Stabilized Productivity of a Hydraulically Fractured Well Producing at Constant Pressure

SPE Journal ◽  
2006 ◽  
Vol 11 (01) ◽  
pp. 120-131 ◽  
Author(s):  
Jacques Hagoort
Keyword(s):  
Flow Conditions ◽  
Productivity Improvement ◽  
Fracture Conductivity ◽  
Fracture Length ◽  
State Flow ◽  
Production Improvement ◽  
Constant Rate ◽  
Infinite Conductivity ◽  
State Production ◽  
Fractured Well

Summary This paper describes a simple and easy-to-construct numerical model for the calculation of the stabilized productivity of a hydraulically fractured well producing at a constant well pressure. The model takes into account both Darcy and non-Darcy pressure losses in the fracture. Dimensionless charts are presented that illustrate productivity improvement as a function of fracture length, fracture conductivity, and non-Darcy flow. For dimensionless fracture lengths in excess of 0.2, constant-pressure productivities are significantly lower than constant-rate productivities as predicted, for example, by the McGuire-Sikora productivity improvement chart. The maximum difference is 20% for an infinite-conductivity fracture with a length of unity. Both fracture conductivity and non-Darcy flow adversely affect well productivity; the reduction in productivity is larger for longer fractures. Introduction The productivity of a well is commonly expressed by a productivity index defined as the ratio of production rate and difference between average reservoir pressure and well pressure. Stabilized productivity refers to production from a well in the semisteady-state flow regime (i.e., the regime beyond the initial transient regime), during which flow in the reservoir is dominated by the reservoir boundaries. In the past, most studies on the stabilized productivity of hydraulically fractured wells were about steady-state production or semisteady-state production at a constant rate. As we shall demonstrate in this paper, the type of well boundary condition has a significant effect on productivity, especially for long fractures. For production by pressure depletion, characterized by declining production rates, constant well pressure is a more appropriate boundary condition. In the late 1950s, McGuire and Sikora (1960) presented a productivity improvement chart for fully penetrating fractured wells producing at a constant rate under semisteady-state flow conditions based on electrical analog model experiments. The chart shows production improvement vs. fracture conductivity for various fracture lengths. The McGuire-Sikora chart is a classic in the fracturing literature and is being used to this day. In the early 1960s, Prats (1961) presented a theoretical study on the productivity of a fully penetrating fractured well under steady-state flow conditions. He showed that the effect of a fracture can be represented by an apparent or effective wellbore radius, which depends on fracture length and fracture conductivity. For fractures that are relatively small and have an infinite conductivity, the effective wellbore radius is equal to half the fracture half-length. In a follow-up study, Prats et al. (1962) demonstrated that this result also holds for stabilized flow of a slightly compressible liquid. In the mid-1970s, Holditch presented a production improvement chart (included in Lee 1989) based on experiments with a numerical reservoir simulator, which essentially confirmed the earlier results of McGuire and Sikora. Although based on production at constant rate, the McGuire-Sikora and Holditch charts are also being used for production at declining production rates (Lee 1989).

Analysis of Pressure Data for Fractured Wells: The Constant-Pressure Outer Boundary

1978 ◽  
Vol 18 (02) ◽  
pp. 139-150 ◽  
Author(s):  
R. Raghavan ◽  
Nico Hadinoto
Keyword(s):  
Constant Pressure ◽  
Outer Boundary ◽  
Reservoir Pressure ◽  
Pressure Gradients ◽  
Pressure Data ◽  
Pressure Behavior ◽  
Fracture Length ◽  
Infinite Conductivity ◽  
Production Pattern ◽  
Fractured Well

