Effect of Partial Completion on the Duration of Afterflow and Beginning of the Formation Straight Line on a Horner Plot
Authors: Streltsova-Adams T.D. , McKinley R.M. 
Published: December 2007

Buildup data from tests in partially completed wells when plotted in standard semilogarithmic coordinates exhibit not one but two straight-line portions which, in turn, usually are distorted by afterflow and reservoir external boundaries. The selection of a straight-line portion indicative of formation properties - i.e., selection of the middle time region properties - i.e., selection of the middle time region (MTR) on a Horner plot -then becomes uncertain. This paper first gives an equation for estimating the time at which the MTR begins on a Horner plot of pressure buildup data for a partially completed well pressure buildup data for a partially completed well producing at a constant rate from a reservoir with producing at a constant rate from a reservoir with impermeable top and bottom boundaries. This is the time after which partial completion no longer affects the rate of pressure buildup. Next, this paper gives an equation for estimating the increased duration of afterflow resulting from partial completion. The larger of the two times estimated by these two equations then fixes the earliest time at which data cart be analyzed by conventional methods on a semilog plot.Pressure buildup computed for a well of partial completion without afterflow (Eq. 14 in Ref. 1) is plotted in Fig. 1. The first straight-line segment plotted in Fig. 1. The first straight-line segment of each pressure curve shows an early formation response localized at the wellbore with fluid flow confined to the interval of well perforation. The second straight-line segment, following a transition period required for propagation of a pressure period required for propagation of a pressure transient out into the formation, indicates the formation response over its entire thickness. The early time slope m1 is related to the middle time slope m2 by the reciprocal of the appropriate penetration ratio, m1 = m2/h'p. The second slope, m2, corresponds to that of a completely penetrating well, m = 2.3026. Each curve, however, is displaced vertically by an amount 2sp which is the additional dimensionless pressure drop due to limited flow entry. The time 4tDp at the start of a straight-line portion with slope m2 is marked on Fig. 1 by vertical portion with slope m2 is marked on Fig. 1 by vertical lines with arrows. As is evident from Fig. 1 these times are controlled by the parameterand are independent of the well partial completion. The top values are found to be related to the rD values by

(1)

Thus, the shut-in time tp required for the pressure in a partially completed well to reach the MTR (from Eq. 1) is

(2)

In oilfield 106 units, the vertical diffusivity eta v = 4.396 × (measured in square feet per minute) and the time tp in Eq. 2 is in minutes. In per minute) and the time tp in Eq. 2 is in minutes. In the mks system of units, eta v = (measured in square meters per second) and the time tp in Eq. 2 is in seconds.Substituting the rD and to parameters into Eq. 1 results in an expression for the radius of investigation at the start of MTR (the radius beyond which the effect of partial penetration is no longer felt) as

(3)

Eq. 2 allows estimation of how long partial penetration effects last during a given test. The penetration effects last during a given test. The restricted flow entry also prolongs duration of afterflow at the sandface after the well is shut in at the surface. Since partial penetration causes an additional skin sp, we may suppose that the time required for the afterflow rate to drop off to 1% of the stable production rate is related to this skin by an equation production rate is related to this skin by an equation of the form

(4)

P. 550