A Robust Type Curve Solution for Analyzing Pressure-Transient Behaviors of both Vertical and Horizontal Fracture Systems

Abstract

Although there have been many analytical studies on pressure-transient behavior of hydraulic fracture systems, no single analytical solution capable of describing both vertical and horizontal fracture transient state behaviors has been developed. The purpose of this work is to develop a single analytical solution that is robust enough to fit this need. This paper presents a type curve solution for a well producing from a solid bar source in an infinite-acting reservoir with impermeable upper and lower boundaries. Computation of dimensionless pressure reveals that the pressure-transient behavior of any hydraulic fracture system is governed by two critical parameters (i) aspect ratio, m, and (ii) dimensionless length, LD. Analysis of a typical log-log plot of pwD vs. tDxf indicated the existence of four distinct flow periods (i) fracture fill-up period causing a typical storage dominated flow, (ii) vertical linear flow period, (iii) transition period, and (iv) radial flow period. As aspect ratio tends to zero, the fracture fill-up periods disappear resulting in typical fully/partially penetrating vertical fracture pressure response. This analytical solution reduces to the existing fully/partially penetrating vertical fracture solution developed by Raghavan et al1 as aspect ratio tends to zero, and a horizontal fracture solution is obtained as aspect ratio tends to unity. This new horizontal fracture solution yields superior early time (tDxf < 10–3) solution compared with the existing horizontal fracture solution developed by Gringarten and Ramey2, and shows excellent agreement for tDxf > 10–3. Introduction Hydraulically fractured wells and horizontal well completions are intended to provide a larger surface area for fluid withdrawal and thus, improve well productivity. This increase in well productivity is usually measured in terms of negative skin generated as a result of a particular completion type. Hydraulic fractures leading to horizontal or vertical fractures could produce the same negative skin effect as a horizontal well, but possibly different transient pressure response; hence, having a good understanding of the transient behavior of hydraulic fractures systems and horizontal well completion is very vital for accurate interpretation of well test data. The orientation of hydraulic fractures is dependent on stress distribution. The orientation of fracture plane should be normal to the direction of minimum stress. Since most producing formations are deep, the maximum principle stress is proportional to the overburden load. Thus, vertical fractures are more common than horizontal fractures. The only difference between a vertical and a horizontal fracture system is the orientation of the fracture plane; a vertical fracture can be viewed as parallelepiped with zero width, while a horizontal fracture, as a parallelepiped with zero fracture height. This same argument can be extended to horizontal well completions; a horizontal wellbore can be viewed as a parallelepiped with the height and width equal to the wellbore diameter. This configuration makes a horizontal well completion behavior like a coupled fracture system made up of both vertical and horizontal fracture systems. Considering the similarity in the physical models, one will expect a single analytical solution can be developed for hydraulically fractured (vertical and/or horizontal) well and horizontal well completions. The primary purpose of this work is to present a general analytical solution for describing the transient pressure behaviors of (i) vertical fracture system, (ii) horizontal fracture system, and (iii) horizontal well or drainhole. New physical insights into the critical variables that govern the performance of these completions are also provided.

A New Model to Predict Productivity of Multiple-Fractured Horizontal Well in Naturally Fractured Reservoirs

“…As for simplification, subsequent works have been focusing on point source functions which neglected the flow in source and its volume. Ogunsanya et al [23,24] pointed out that point source functions have computational problems and the no volume assumption may not be adequate in some specific situations, and then they revisited the concept of volumetric source and presented a new "solid bar source" model. Amini et al [11][12][13][14] developed distributed volumetric source (DVS) model of homogeneous reservoirs and validated the applications in vertical well, horizontal well, and fractured vertical well with well-known existing solutions.…”

Revising Transient-Pressure Solution for Vertical Well Intersected by a Partially Penetrating Fracture with Non-Darcy Flow Effect

“…At depths deeper than approximately 2000 ft in the unconventional reservoir, the direction of the least principal stress is generally parallel to the formation plane [14], and as a result, the hydraulic fractures are generated principally in the vertical direction. Although the intention was for oil companies to create fully penetrating hydraulic fractures, the actual measurement shows that hydraulic fracture may not extend throughout the entire vertical extent of the formation thickness [15,16]. Only the effective height of the fracture that is propped open contributes to the production, and the three-dimensional flow pattern occurs in the reservoir.…”

Volumetric Source Model to Predict Productivity of Fractured Horizontal Well in Naturally Fractured Reservoirs

“…But most works have been focusing on point source functions which neglected the flow in source and its volume. While Ogunsanya et al [15,16] pointed out that source functions have computational problems and the no volume assumption may not be adequate in some specific situations, then revisited the concept of volumetric source and presented a new "solid bar source" model. Amini et al [17][18][19][20] developed distributed volumetric source (DVS) model of homogeneous reservoirs, and validate the applications in vertical well, horizontal well and fractured vertical fractured well with well-known existing solutions.…”