## Formation Damage and Effective Well Radius

During drilling of a well, drilling mud can invade the aquifer and change its permeability in the vicinity of the well and cause formation damage or skin effect. The thickness of the "skin zone" will depend not only on drilling technology but also on the permeability of the aquifer. High-permeability aquifers exhibit a larger skin zone than low-permeability aquifers. However, the reduction in permeability is smaller in a high-permeability zone than in a low-permeability zone. The additional drawdown due to the change in permeability and the turbulent flow around the well is called well losses. Because of lower flow rate per unit screen length, horizontal wells show smaller well losses due to drilling mud invasion than vertical wells. Van Everdingen [14] defined a dimensionless "skin factor" s as where rs is the radius of the skin zone with permeability ks in an aquifer of permeability k, [L2].

The effective radius of a well, r'w, is defined as the theoretical radius of the well required to match the observed pumping rate and drawdown. The effective radius of a hypothetical vertical well that pumps at the same rate as a horizontal well can be computed using the equation

Reh[U2)

Reh[U2)

1000

1000

.001

1000

Kh/Kv

Figure 2 Productivity ratio vs. anisotropy.

The following formula relates the skin factor, s, and the effective radius of a well, r'w: r'w = rw exp( —i) (9)

Renard and Dupuy [15] gave the following solution for computing flow rate, Qh, from a horizontal well with the skin factor s:

If the length of a horizontal well greatly exceeds aquifer thickness, L > B, or if well length is small compared to drainage radius, Reh, Equation (5) reduces to the well-known Thiem's equation,

2nKBAs

log(4Reh/L)

with the effective well radius being equal to one-fourth of the horizontal well length, r'w = LIA. D. Off-Center Horizontal Well

All solutions presented so far have assumed that the horizontal well is located at midheight in the aquifer cross section. The distance, 6, from aquifer mid-height to the horizontal well is called the eccentricity of the well. The flow rate of an eccentric horizontal well can be calculated using the formula

As long as the horizontal well eccentricity is relatively small, 6 < ± B/4, the performance of a horizontal well is not significantly affected [16].

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