Abstract Analysis of flowing and shut-in pressure behavior of a fractured well in a developed live-spot fluid injection-production pattern is presented. An idealization of this situation, a fractured well located at the center of a constant pressure square, is discussed. Both infinite-conductivity and uniform-flux fracture cases are considered. Application of log-log and semilog methods to determine formation permeability, fracture length, and average reservoir pressure A discussed. Introduction The analysis of pressure data in fractured wells has recovered considerable attention because of the large number of wells bat have been hydraulically fractured or that intersect natural fractures. All these studies, however were restricted to wells producing from infinite reservoirs or to cases producing from infinite reservoirs or to cases where the fractured well is located in a closed reservoir. In some cases, these results were not compatible with production performance and reservoir characteristics when applied to fractured injection wells. The literature did not consider a fractured well located in a drainage area with a constant-pressure outer boundary. The most common example of such a system would be a fractured well in a developed injection-production pattern. We studied pressure behavior (drawdown, buildup, injectivity, and falloff) for a fractured well located in a region where the outer boundaries are maintained at a constant pressure. The results apply to a fractured well in a five-slot injectionproduction pattern and also should be applicable to a fractured well in a water drive reservoir. We found important differences from other systems previously reported. previously reported. We first examined drawdown behavior for a fractured well located at the center of a constant-pressure square. Both infinite-conductivity and uniform-flux solutions were considered. The drawdown solutions then were used to examine buildup behavior by applying the superposition concept. Average reservoir pressure as a function of fracture penetration ratio (ratio of drainage length to fracture length) and dimensionless time also was tabulated. This represented important new information because, as shown by Kumar and Ramey, determination of average reservoir pressure for the constant-pressure outer boundary system was not as simple as that for the closed case since fluid crossed the outer boundary in an unknown quantity during both drawdown (injection) and buildup (falloff). MATHEMATICAL MODEL This study employed the usual assumptions of a homogeneous, isotropic reservoir in the form of a rectangular drainage region completely filled with a slightly compressible fluid of constant viscosity. Pressure gradients were small everywhere and Pressure gradients were small everywhere and gravity effects were neglected. The outer boundary of the system was at constant pressure and was equal to the initial pressure of the system. The plane of the fracture was located symmetrically plane of the fracture was located symmetrically within the reservoir, parallel to one of the sides of the boundary (Fig. 1). The fracture extended throughout the vertical extent of the formation and fluid was produced only through the fracture at a constant rate. Both the uniform-flux and the infinite-conductivity fracture solutions were considered. P. 139

Transient Flow in Elliptical Systems

1979 ◽  
Vol 19 (06) ◽  
pp. 401-410 ◽  
Author(s):  
Fikri Kucuk ◽  
William E. Brigham
Keyword(s):  
Porous Medium ◽  
Line Source ◽  
Vertical Fracture ◽  
Constant Rate ◽  
Flow Geometry ◽  
Elliptical Flow ◽  
Long Time ◽  
Infinite Conductivity ◽  
Fractured Well ◽  
Anisotropic Reservoirs

Abstract This study presents analytical solutions to elliptical flow problems that are applicable to infinite-conductivity vertically fractured wells, elliptically shaped reservoirs, and anisotropic reservoirs producing at a constant rate or pressure. Type curves and tables are presented for the dimensionless flow rate and the dimensionless wellbore pressure for various inner boundary conditions ranging from K = 1 1, which corresponds to a circle, to K =, which corresponds to a vertical fracture. For elliptical reservoirs, K is the ratio of the major to minor axes of the inner boundary ellipse; for anisotropic reservoirs, it is the square root of the ratio of maximum to minimum permeabilities. Introduction Flow in a homogeneous and isotropic porous medium usually will be radial or linear, depending on the shape of the boundary. But in the area surrounding a vertical fracture, an anisotropic formation, or an aquifer with an elliptical inner boundary, flow will be elliptical.The study of elliptical flow in porous media is more recent than the usual radial and linear flow studies, but even elliptical flow studies date back at least several decades. The earliest discussion of steady-state elliptical flow usually is attributed to Muskat. He presented a steady-state analytical solution for the now from a finite-length line source into an infinitely large reservoir.One of the classic papers on elliptic flow by Prats et al. considered flow of compressible fluids from a vertically fractured well in a closed elliptical reservoir producing at a constant pressure. Prats et al. also producing at a constant pressure. Prats et al. also presented a solution for long times for the presented a solution for long times for the constant-rate case.Gringarten et al. found that older studies by Russell and Truitt (where flow is to a vertically fractured well) are unsuitable for short-time analysis. Gringarten et al. presented analytical solutions for fractures with infinite conductivity and with uniform flux. These solutions were for both closed squares and infinite reservoirs produced at a constant rate.In the last few years considerable work has been done on fracture systems, including numerical solutions and a semianalytical solutions for both finite and infinite fracture conductivities. Most of these studies, however, have not used the concept that the fracture is an elliptical flow system. Nevertheless, the results they obtain are important for well testing.Another problem related to elliptical flow is flow through an anisotropic porous medium. For this problem, a line source solution and a long-time problem, a line source solution and a long-time approximation presented by Earlougher are available for the constant-rate case.The purpose of this paper is to study elliptical flow in a broad sense with regard to reservoir engineering problems and to see whether these problems can be problems and to see whether these problems can be solved and whether elliptical problems can be handled in a unified, consistent manner. Development of Elliptical Flow Models The flow from an isotropic and homogeneous medium to a map usually will be radial, but lack of homogeneity will distort the radial flow geometry. In particular, flow will be elliptical through a porous particular, flow will be elliptical through a porous medium with directional permeability distribution (simple anisotropy). The inner geometry of a well also can distort radial flow geometry. For example, the flow will be elliptical if the well has an infinite-conductivity vertical fracture. Elliptical flow also will be encountered in flow from an aquifer to a reservoir that has an elliptical boundary at the oil/water contact. SPEJ P. 401

