Non-Darcy Flow Near Hydraulically Fractured Wells
- Jacques Hagoort (Hagoort and Assocs. B.V.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2004
- Document Type
- Journal Paper
- 180 - 185
- 2004. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 5.6.8 Well Performance Monitoring, Inflow Performance, 4.3.4 Scale, 5.1.1 Exploration, Development, Structural Geology, 5.6.4 Drillstem/Well Testing
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In this work, we analyze the effect of non-Darcy flow near hydraulically fractured wells on well inflow performance. It is based on a dedicated numerical model of plane, steady-state flow of an incompressible fluid toward a vertically fractured well in the center of a circular reservoir. The results show that non-Darcy flow manifests itself as a positive skin factor, which is the product of a non-Darcy flow factor and the production rate, as is the case with nonfractured wells. An empirical relationship is presented that enables the estimation of the non-Darcy flow factor of fractured wells as a function of fracture length. Compared with nonfractured wells, hydraulic fractures will reduce the effect of non-Darcy flow in all practical situations. An intuitive approach to incorporate non-Darcy flow in the inflow performance relationship of fractured wells on the basis of total inflow area is a good first-order approximation.
Non-Darcy flow occurs when inertial forces may no longer be neglected compared with viscous forces. It is very common near gas production wells where local velocities can be very high. In production wells, non-Darcy flow manifests itself as a positive skin factor, which is linearly proportional to production rate.1 The proportionality constant is known as non-Darcy flow factor and can be derived from multirate well tests. In the simple case of steady-state radial flow, this non-Darcy flow factor can be directly related to the coefficient of inertial resistance of the porous medium, commonly called beta factor.
According to conventional wisdom, non-Darcy flow effects in the reservoir are reduced drastically near hydraulically fractured wells, depending of course on the dimensions of the fracture. The argument is that because of the increased inflow area of fractured wells compared with nonfractured wells, average flow velocities near the fracture are significantly lower for the same overall well production rate. However, local flow velocities near the tip of the fracture are extremely high, and this will enhance non-Darcy flow. To the best of our knowledge, no studies have been published in which this assumed reduction in non-Darcy flow has been quantified.
The objective of this work is to quantify the effect of non-Darcy flow in the reservoir on the inflow performance of a hydraulically fractured well. As an analysis tool, we have used a dedicated numerical model that describes single-phase, 2D, Darcy, and non-Darcy flow toward a hydraulically fractured well under steady-state conditions. In the model, the fracture is approximated by a thin vertical slit with a uniform pressure. As the scope of this work is limited to non-Darcy flow in the reservoir, non-Darcy flow effects within the hydraulic fracture itself are not considered. That is not to say that the effect of non-Darcy flow in the fracture is insignificant. On the contrary, non-Darcy flow in the fracture will, in general, be more important than non-Darcy flow in the reservoir.
Using the numerical model, we have determined well production rates for a wide range of fracture lengths and ratios of inertial to viscous forces. We have captured the results of the numerical experiments in an empirical relationship that can be directly included in the inflow performance relationship of a hydraulically fractured well. The results of the study provide a better understanding of the effect of non-Darcy flow on the inflow performance of fractured wells.
The physical model that underlies the numerical model is a circular-shaped reservoir that is drained by a single, hydraulically fractured, vertical well, located in the center of the reservoir. The reservoir has a constant thickness and has homogeneous and isotropic physical properties. It contains a noncompressible fluid with a constant viscosity. The hydraulic fracture is oriented vertically and covers the entire reservoir thickness. The hydraulic fracture itself is modeled by a thin vertical slit with a uniform pressure. This represents a well-designed fractured well where the greater part of the pressure drop occurs in the reservoir. The pressures in the fracture and at the circular outer boundary of the reservoir are kept at a constant value. Under these conditions and assumptions, flow in the reservoir is steady-state and 2D.
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