build-up analysis — how skin is found from a pressure build-up curve.
Pressure drawdown analysis — how to find skin from a pressure drawdown curve.
Formation damage and damage skin — mechanisms of damage to the near-wellbore zone and how to prevent it.
Acid treatments: principle, economics and candidate selection — how an acid treatment reduces damage skin.
Hydraulic fracturing: purpose and well selection — how a fracture gives a strongly negative skin.
Partial penetration and well deviation — pseudo-skins of partial penetration and of a deviated wellbore.
Inflow at high rates: non-Darcy flow — skin that grows with the flow rate, and tests at several rates.
Nodal analysis of the production system — when reducing the skin really does increase the flow rate.

Check yourself

1
A well of radius 0.1 m can suffer two kinds of damage: (a) permeability reduced three-fold in a zone of radius 1.5 m; (b) reduced 15-fold in a zone of radius 0.25 m. Which reduces the productivity more?
1. A.(b)
2. B.Cannot say without knowing the flow rate
3. C.(a): the zone is deeper
4. D.Equally
Show the answer
Correct answer: A. (b)
By the Hawkins formula, (a) gives $S = 2\cdot\ln 15 \approx 5.4$ , and (b) gives $S = 14\cdot\ln 2.5 \approx 12.8$ . The degree of permeability reduction enters the skin linearly, and the depth of the zone enters only through a logarithm.
2
Acid has treated a zone of radius 1 m around a wellbore of radius 0.1 m. What is the lowest skin such a treatment can give?
1. A.−2.3
2. B.−0.5
3. C.As low as desired, with a strong enough acid
4. D.−5
Show the answer
Correct answer: A. −2.3
As $k_s \to \infty$ the Hawkins formula gives $S \to -\ln(r_s/r_w) = -\ln 10 \approx -2.3$ . The treated zone cannot work better than a wellbore of radius $r_s$ . A fracture that reaches far beyond the near-wellbore zone is what gives a skin of −4 to −6.
3
A test at a flow rate of 100 m³/d gives a skin of +8 and a skin pressure drop of 3 MPa. What will the skin pressure drop be at 50 m³/d, and will the skin change?
Show the answer
If Darcy's law holds, the skin does not depend on the flow rate and stays at +8. The pressure drop $\Delta p_s$ is proportional to the flow rate, so it is halved, to 1.5 MPa. If the skin measured at different flow rates changed noticeably, that would point to inertial losses, which are typical of gas wells and high-rate wells.
4
A well has $\ln(r_e/r_w) - 3/4 = 7$ and a skin $S = +7$ . By what factor will the flow rate increase at the same drawdown if the skin is removed completely?
1. A.By a factor of 1.1
2. B.By a factor of 2
3. C.By a factor of 7
4. D.It will not change
Show the answer
Correct answer: B. By a factor of 2
$\text{FE} = 7/(7 + 7) = 0.5$ . The well gives half of what is possible, and removing the skin doubles the flow rate, as long as the lift system can lift the extra liquid.
5
A well penetrates a third of the reservoir thickness, and its skin from the pressure build-up curve is +9. Can we count on an acid treatment to bring the skin down to zero?
Show the answer
No. Part of the skin is the pseudo-skin of partial penetration: the flow converges on a short interval, and acid cannot remove this resistance. First we estimate the pseudo-skins of imperfect penetration and of perforation, and subtract them. A treatment can reduce only the damage skin that is left. Also, damage in a short interval “weighs” more: when we convert it to the whole thickness, its contribution grows by roughly a factor of $h/h_w$ .
6
Why can reducing the skin from +3 to 0 hardly increase the flow rate in a high-productivity well with narrow tubing?
Show the answer
In such a well most of the pressure drop is used up in lifting the liquid up the tubing, not in the reservoir. Reducing the skin raises the inflow performance curve, but the point where it crosses the lift curve shifts little. A treatment gives a large gain in wells where the reservoir and the near-wellbore zone limit the flow rate.

Updated: 26 October 2026