Hawkins’ formula. While the skin effect is dimensionless, the associated dmage zone is not.Figure 5-1 is a typical depiction of the near-wellbore condition, with rs and ks being the penetration of damage and permeability, respectively. Outside this zone the reservoir remains undisturbed, with permeability k. A well-known equation relating the skin effect and the above variables has been presented by Hawkins (1956) and is frequently referred to as Hawkins’ formula. Figure 5-2 provides an easy means for the development of this relationship. If the near-wellbore permeability is the reservoir permeability (i.e., no damage), then a steadystate pressure drop between the outer boundary pressure (ps) and the well would result in a pwf,ideal given by 5-1 If, thoufh, the near-wellbore permeability is altered to ks, then the real bottomhole pressure is related by 5-2 The difference between pwf,ideal and pwf,real is exactly the pressure drop due to the skin effect, Δps, which was given in Chapter 2 by Eq. (2-12). Therefore, from Eqs. (5-1), (5-2), and 5-3 EXAMPLE 5-1 Permeability impairment versus damage penetration. Assume that a well has a radius rw equal to 0.328 and a penetration of damage 3 ft beyond the well (i.e. rs=3.328 ft). What would be the skin effect if the permeability impairment results in k/ks equal to 5 and 10, respectively. What would be the required penetration of damage to provide the same skin effect as the latter case but with k/ks=5? Solution: From Eq. (5-4), k/ks=5, and the given rs and rw, 5-5 For k/ks=10 and rs=3.328 then, However, if s=20.9 ad k/ks=5, then similarly, s=20.9. 5-6 This exercise suggests that permeability impairment has a much larger effect on the value of the skin effect tha the penetration of damage. Except for a phase change-dependent skin effect, a penetration of damage such as ghe one calculated in Eq. (5-6) is impossible. Thus, skin effects derived from well tests (frequently ranging between 5 and 20) are likely to be caused by substantial permeability impairment very near the well. This is a particularly important point in the design of matrix stimulation treatments. EXAMPLE 5-2 Pressure drop in the near-wellbore zone versus in the reservoir The skin effects calculated in Example 5-1 for the 3-ft damage zone are 9.51 and 0. sc+θ is the skin due to partial completion and slant. after reopening the well. much larger than the non-ratedependent skin effect.328 ft.and rate-dependent effects. The rate-dependent effect has been discussed in Chapter 4 in conjunction with the turbulence in high-rate gas producers. This is the proper manner for the field determination of D and the forecast of the impact of the ratedependent skin of future well production. causing a reduction in the gas permeability. s. Thus. THE SKIN COMPONENTS. Phase-dependent skin effects are associated with phase changes because of the near-wellbore pressure gradient. In the case of oil wells. (The diffefence will be in the reservoir).3 and 20. ln re/rw=9. where liquid is formed around the well. Assume that A=640 acres (re=2980 ft). Subsequent section will discuss the mechanical skin components. in certain instances. at a constant pe-pwf. consists of a number of components.. as can be seen readily from Eq. (2-13). if the flowing bottom hole pressure is below the bubble-point pressure. Solution: The ratio of the pressure drop due to damage within the near-wellbore zone to the total pressure drop is proportional to s/(ln(re/rw)+s) (for steady-state flow). from a well test. the gas . and therefore 5-7 where sd is the damage skin. causing a reduction in the effective permeability to oil even if the gas phase is not mobile.9 suggesting that the portions of the total pressure drop due to damage would be 0. an apparent skin. compare the portions of the pressure drop due to damage within the near-wellbore zone versus the total pressure drop. For re=2980 ft and rw=0..With the skin effects calculated in Example 5-1. respectively. and sp is the perforation skin effect. A similar phenomenon can be observed in the case of gas retrograde condensate reservoir.70. This quantity well be largely constant for almost all drainage/wellbore radius combinations. Generally these can be added together. where D is the non-Darcy coefficient (see Section 4-4).1. The skin effect extracted from a well test in a high-rate gas well is likely to be larger and. Possible elimination of these skin effects. These pseudo-skins include all phase.g. 1973. 