Introduction and Darcy S Law

PETE 4052 Well Testing Spring 2002

Lecture 4 Damage and Stimulation: The Skin Effect February 4

Damage and Stimulation: The Skin Effect

Outline

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

4.0 Synopsis

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 zero-thickness “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

4.1 Description of Damage and Stimulation

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 open-hole 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.

4.2 A Radial Composite Model for Damage and Stimulation

The simplest model for wellbore alteration is a radial composite model. The permeability is assumed to be altered from the formation permeability,, to the “altered” or “skin” permeability, , in a region (Fig. 4.1). For situations with ks < k (damage), this results in an increased pressure drop, . Note that is NOT the pressure drop across the 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, is positive whereas is negative for stimulation. I guarantee some students will confuse 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

(4.1)

Note that this pressure drop increases as rs increases and ks 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

(4.2)

Combining Eqns. (4.1) and (4.2), we get an equation for :

(4.3)

Examine the term . Note that will be positive when kks, and negative when kks. If the well is very damaged, and , then this term will be positive, and will tend to be large (and could approach infinity). If the well is stimulated, , and the and 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 will always be positive for a producing well, can be negative (for stimulation) or positive (for damage). The magnitude of the pressure drop also increases as the dimensionless skin radius increases due to the term . This makes sense: thicker skin, more effect. Finally, the pressure drop is scaled by the group . Thus, for example, higher flow rates imply higher .

Let’s examine this group, , more closely. Because the left hand side (LHS) of Eqn. (4.3) is a pressure, and the terms and are dimensionless, the dimensions of must be pressure. That is, scales the dimensionless groups ×. 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.

4.3 A Lumped Model for Damage and Stimulation: Skin Effect

As it turns out, well test analysis allows us to estimate but it does not allow us to estimate either ks or rs. 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 × reservoir engineers usually must work with another variable called skin and represented as s. Rewriting Eqn. (4.3),

(4.4)

The definition of skin in terms of the composite radial model is

(4.5)

and in terms of pressure drop s is

(4.6a)

in consistent units, or

(4.6b)

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 , 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

(4.7a)

in consistent units, or

(4.7b)

in field units. We will use these definitions extensively in well test design and analysis.

4.3 Inflow Equation Including Skin

We know the steady-state radial flow of incompressible liquids can be expressed as

Solving for

Using the concept of

(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.

4.4 Discussion

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 and radius ration .

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 (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 . For typical well spacings, 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.

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)],

(4.9)

Eqn. (4.9) applies to steady-state systems only. As noted by Horne, FE 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)]:

Rearranging,

(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.

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):

(4.11)

Thus, very long fractures will have large negative skins.

Page 6 of 13