Miembros de la plana gerencial y cambios en el periodo informado

Modern well perforating is done with perforating guns that are attached either to a wireline or to tubing or coiled tubing. Figure 6-13 shows a schematic of a gun system with the shape charges arranged in a helical pattern. This pattern allows good perforation density with small phasing (i.e., the angle between adjoining perforations).

Figure 6-13. Perforating gun string. (Courtesy of Schlumberger.)

The perforating string contains a cable head, a correlation device, a positioning device, and the perforation guns. The cable head connects the string to the wireline and at the same time provides a weak point at which to disconnect the cable if problems arise. The correlation device is used to identify the exact position with a previously run correlation log, and frequently it locates casing collars. The positioning device orients the shots toward the casing for more optimum perforation geometry. The perforating guns are loaded with shape charges, which consist of the case, the explosive, and the liner, as shown in Figure 6-14. Electric current initiates an explosive wave; the sequences of the detonation process are shown in Figure 6-14. Perforations with a diameter between 0.25 and 0.4 in. and a length between 6 and 12 in. are typically created. Significantly longer perforations can be created with special charges in some formations.

Figure 6-14. Detonation process of a shaped charge. (Courtesy of Schlumberger.) Perforating is often done underbalanced; that is, the pressure in the well is less than the reservoir pressure at the moment the perforations are created. This facilitates immediate flow-back following the detonation, carrying the debris out of the perforations and resulting in a cleaner perforation cavity. The dimensions, number, and phasing of perforations have a controlling role in well performance.

6.6.1.1. Calculation of the Perforation Skin Effect

Based on detailed finite element simulations, Karakas and Tariq (1988) presented an empirical model of the perforation skin effect, which they divide into components: the planar flow effect, s_H; the vertical convergence effect, s_V; and the wellbore blockage effect, s_wb. The total perforation skin effect is then

Figure 6-15 gives all relevant variables for the calculation of the perforation skin. These include the well radius, r_w, the perforation radius, r_perf, the perforation length, l_perf, the perforation phase angle, θ, and, very importantly, the distance between the perforations, h_perf, which is exactly inversely

proportional to the perforation density (e.g., two shots per foot (SPF), result in h_perf = 0.5 ft). Below, the method of estimating the individual components of the perforation skin is outlined.

Figure 6-15. Well variables for perforation skin calculation. (From Karakas and Tariq, 1988.)

6.6.1.2. Calculation of sH

where is the effective wellbore radius and is a function of the phase angle θ:

The constant a_θ depends on the perforation phase angle and can be obtained from Table 6-1. This skin effect is negative (except for θ = 0), but its total contribution is usually small.

Table 6-1. Constants for Perforation Skin Effect Calculation From Karakas and Tariq (1988).

6.6.1.3. Calculation of sV

To obtain s_V, two dimensionless variables must be calculated:

where k_H and k_V are the horizontal and vertical permeability values, respectively, and

The vertical pseudoskin is then

with and

The constants a₁, a₂, b₁, and b₂ are also functions of the perforation phase angle and can be obtained from Table 6-1. The vertical skin effect, s_V, is potentially the largest contribution to s_p; for small

perforation densities (i.e., large h_perf), s_V can be very large.

6.6.1.4. Calculation of swb

For the calculation of s_wb, a dimensionless quantity is calculated first:

Then

The constants c₁ and c₂ can also be obtained from Table 6-1.

Example 6-6. Perforation Skin Effect

Assume that a well with r_w = 0.328 ft is perforated with 2 SPF, r_perf = 0.25 in. (0.0208 ft), l_perf = 8 in.

(0.667 ft), and θ = 180°. Calculate the perforation skin effect if k_H/k_V = 10.

Repeat the calculation for θ = 0° and θ = 60°.

If θ = 180°, show the effect of the horizontal-to-vertical permeability anisotropy with k_H/k_V = 1.

Solution

From Equation (6-43) and Table 6-1 (θ = 180°), Then, from Equation (6-42),

From Equation (6-44) and remembering that h_perf = 1/SPF,

and

From Equations (6-47) and (6-48) and the constants in Table 6-1, and

From Equation (6-46),

Finally, from Equation (6-49),

and with the constants in Table 6-1 and Equation (6-50), The total perforation skin effect is then

If θ = 0°, then s_H = 0.7, s_V = 3.6, s_wb = 0.4, and therefore s_p = 4.7.

If θ = 60°, then s_H = –0.9, s_V = 4.9, s_wb = 0.004, and s_p = 4.

For θ = 180° and k_H/k_V = 1, s_H and s_wb do not change; s_V, though, is only 1.2, leading to s_p = 0.9,

reflecting the beneficial effects of good vertical permeability even with relatively unfavorable perforation density (only 2 SPF).

Example 6-7. Perforation Density

Using typical perforation characteristics such as r_perf = 0.25 in. (0.0208 ft), l_perf = 8 in. (0.667 ft), θ = 120°, in a well with r_w = 0.328 ft, develop a table of s_V versus perforation density for permeability anisotropies k_H/k_V = 10, 5, and 1.

Solution

Table 6-2 presents the skin effect s_V for perforation densities from 0.5 SPF to 4 SPF using Equations (6-44) to (6-48). For the higher perforation densities (3–4 SPF), this skin contribution becomes small. For low shot densities, this skin effect in normally anisotropic formations can be substantial. For the well in this problem, s_H = –0.7, and s_wb = 0.04.

Table 6-2. Vertical Contribution to Perforation Skin Effect

6.6.1.5. Near-Well Damage and Perforations

When there is formation damage around a cased, perforated completion, the combined effect of the perforation skin factor and the damage skin factor can be much greater than the sum of these separate effects. This is because the converging flow to the perforations creates a high-pressure drop if the permeability is reduced in this region. Karakas and Tariq (1988) have also shown that damage and perforations can be characterized by a composite skin effect.

if the perforations terminate within the damage zone (l_perf < r_s). In Equation (6-61), (s_d)_o is the open-hole equivalent skin effect given by Hawkins’ formula [Equation (6-4)]. If the perforations terminate outside the damage zone, then

where is evaluated at a modified perforation length, , and a modified radius, . These are

and

These variables are used in Equations (6-41) to (6-50) for the calculation of the skin effects contributing to the composite skin effect in Equation (6-62).

6.6.1.6. Perforation Skin Factor for Horizontal Wells

The impact of horizontal to vertical permeability anisotropy is different for perforations in a horizontal well than in a vertical well. In both cases the pressure drop associated with flow to the perforation cavity depends on the orientation of the perforation relative to the orientation of the permeability anisotropy. Because of the vertical permeability often being significantly lower than the horizontal permeability, the skin factor for a perforated horizontal well completion can be different from that of a vertical well. Perhaps more significantly, a horizontal perforated completion’s productivity depends on the orientation of the perforations relative to the permeability field. In a formation with low vertical permeability (high I_ani), perforations oriented up and down will be more productive than perforations oriented horizontally. Following a similar approach to that of Karakas and Tariq, Furui et al. (2008) developed skin factor models for perforated horizontal wells that include this perforation orientation effect. The reader is referred to their work for more details.