Optimization of Spacing and Penetration Ratio for Infinite-Conductivity Fractures in Unconventional Reservoirs: A Section-Based Approach

SPE Journal ◽  
2017 ◽  
Vol 22 (06) ◽  
pp. 1877-1892 ◽  
Author(s):  
S.. Liu ◽  
P. P. Valkó
Keyword(s):  
Shale Gas ◽  
Optimization Method ◽  
Limited Range ◽  
Productivity Index ◽  
Optimal Decision ◽  
Fracture Length ◽  
Penetration Ratio ◽  
Feasible Range ◽  
Infinite Conductivity ◽  
Total Fracture

Summary In this paper, we consider the development plan of shale gas or tight oil with multiple multistage fractured laterals in a large square drainage area that we call a “section” (usually 640 acres in the US). We propose a convenient section-based optimization of the fracture array with two integer variables, the number of columns (horizontal laterals) and rows (fractures created in a lateral), to provide some general statements regarding spacing of wells and fractures. The approach is dependent on a reliable and efficient productivity-index (PI) calculation for the boundary-dominated state (BDS). The dimensionless PI is obtained by solving a time-independent eigenvalue problem by use of the finite-element method (FEM) combined with the Richardson extrapolation. The results of the case study demonstrate two decisive factors: the dimensionless total fracture length, related to the total amount of proppant and fracturing fluid available for the section, and the feasible range of actual fracture half-lengths, related to current fracturing-technology limitations. Under the constraint of dimensionless total fracture length, increasing the number of columns (horizontal laterals) increases the total PI but with only diminishing returns, whereas the optimal fracture-penetration ratio decreases somewhat, but is still near unity. When adding the technological constraint of a limited range of fracture half-lengths that can be routinely and reliably created, only a few choices remain admissible, and the optimal decision can be easily made. These general statements for the ideal homogeneous and isotropic formation can serve as a reference in the more-detailed optimization works. In other words, we offer a first-pass method for decision making in early stages when detailed inputs are not yet available. The information derived from the section-based optimization method and the efficient and reliable algorithm for PI calculation should help the design of multistage fracturing in shale-gas or ultralow-permeability oil formations.

Parameters Optimization of Fractures with One for Injection and Two Others for Production of Horizontal Wells Fracturing on Offshore Oilfields

2014 ◽  
Vol 962-965 ◽  
pp. 489-493
Author(s):  
Zhi Qiang Li ◽  
Yong Quan Hu ◽  
Wen Jiang Xu ◽  
Jin Zhou Zhao ◽  
Jian Zhong Liu ◽  
...  
Keyword(s):  
Horizontal Well ◽  
Oil Production ◽  
Horizontal Wells ◽  
Simulation Method ◽  
Parameters Optimization ◽  
Development Mode ◽  
Fracture Conductivity ◽  
Fracture Length ◽  
Fractured Horizontal Well ◽  
Production Research

This article presents a new exploitation method based on the same fractured horizontal well with fractures for injection or production on offshore low permeability oilfields for the purpose of adapting to their practical situations and characteristics, which means fractures close to the toe of horizontal well used for injecting water and fractures near the heel of horizontal well used for producing oil. According to proposed development mode of fracturing, relevant physical model is established, Then reservoir numerical simulation method has been applied to study the effect of arrangement pattern of injection and production fractures, fracture conductivity, fracture length on oil production. Research indicates cumulative oil production is much higher by employing the middle fracture for injecting water compared with using the remote one, suggesting that the middle fracture adopted for injecting water, and hydraulic fracture length and conductivity have been optimized. The proposed development pattern of a staged fracturing for horizontal wells with some fractures applied for injecting water and others for production based on the same horizontal well provides new thoughts for offshore oilfields exploitation.

