Evaluation and Modification of Current Fractured Horizontal Well Inflow Models
Authors: Kustamsi A. , Hareland G. , Rampersad P. , Permadi P. 
Published: December 2007

Abstract
This paper evaluates and compares current multifractured horizontal well inflow models for possible use in a nodal analysis fractured horizontal well simulator. Nine different inflow models have been proposed for vertical hydraulic fractures intersecting a horizontal wellbore The fracture inflow model types consist of analytical and numerical models which assume either uniform flux, infinite conductivity and finite conductivity fractures. This paper discusses these models.
Soliman et al. and others have presented numerical results of a horizontal well intersecting vertical fractures, which creates radial flow within fracture. Modifications are suggested to the current linear fracture flow models used in the three fracture inflow model types mentioned above. One of the types uses a limited communication term proposed by Schulte and another uses a skin effect introduced by Mukherjee and Economides.
The results of this study suggest the best inflow equations for various assumed fractured horizontal well scenarios.

Introduction
Fracturing horizontal well in reservoir that commonly fracture stimulated when drilled vertically may further improve well productivity. But there are particular situations where fracturing a horizontal well is an economically attractive completion option. It may take place under several scenarios, some of which are low vertical permeability, presence of shale streaks, low formation permeability, small stress contrast between pay zone and adjacent layers. A complete understanding of the in situ stress is essential before the well is drilled because of the dependence of fracture orientation of well direction with respect to the stress field. At depths usually encountered in the oilfield &gt;1500 ft) an induced fracture may normally be assumed to be vertical and perpendicular to the minimum horizontal stress. There are two distinct directions the wellbore can be drilled to enhance fracturing operations. If the horizontal well is drilled in the direction of the least horizontal stress, several vertical fractures may be spaced along its axis wherever perforations are located. This spacing is one of the design parameters to be selected. By changing the wellbore azimuth by 900 and drilling normal to the least stress, fracture will propagate along the wellbore resulting in longitudinal fracture. When the wellbore is not in one of these two major directions, several scenarios may occur, depending on the angle between the borehole and the stress direction and on the perforation distribution and density. In this paper only the presence of fractures perpendicular to the horizontal wellbore is discussed.
The effect of hydraulic fracture on pressure behavior has been investigated in great detail since early 60s. Prats et al. discussed the performance of vertically fractured wells for the cases of incompressible as well as compressible field. Russell and Truitt solved the pressure behavior of an infinite conductivity vertical fracture by means of finite difference method. Since then, three different models have been proposed for vertical hydraulically fractured wells. They are uniform flux fracture, infinite conductivity fracture, and finite conductivity fracture.
The analytical solution for the uniform flux fracture model was developed by Gringarten et al. The assumption they made is that the flow rate per unit length of fracture is constant along its entire fracture. The infinite conductivity fracture model, also contributed by Gringarten et al. assumes that the fluid entry flux along the fracture caused a constant pressure along the fracture. The analytical expression for the pressure distribution created by the plane vertical fracture may be obtained by the Green's function and product solution method using appropriate source functions presented by Gringarten and Ramey.
The weakness of these two models to exemplify nonideality led to the solution for finite conductivity fractures by Cinco-Ley et al.