Unsteady-State Pressure Distribution Created By a Directionally Drilled Well

Abstract

Analysis of a solution derived to study, the unsteady-state pressure distribution created by a directionally drilled well indicates that the slant of a fully penetrating well creates a negative skin effect that is a function of the angle of slant and the formation thickness. Calculation of this pseudoskin factor permits evaluation of the actual well condition. Introduction Many methods have been developed to analyze transient wellbore pressure data to determine the formation permeability, porosity, average pressure, and well permeability, porosity, average pressure, and well condition. These methods usually are based on solutions of unsteady-state flow problems that consider a fluid flowing toward a fully penetrating well that is perpendicular to the upper and lower formation boundary perpendicular to the upper and lower formation boundary planes. Actually, most wells do not penetrate the planes. Actually, most wells do not penetrate the producing formation perpendicularly. Instead, there is a producing formation perpendicularly. Instead, there is a certain angle between the normal to the formation plane and the well axis, such as when a vertical well penetrates a dipping formation or when a directionally drilled penetrates a dipping formation or when a directionally drilled well penetrates a horizontal formation. These kinds of wells are called "slanted wells." Although such wells are common, there appears to have been only one study of the performance of such completions. Roemershauser and Hawkins studied steady-state flow in a reservoir producing through a fully penetrating, slanted well using an electrical model. They considered a circular reservoir of finite extent and concluded that the slant of a fully penetrating well causes an increase in the well productivity. The increase in well productivity results from the decrease in the resistance productivity results from the decrease in the resistance to flow around the wellbore caused by an increase in the producing-interval area exposed to flow. This increase producing-interval area exposed to flow. This increase in well productivity indicates that a fully penetrating, slanted well creates a negative skin effect. Roemershauser and Hawkins graphed the increase in well productivity vs the angle of slant of the well. There productivity vs the angle of slant of the well. There appears to have been no study of the unsteady-state performance of slanted wells. performance of slanted wells. Mathematical Derivation The unsteady-state laminar flow of a slightly compressible fluid through an anisotropic, homogeneous, porous medium can be described after assuming small porous medium can be described after assuming small pressure gradients everywhere in the reservoir and pressure gradients everywhere in the reservoir and neglecting gravity effects: +++=, ......(1) wherekr= ------- = constant.ct In Eq. 1, it is also assumed that the horizontal permeabilities kx and ky are equal and constant, thus permeabilities kx and ky are equal and constant, thus equaling kr. This assumption is not necessary, and the following results can be generalized to the case of simple anisotropy, where kx, ky, and kr are all constant but are not equal, by redefinition of the horizontal variables x and y. For example, we define z' as z' = z kr/kz................................(2) JPT P. 1392

Assessment of Total Skin Factor in Perforated Wells

“…(Cinco-Ley et al 1975a, 1975bOzkan and Raghavan 2000). During the early-time period, only the formation in the immediate vicinity of the wellbore contributes to flow, and the flow is perpendicular to the well axis.…”

“…Several researchers have presented equations to compute the pseudoskin due to inclined well geometry (Cinco-Ley et al 1975a, 1975bBesson 1990;Rogers and Economides 1996;Ozkan and Raghavan 2000). The slant pseudoskin equation presented by Cinco-Ley et al (1975a) has been used widely to predict the influence of inclination on well productivity. Once the inclination pseudoskin is available, the additional pressure change due to well deviation is formulated as below.…”

“…24 for the PTIDZ and the 3D semianalytical model for the PEBDZ. Additionally, for fully perforated inclined wells, the inclination pseudoskin s is estimated with the equation presented by Cinco-Ley et al (1975a). For partially perforated inclined wells, the s pp term, accounting for both the well inclination and partial completion, is estimated with the Ozkan-Raghavan (2000) model.…”

“…14. Inclination pseudoskin predicted from the Cinco-Ley et al (1975a) is also plotted in Fig. 14. The results for the Pucknell-Clifford (1991) model are obtained by incorporating the s pdc formulation from the Karakas-Tariq algorithm into Eq.…”

Pressure-Transient Analysis for a Slanted Well in a Reservoir With Vertical Pressure Support

“…[1][2][3][4][5][6][7][8] Various interpretation techniques, including type curves, 6,8,9 analyzed well tests from these systems. Analytical solutions for vertical limited-entry wells and horizontal wells in a reservoir with one constant-pressure boundary created by a supporting gas cap or aquifer have been derived.…”