5-3 of s’ versus q suggests that s is the intercept and D is the slope. Several authors (Fussell. Cvetkovic et al. s’ can be obtained that is equal to 5-8 Test performed at several different rates can be used t isolate the skin effects. A version of Hawkins’ formula with k/ks substituted by the ratio of the effective (or relative) permeabilities can be used. This skin effect is equal to Dq. 1990) have studied the process of liquid condensate deposition with time an have shown that permeability impairment to gas in gas condensate reservoirs is not eliminated following a shut-in. in the case of a gas condensate reservoir much of the formed condensate will not reenter the gas. Following is a discussion of these skin effects. Thus. would result in production rate increases of 104% and 233% respectively. as the pressure builds up when the well is shut in). A plot such as the one shown in Fig. While in the case of gas that is formed in an oil reservoir the gas will reenter solution at an elevated pressure (e. The total skin effect for a well. (It can also affect very high-rate oil wells). This is a particularly adverse occurrence. then a gas saturation will form. s. All “pseudo-skins” are grouped together within the summation sign. (1975) solved the problem semi analytically and presented tables of these skin effects for various combinations of partial completion. If the completed interval is 75% of the reservoir height or more. respectively. Phase. h is the reservoir height. the problem will be aggravated further. and rw is the well radius. The smaller the perforated interval compared to the reservoir height and the more skewed the completion. hD (=h/rw) equal to 100 and 1000. partial penetration may be created to form early-time spherical flow to allow the calculation of the vertical permeability. Sc+θ. In certain modern reservoir testing practices. especially associated with fractures (choke fracture face) or fracture-to-well contact as in the case of a largely vertical fracture intersecting a horizontal well transversely. and well deviation. The larger the angle of slant. 5-4 SKIN FROM PARTIAL COMPLETION AND SLANT. the height that is open to the formation is smaller than the reservoir height. this skin effect becomes negligible. zw is the elevation of the perforation midpoint from the base of the reservoir. reflecting the longer penetration of flow line distortion. Sp) are bypassed and have no impact on the posttreatment well performance. the larger the skin effect would be. EXAMPLE 5-3 Partial penetration and slant skin effect . Tables 5-1 and 5-2 give the results for reservoir dimensionless thicknesses. (5-7) are those that cause an alteration of the flow near a vertical or inclined well I a radial reservoir. The composite skin effect. and the composite skin from partial completion and slant is denoted by sc-θ. are listed. This “huff and puff” operation can be repeated periodically. Sometimes this is known as partial penetration.and rate-dependent skin effects are either eliminated or contribute in the calculation of the fracture skin effects. Other skin effects have been introduced for other flow configurations. In all of these cases the ensuing bending of the flow lines would result in a skin effect denoted by Sc. Relevant ratios are zw/h (elevation ratio) and hw/h completion ratio). Cinco-Ley et al. Finally. completion elevation. and the individual parts. Figure 5-4 shows the relevant variables. Late-time radial flow would have the distinguishing characteristics of partial completion. the absolute value of sθ increases with the angle of slant and in certain cases may render sc+θ negative in spite of the positive sc associated with a partial completion. sc+θ. θ is the angle of well deviation. Similar phenomena may be in effect in the case of a deeply penetrating perforation that may bypass the near-wellbore damage. that is. Frequently.flow rate is still affected by the nearwellbore permeability reduction. These skins are addressed in Chapter 18. A method to combat this skin effect is by the injection of neat natural gas. This situation can occur as a result of a bad perforation job or by deliberate under completion to retard or retard or avoid coning effects. well are partially completed. The skin effects in Eq. the reader must be alerted here that once a hydraulic fracture is generated. the corresponding skins for the same completion and elevation ratios are larger when hD=1000 rather than 100. While partial completion generates a positive skin effect by reducing the well exposure to the reservoir. a deviated well results in the opposite. The skin effect due to slant is denoted by Sθ. sc and sθ. If the well is not completed at the middle of the reservoir