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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Well inclination angle		°
Well radius		ft
Perforated length		ft
Formation thickness		ft
Horizontal permeability		mD
Vertical permeability		mD
Perforation radius		ft.
Perforations spacing		ft
Perforation length		ft
Perforation phasing angle		°

Approx. Location of Perforation

Top of reservoir   Middle

Extra Data For Efficiency Estimation (Optional)

Skin due to formation damage
Radius of external boundary		ft

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OUTPUT   VARIABLES

PseudoSkin, due to:	Skin Factor	Totals
♦  Well Inclination, sθ
♦  Partial penetration, sc
♦♦  Slant & partial penetration, sc+θ
♦  Perforation: planar flow effects, sH
♦  Perforation: vertical flow effects, sV
♦  Perforation: wellbore effects, swb
♦♦  Perforation sp
♦♦♦  Total Skin, st
♦♦♦  Completion Efficiency, Ec

Skin Factors In Perforated Vertical Completions

The analysis of the different skin effects in a well completion is a necessary step in the optimization of completion and stimulation designs. The total skin is usually determined by the conventional transient pressure test analysis.

In a cased-hole perforated completion for a vertical well, the total skin effect s_t is made of the following main components: skin due to formation damage/stimulation s_d, due to restricted entry/partial penetration s_c , skin due to well deviation/slant s_θ and skin due to perforation s_p.

s_t = s_d + s_c + s_θ + s_p

The perforation process depends mainly on the following parameters (shot density, hole-size, penetration, phasing). The perforation skin s_p is comprised of 3 sub-components: Horizontal (2D plane flow) s_H , vertical (3D convergence flow) s_V and wellbore blockage effects s_wb.

s_p = s_H + s_V + s_wb.

Herein is presented the means for estimating the completion-dependent skin factors for a vertical or deviated well, based on published semi-analytic models. The key equations underpinning these models are given below.

Skin Due To Partial Penetration (Brons et al):

G(b) = 2.948 + 7.363b + 11.45b² + 4.675b³

Skin Due To Well Inclination (Cinco et al):

Skin Due To Perforation-induced Horizontal flow effects (Karakas & Tariq):

Skin Due To Perforation-induced Vertical flow effects:

Skin Due To Perforation-induced Wellbore effects:

Also, the Completion Efficiency Factor, E_c (also referred to as the Productivity Ratio, PR) is defined as follows:

where
     h = reservoir thickness, ft
     h_d = fractional penetration = perforated height/h
     b = h_d modified for completion placement as defined in Brons et al.
     h_perf = vertical distance between perfs = reciprocal of shots-per-ft
     r_w = wellbore radius, ft
     r_e = radius of external drainage boundary, ft
     r_perf = radius of tunnel created by perforation bullet, ft
     l_perf = length of perforation tunnel, ft
     k_h = horizontal permeability of formation, mD
     k_v = vertical permeability of formation, mD
     θ = well deviation angle, degrees
     θ_perf = angle of perforation phasing, degrees
     a₀,a₁,a₂,b₁,b₂,c₁,c₂ = Phasing-dependent constants tabulated in Karakas & Tariq.

Tips

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BIBLIOGRAPHY

• Al-Qahtani A.M. & Al-Shehri D.A.; The E_c factor: A new correlation for optimizing completion efficiency; paper SPE-81490, 2003.
• Brons F. & Marting V.E.; The effect of restricted fluid entry on well productivity; JPT, Feb. 1961, p. 172-174.
• Cinco H., Miller F.G. & Ramey H.J.; Unsteady-state pressure distribution created by a directional drilled well; JPT, Nov. 1975, p. 1392-1400.
• Karakas M. & Tariq S.M.; Semianalytical productivity models for perforated completions; SPEPE, Feb., 1991, p. 73-82.
• Economides M.J., Hill A.D. & Ehlig-Economides C.; Petroleum Production Systems; PTR Prentice Hall Inc. Englewood Cliffs, NJ, 1994, chap. 5.