PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
0.
Synopsis
1.
Description of Damage and Stimulation
2.
A Radial Composite Model for Damage and Stimulation
3.
A Lumped Model for Damage and Simulation: Skin Effect
4.
Inflow Equation Including Skin
5.
Discussion
Related reading
Dake: p 115-121.
Horne: Section 2.3, p. 12-16 (attached)
We have discussed radial and linear flow in composite systems in Lecture 3. When the region of alteration is very small, it may be necessary and useful to idealize the altered region as a zerothickness “skin.” Skins are used to describe both “damage” and “stimulation”.
Key concepts:

Representation of damage or stimulation as an altered region around the wellbore

Pressure drop across the altered zone

Idealization of the altered zone as a zero-thickness skin

Definition of skin

Dimensionless pressure

Flow efficiency

Apparent wellbore radius
The processes of drilling, completing and producing an oil or gas well include many mechanical, hydraulic, and chemical processes. Many wells are drilled overbalanced, so that drilling fluids migrate into the near-well area. The fine particles in the muds may plug pore throats, or the filtrate may react chemically with clays in the formation – either of these processes can reduce the near-well permeability dramatically. Completions may further reduce the productive capacity of the well: the well may be cased and perforated (reducing the inflow area compared to an openhole completion), partially penetrating (reduced thickness for inflow), or internal gravel-packed
(pressure loss through perforations, gravel, and screen). On the other hand, the pressure-drop in the near-well area can sometimes be increased. This could be accomplished by fracture treatments or acid treatments. Attempts to lower the pressure drop in the near-well area are often called
“stimulation.”
We will present some sketches of these situations in the lecture.
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PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
The simplest model for wellbore alteration is a radial composite model. The permeability is assumed to be altered from the formation permeability, permeability, k , to the “altered” or “skin” k s
, in a region r w
 r
 r s
(Fig.
4.1). For situations with k s
< k (damage), this results in an increased pressure drop,
 p s
. Note that
 p s is NOT the pressure drop across the
Figure 4.1
– From the centerline (CL), the wellbore extends to r w
. A region of altered permeability, k s
, extends r w
to the skin radius, r s
. The unaltered permeability, k, then extends to the outer radius, r e
. From Horne.
skin region! It is the change in pressure drop for the composite model (the model with altered permeability) compared with the model with no altered permeability region. For damage,
 p s
is positive whereas
 p s is negative for stimulation.
I guarantee some students will confuse p ( r s
)
 p
  w
 p s with
. Look at Figure 4.1, and make certain that you understand the difference!
We can now write expressions for the pressure drops using our knowledge of the radial flow equation and series flow. The pressure drop across the skin region is
 p ( r s
)
 p ( r w
)
 s
 q

2
 k s
B h ln

 r r w s

 .......................................... (4.1)
Note that this pressure drop increases as r s
increases and k s
decreases: this makes senses, because thicker, lower permeability skin zones cause more pressure drop, and more damage. If the permeability had not been altered, the pressure drop would be
 p ( r s
)
 p ( r w
)

0
 q

B
2
 kh ln

 r s r w

 ........................................... (4.2)
Combining Eqns. (4.1) and (4.2), we get an equation for
 p s

 p ( r s
)
 p ( r w
) s p ( r s
 p s
:
)
 p ( r w
)
0

 q

B
2
 h ln


 r r w s






1 k s

1 k 


...................................... (4.3)
Examine the term

 k k s
 q

B
2
 k h ln


 r r w s





 k k s

1

 . Note that
 p s

1


 will be positive when k > k s
, and negative when k < k s
.
If the well is very damaged, and k s
 k , then this term will be positive, and
 p s will tend to be large (and could approach infinity). If the well is stimulated, k s
 k , and the and

 k k s

1

 can be no smaller than -1. This is an important point: the amount of damage is theoretically unlimited, but the maximum possible stimulation is limited. The pressure drop p ( r s
)
 p
  w
will always
Page 2 of 13

PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4 be positive for a producing well,
 p s can be negative (for stimulation) or positive (for damage).
The magnitude of the pressure drop also increases as the dimensionless skin radius

 r r w s

 increases due to the term r s r w



. This makes sense: thicker skin, more effect. Finally, the pressure drop is scaled by the group q

B
2
 kh
. Thus, for example, higher flow rates imply higher
 p s
. ln



Let’s examine this group, a pressure, and the terms q

B
2
 kh
, more closely. Because the left hand side (LHS) of Eqn. (4.3) is ln


 r r w s



and

 k k s

1

 are dimensionless, the dimensions of q

B
2
 kh must be pressure. That is, q

B
2
 kh
scales the dimensionless groups ln


 r s r w



×

 k k s

1

 . The pressure drop is proportional to this group; increasing q has the same effect as decreasing h or k by the same factor. We will use this scaling later in the course, and in the discussion of skin below: it is the basis of dimensionless pressure for radial flow.
As it turns out, well test analysis allows us to estimate
 p s
but it does not allow us to estimate either k s or r s
. These would be nice to know, it is just that the time scales and physical limitations of well tests usually prevent their estimation. For this reason, instead of the product ln


 r r w s



×

 k k s

1

 reservoir engineers usually must work with another variable called skin and represented as s . Rewriting Eqn. (4.3),
 p s

 q

B
2
 k h ln


 q

B s
2
 k h r s r w





 k k s

1 


................................................ (4.4)
The definition of skin in terms of the composite radial model is s
 ln

 r r s w



 k k s

1

 ..................................................... (4.5) and in terms of pressure drop s is s