height. Here hw es the perforated height. In general. the larger the negative contribution to the total skin effect will be. it is not correct to add pretreatment skin effects to any postfracture skin effects. As can be seen. However. which may redissolve the condensate and displace it into the reservoir. most pretreatment skin effects (Sd. the angle between adjoin perforations). lperf. Perforating is usually done at underbalance. sc+θ=8.875. This pattern allows good perforation density with small phasing (i. the distance between the perforations. From Table 5-1 for a vertical well (θ=0°). and the wellbore effect.A well with a radius rw=0. the perforation length. These include the well radius. and the liner. Calculate the skin effect due to partial completion for a vertical well. The correlation device is used to identify the exact position with a previously run correlation log. hw=80 ft. and frequently it locates casing collars. as shown in Fig. 5-5. The dimensions. and phasing of perforations have a controlling role in well performance.4 in.5 ft). Below. Figure 5-5 shows a schematic of a gun system with the shape changes arranged in a helical pattern. In order to avoid severe water coning problems only 8 ft are completed and the midpoint of the perforations is 29 ft above the base of the reservoir.g. Sec. What would be the composite skin effect if θ=45°? Repeat this problem for h=330 ft. whick is exactly inversely proportional to the perforation density (e.328 is completed in a 33-ft reservoir. SPF. the elevation ratio is zw/h=29/33=0. a positioning device. The total perforation skin effect is then 5-9 Figure 5-7 gives all relevant variables for the calculation of the perforation skin. sc+θ=15. then sc=8. rw. number. very important. the vertical converging effect. a correlation device. that is. from Table 5-2.6 but sθ=-2. result in hperf=0. Modern well perforation is done with perforating guns that attached either to a wire line or to coiled tubing. The perforating string contains a cable head.25 and 0. sH. and the completion ratio is hw/h=8/33=0. the angle of perforation phasing. are typically created. The perforating guns are loaded with shape changes.. Perforations with a diameter between 0. the pressure in the well is less than the reservoir pressure. hperf. 5-5 WELL PERFORATION AND SKIN EFFECT. which they divide into components: the plane flow effect.328 ≈ 100.. The dimensionless reservoir thickness hD is h/rw=33/0. swb. Solution. rperf.1 CALCULATION OF THE PERFORATION SKIN EFFECT.6 and sθ=0.6. 2 shots per foot.7.e. and 5-16 5-18 5-17 . If θ=45°. and a tunnel between 6 and 12 in. and zw=290 ft.4 for the 45° slant. The positioning device orients the shots toward the casing for more optimum perforation geometry. the explosive. θ. The cable head connects the string to the wire line and at the same time provides a weak point at which to disconnect the cable if problems arise. 5-6. the method of estimating the individual components of the perforation skin is outlined. of which sc=8. 5-6. the perforation radius. This facilitates immediate flow back following the detonation. resulting in sc+θ ≈ 6. and.338 ≈ 1000 although all other ratios are the same.25. and the perforation guns. Electric current initiates an explosive wave. sv. 5-5 Well Perfotation and Skin Effect. carrying the debris and resulting in a cleaner perforation tunnel.7 for the vertical well and sc+θ=10. the phases of the detonation are shown in Fig. which consist of the case. If hD=330/0. Karadas and Tariq (1998) have presented a semi analytical solution for the calculation of the perforation skin effect. . show the effect of the horizontal-to-vertical permeability anisotropy with kH/kv=1. Assue that a well with rw=0. b1. EXAMPLE 5-4 Perforation skin effect. Calculate the perforation skin effect if kH/kv=10. 5-19 Then. (5-12) and remembering that hperf=1/SPF.328 ft is perforated with 2 SPF. rperf=0. a dimensionless quantity is calculated first. 5-21 And 5-22 From Eqs. lperf= in. sv. (5-10). (0. a2.25 in. (5-11) and Table 5-3 (θ=180°). is potentially the largest contributor to sp.The constants a1. and θ=180°. sv can be very large. (5-15) and (5-16) and the constants in Table 5-3. 5-20 From Eq. If θ=180°. large hperf. Repeat the calculation for θ=0° and θ=60°. Calculation of swb. that is.0208 ft). Then The constants c1 and c2 also can be obtained from Table 5. (0.3. The vertical skin effect. and b2 are also functions of the perforation phasing and can be obtained from Table 5-3. For the calculation of swb. Solution From Eq. from Eq. . for small perforation densities.667 ft).