Effect of Finite Conductivity Horizontal Well on Transient-Pressure Behavior

Abstract

Abstract This study investigates the effect of horizontal wellbore hydraulics on the early time dynamic behavior of horizontal wells. A finite conductivity model has been developed to couple infinite-conductivity horizontal well model based on uniform flux solution and finite conductivity wellbore hydraulic model. A sensitivity study is presented to show:The effect of horizontal well conductivity on production distribution along the wellbore at different time-steps, including early time radial flow, intermediate time linear flow and late time radial flow.The effect of wellbore length on the magnitude of wellbore-pressure drop under different values of Horizontal Well Conductivity, CHD, and Reynolds number, NRe.The effect of pipe roughness, Rp.The effect Reynolds number at the downstream end of the well, NRe. The new finite conductivity model is evaluated by setting a computer programs using Mathlab programming. The programs can include any friction factor correlation and production scheme. Type curves, of dimensionless pressure and pressure derivative versus dimensionless time, are obtained for different values of horizontal well conductivity and Reynolds number. These sets of curve can be used for type curve matching techniques. Correlations of the additional pressure drop due to finite conductivity solution over infinite conductivity solution, ?PD(tD), are presented for different values of dimensionless well length, LD, horizontal well dimensionless conductivity, CHD, Reynolds number, Re, and pipe roughness, Rp. Introduction The magnitude of wellbore pressure drop has been considered negligibly small in order to satisfy the infinite conductivity and uniform flux idealization. However in some circumstances the pressure drop in the horizontal wellbore can have an effect on the horizontal well behavior. This is supported by the numerous studies incorporating the effect of pressure drop in horizontal well models. In practice, some pressure drop from the tip of a horizontal well to the producing end is needed to maintain fluid flow within the wellbore. As a result, the downstream end of the horizontal well will be subjected to a lower pressure than the upstream end. Hence, for better understanding of horizontal well behavior, a good estimate of the pressure drop within the horizontal portion of the well is needed. This estimation can help reservoir engineers in optimizing an individual completion and/or optimizing the depletion plan for a reservoir. The major reason for drilling a horizontal well is to produce with a higher flow rate at a lower reservoir pressure drawdown. Frictional pressure losses could be comparable to the pressure drop within the reservoir. In such a case, drilling a longer horizontal well may not enhance the productivity. In this study, a semi-analytical model is developed and a sensitivity study is performed on the parameters affecting finite conductivity pressure solution. Literature Review The intensive theoretical studies of horizontal wells over the last two decades have shown that the incorporation of horizontal wellbore hydraulics into the horizontal well model is a challenging issue. This section will review the relevant literature concerning the effect of hydraulics on horizontal well performance. Dikken1 was the first to incorporate the effect of frictional wellbore pressure drop in horizontal well productivity. His basic assumption is that the productivity index per unit length of horizontal well is constant. He developed a second order differential equation to determine the wellbore flow rate at any location in the wellbore. He then solved analytically the differential equation for the case of infinite wellbore length and numerically for the actual case. Novy7 extended Dikkin's1 work to gas wells. Landman8 and Halvorson9 presented analytical solution to the non-linear differential equation. However, both of their solutions were limited to special cases.