2
 kh q

B
 p s
........................................................ (4.6a) in consistent units, or s

0 .
00708 kh
 p s q

B
................................................... (4.6b)
Page 3 of 13

PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4 in field units.
We can use Eqn. (4.5) to obtain a skin value if we have a model for the radial distribution of permeability, whereas we will use Eqn. (4.6) to estimate s from
 p s
, which can be inferred from a well test.
Skin as a Dimensionless Pressure
The skin factor s is dimensionless. In fact, it can be thought of as the dimensionless pressure drop due to near-well permeability alteration. In radial flow, the dimensionless pressure and dimensional pressure are related by p
D

2
 kh q

B
 p ....................................................... (4.7a) in consistent units, or p
D

0 .
00708 kh
 p .................................................. (4.7b) q

B in field units. We will use these definitions extensively in well test design and analysis.
We know the steady-state radial flow of incompressible liquids can be expressed as q

2

 kh
B
( p ln


 r r p w w


)
Solving for ( p
 p w
),
( p
 p w
)
 q

B
2
 kh ln

 r r w


Using the concept of
 p s
( p
 p w
)

( p
 p w
)
 q

B
2
 k h ln


 q

B
2
 k h ln


 r r w r r w



  p s



 q

B
2
 k h s
( q p

 p w
)
 q
2


B k h

 
 ln



2
 k h (

B 
 
 ln


 p r r w



 p w
)
 s 
 
 r r w



 s 
 

........................................... (4.8)
Skin is simply added to the log term in the denominator of the inflow equation. So we can
“visualize” s as a sort of additional distance that the fluid must flow. Of course, it is actually dimensionless.
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PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
Range of Skin Values
Skin values can easily be computed using Eqn. (4.5). Such a plot is shown in Figure 4.2. The most important thing to note is how very large the positive (damage) skins can be; the absolute value of the stimulated skins is very small in comparison (for the same permeability ratio k s
/ k and radius ration r s
/ r .
225
200
175
150
125
Skin
100
75
50
200-225
175-200
150-175
125-150
100-125
75-100
50-75
25-50
0-25
-25-0
25
0.01
0
0.1
-25
1
Permeability Ratio
8
4
100
10
2
Radius Ration
1.4
1.2
1.1
Figure 4.2
– Skin as a function of size and permeability of altered zone.
This behavior is easy to understand if we consider the pressure profiles. Rather than looking at the profiles in r (Fig. 4.1), it is easier to plot them in ln( r ) (Fig 4.3). Note that the profiles take a different form if we assume constant rate versus constant pressure drop. Take a while to study this diagram; think about it and make sure you understand it.
Effect of Skin on Rate
If we examine the radial inflow equation with skin [Eqn. (4.8)], we can see flow rate for a given available pressure drop is inversely related to


 ln

 r r w


 s



. For typical well spacings, r e
/ r w

2000 so than the logarithm will have a value of about 8 (note that our analysis isn’t very sensitive to the ratio because we are taking its log). This means that a skin value of 8 roughly cuts the flow rate in half, or of -4 will roughly double the flow rate. Keep in mind that this simple analysis does not consider tubing pressure drops.
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PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
Figure 4.3 Radial pressure profiles. The vertical axis is pressure, the horizontal axis is the log of radius. The left side of the figure is the well, the right side is the outer boundary. The hatched region has altered permeability.
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PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
Flow Efficiency
The flow efficiency of a well is simply the ratio of its unaltered flow capacity to it actual flow capacity. This is [from Eqn. (4.8)],
F
E
 q ( q ( s ) s

0 )
 ln


 ln


 r r e w r e r w






 s
.......................................................... (4.9)
Eqn. (4.9) applies to steady-state systems only. As noted by Horne, F
E
is harder to interpret in general (for example, for transient systems). It is usually more consistent to use s , but flow efficiency can be a useful and simple-to-explain quantification of rate change due to damage or stimulation.
Apparent Wellbore Radius
We can also express the effect of skin as an equivalent wellbore radius, using the radial inflow equation with skin [Eqn. (4.8)]:
2
 kh
 p

2
 kh
 p ln

 r e r e


 s ln

 r w a r e


Rearranging, ln


 r e r wa r r r r r wa wa w e e a



 ln


 r r w e

 exp



 ln


 e s


 r r e w


 r r w e
 r w e
 s



 s



 s 
 

................................................. (4.10)
Positive skins cause an additional resistance; this effect is similar to reducing the wellbore radius.
Conversely, negative skins are analogous to increasing the wellbore radius.
Page 7 of 13

PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
Approximation for Fractures
The apparent wellbore radius of a infinite-conductivity fracture (we will discuss the ideas of uniform flux , finite-conductivity , and infinite-conductivity later in the course) can be related to the fracture half-length and thus to the skin (Earlougher, p. 154): r wa
 x f
2 e
 s s

 x f
2 r w
 ln


 x f
2 r w



........................................................ (4.11)
Thus, very long fractures will have large negative skins.
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PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
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PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
Page 10 of 13

PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
Page 11 of 13

PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
Page 12 of 13

PETE 4052
Lecture 4
Well Testing
Damage and Stimulation: The Skin Effect
Spring 2002
February 4
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