In the above equation, we assume a perfect connection between the well and the porous medium. In practice, an additional pressure drop Δpskin exists, better known as the dimensionless skin value S:
In the oilfield units, we have:
The skin is proportional to KH/(qβμ), where q is the well rate (stb/d), β is the fluid formation volume factor, H is the net reservoir thickness (feet), K the reservoir permeability in the horizontal plane (mD) and μ the fluid viscosity (cp).
This additional pressure drop Δpskin has to be subtracted from the pressure P(rw,t) to obtain the well flowing pressure Pwf (t):
This skin value could be nicely integrated in the above first equation by using the wellbore effective radius rwe = rw e-S, instead of rw.
It is worth noticing that in a high KH reservoir, with low fluid viscosity, a high skin value does not necessarily mean a high pressure drop. The more permeable the reservoir, the higher the skin value.
The skin characterizes the well damage
A large pressure drop will represent a large well damage. Since Δpskin is not a very convenient term to use, the skin factor is then defined to characterize the well condition and the degree of connectivity between the well and the reservoir. The higher the damage, the higher the skin value.
For a damaged well: S >0
A flow restriction is present between the well and the reservoir, with an increase in pressure drop. The poor connection between the well and reservoir could be due to some insufficient or plugged perforations, some mud invasion, partial penetration, etc…
A large positive skin can represent an opportunity to increase the production rate or decrease the drawdown. Well treatments such as new perforations, acidification or hydraulic fracturing could be performed to reduce the skin factor and improve the near wellbore area.
For a stimulated well: S <0
In this case, the flow conditions are improved near the wellbore and the pressure drop is reduced.
We have: rwe > rw, the contact area between the well and the reservoir has been increased. Some small negative skin values can be explained by the well geometry, acidification or the presence of some natural fractures/fissures in the reservoir. Large negative skin values are created by hydraulic fractures.
The skin can vary between -7 and up to +100s. The lowest values could be explained by some acid-frac operations while the highest skin values by some partial penetration/limited perforations.
How to derive the skin factor from well test analysis
First, the radial flow regime has to be identified on the derivative plot with the stabilization line. This will result in a permeability-thickness KH value, a total skin value and a radius of investigation.
If the derivative plot is too noisy, the superposition plot could be used. From the radial flow straight line, a total skin value is obtained.
The skin value has an uncertainty of +/- 0.5 and it could then be rounded to one decimal place, for example S= +3.3 with the above example.
The PBU tests (shut-ins) should share the same stabilization on the derivative, indicative of radial flow regime (if this is not the case, then there is an issue with the rate measurement/allocation or a change in reservoir performance).
Then by looking at the changes in ΔP plots, we can monitor the changes in skin or damage over time. If the ΔP plots are shifted upwards, the skin is increasing over time. This could be due to some blockage, plugging (fines accumulation, scale deposit, hydrates, wax, debris, etc) or a gas break out at the perforations (condensate drop out at the perforations for gas wells), etc…
Different skin elements
The above definition of the skin applies for a fully penetrated vertical well in a homogeneous reservoir with isotropic permeability. In this case, the total skin is equal to the wellbore skin (also called perforation skin, infinitesimal skin or mechanical skin).
For different types of wells and reservoirs, various flow regimes (geometries) can be observed and several skin factors can be defined.
Wells with Partial Penetration/ Limited Perforations
For a well with limited perforations or partial penetration, three types of flow geometries are usually observed along the reservoir: a radial flow regime across the producing well segment, a spherical flow then a radial flow regime across the entire reservoir thickness.
The total skin is equal to:
With h the entire net reservoir thickness, hP the limited perforation height, Sw the wellbore damage. With high values of h / hP (small producing well segment), the wellbore damage effect is accentuated.
Sg is the geometrical skin. This positive skin value accounts for the extra pressure drop that is created as the flowlines converge towards the flowing section of the well.
When the total skin is higher than 20-30, the cause could be partial penetration or limited perforations, even if a spherical flow is not visible (it could be masked by some wellbore storage effect or the test duration could be too short). As we will see later on, this high skin could also be created by some pressure loss in the tubing, when a gauge is located at a shallow position.
Fractured Wells with “Fracture-skin”
Some damage could be present around a hydraulic fracture, with the presence of a region of reduced permeability due to the frac fluid losses (fluid loss damage). Some damage could also be located within the fracture itself (choked fracture).
Fracture skin values are usually quite small, lower than 0.5. Since the total skin is a better understood term, it is recommended to convert the fracture-skin value into a total skin with the graph below from SPE 10179.
Let’s assume that the results from pressure transient analysis show a fracture-skin Sf = 0.3. Then:
Looking at the above graph, this gives us :
And therefore the total skin value associated to the hydraulic fracture is:
With a damaged fracture, some wellbore storage effect may be visible with a unit-slope straight line at the beginning of the derivative. The fracture behaviour may then be observed after the wellbore storage effect or may be entirely masked by it. An example is shown below.
Gas and Gas Condensate Wells
Due to the high gas velocity, the flow near the wellbore could become turbulent in gas and gas condensate wells. This turbulence can create an additional pressure drop Dq, with D the non-Darcy flow coefficient (D/Mscf).
The total skin is then: S= SDarcy + Dq.
The non-Darcy skin Dq is the skin due to the turbulence, also called turbulent skin. The factor D can be evaluated with several rate periods, from a simple step rate test.
Depending on the deviation angle, three different flow geometries can be observed around a horizontal well: a vertical radial flow regime along the drain length, an intermediate flow regime (spherical up to linear flow regime) and the horizontal radial flow regime.
For a horizontal well, the total skin is equal to:
Sg is the geometrical skin (that can be positive or negative in this case). This accounts for the extra pressure drop that is created as the flowlines converge towards the flowing section of the well.
h is the net reservoir thickness, L the horizontal length, Kh the horizontal permeability and Kv the vertical permeability.
With the non-Darcy skin, the total skin can be written as:
We can note that for long horizontal wells (h/L << 1) or high vertical permeability (Kh/Kv << 1), the wellbore damage effect is reduced.
There are some additional skin elements associated with heterogeneous reservoirs, for example some skin factors due to a composite behaviour (changes in reservoir mobility and/or storativity), due to a dual-porosity behaviour, etc…
Non-uniform skin distribution in multi-layer reservoirs
A well in a multi-layer reservoir can have several perforation intervals with different skin values:
In this case, the skin factor is defined for each perforation interval using its rate QP and length HP.
A non-uniform skin distribution along the perforation intervals may create some crossflow in the reservoir and other multilayer effects.
A non-uniform skin distribution along the wellbore may also create a “false” derivative stabilization that could be mistakenly taken as radial flow regime. Particular care should be taken during well test design and analysis studies.
Is the skin always representative of the well damage ?
Well test analysis assumes that the pressure gauge is located near the well perforations. If this is not the case and the gauge is located in the tubing at some distances away from the perforations, then the total skin will account for the additional friction loss (pressure drop) along the tubing, below the gauge.
For shallow gauges, this could account for some high positive skin values, when in fact the well may not be damaged. To obtain the correct skin and turbulence factors, the data should be corrected from the pressure loss in the tubing. This will be the subject of another post.