Effect of Non-Darcy Flow on the Constant-Pressure Production of Fractured Wells

1981 ◽  
Vol 21 (03) ◽  
pp. 390-400 ◽  
Author(s):  
K.H. Guppy ◽  
Heber Cinco-Ley ◽  
Henry J. Ramey
Keyword(s):  
Constant Pressure ◽  
Darcy Flow ◽  
Flow In Porous Media ◽  
Graphical Form ◽  
Finite Conductivity ◽  
Fracture Conductivity ◽  
Type Curves ◽  
Pressure Behavior ◽  
Apparent Conductivity ◽  
Constant Rate

Abstract In many low-permeability gas reservoirs, producing a well at constant rate is very difficult or, in many cases, impossible. Constant-pressure production is much easier to attain and more realistic in practice. This is seen when production occurs into a constant-pressure separator or during the reservoir depletion phase, when the rate-decline period occurs. Geothermal reservoirs, which produce fluids that drive backpressure turbines, and open-well production both incorporate the constant-pressure behavior. For finite-conductivity vertically fractured systems, solutions for the constant-pressure case have been presented in the literature. In many high-flow-rate wells, however, these solutions may not be useful since high velocities are attained in the fracture, which results in non-Darcy effects within the fracture. In this study, the effects of non-Darcy flow within the fracture are investigated. Unlike the constant-rate case, it was found that the fracture conductivity does not have a constant apparent conductivity but rather an apparent conductivity that varies with time. Semianalytical solutions as well as graphical solutions in the form of type curves are presented to illustrate this effect. An example is presented for analyzing rate data by using both solutions for Darcy and non-Darcy flow within the fracture. This example relies on good reservoir permeability from prefracture data to predict the non-Darcy effect accurately. Introduction To fully analyze the effects of constant-bottomhole-pressure production of hydraulically fractured wells, it is necessary that we understand the pressure behavior of finite-conductivity fracture systems producing at constant rate as well as the effects of non-Darcy flow on gas flow in porous media. Probably one of the most significant contributions in the transient pressure analysis theory for fractured wells was made by Gringarten et al.1,2 In the 1974 paper,2 general solutions were made for infinite-conductivity fractures. Cinco et al.3 found a more general solution for the case of finite-conductivity fractures and further extended this analysis in 1978 to present a graphical technique to estimate fracture conductivity.4 For the case of constant pressure at the wellbore, solutions were presented in graphical form by Agarwal et al.5 In his paper, a graph of log (1/qD) vs. log (tDxf) can be used to determine the conductivity of the fracture by using type-curve matching. Although such a contribution is of great interest, unique solutions are difficult to obtain. More recently, Guppy et al.6 showed that the Agarwal et al. solutions may be in error and presented new type curves for the solution to the constant-pressure case assuming Darcy flow in the fracture. That paper developed analytical solutions which can be applied directly to field data so as to calculate the fracture permeability-width (kfbf) product.

A new approach to evaluate the performance of partially propped hydraulic fractures

2013 ◽  
Vol 53 (1) ◽  
pp. 355 ◽  
Author(s):  
Luiz Bortolan Neto ◽  
Aditya Khanna ◽  
Andrei Kotousov
Keyword(s):  
Sensitivity Study ◽  
Economic Benefits ◽  
Productivity Index ◽  
Hydraulic Fractures ◽  
Fracture Geometry ◽  
Fracture Conductivity ◽  
New Approach ◽  
Fracture Length ◽  
Compressive Stresses ◽  
Initial Fracture

A new approach for evaluating the performance of hydraulic fractures that are partially packed with proppant (propping agent) particles is presented. The residual opening of the partially propped fracture is determined as a function of the initial fracture geometry, the propped length of the fracture, the compressive rock stresses, the elastic properties of the rock, and the compressibility of the proppant pack. A mathematical model for fluid flow towards the fracture is developed, which incorporates the effects of the residual opening profile of the fracture and the high conductivity of the unpropped fracture length. The residual opening profile of the fracture is calculated for a particular case where the proppant pack is nearly rigid and there is no closure of the fracture faces due to the confining (compressive) stresses. A sensitivity study is performed to demonstrate the dependence of the well productivity index on the propped length of the fracture, the proppant pack permeability, and the dimensionless fracture conductivity. The sensitivity study suggests that the residual opening of a fracture has a significant impact on production, and that partially propped fractures can be more productive than fully propped fractures. Application of this new approach can lead to economic benefits.

Constant rate solutions for a fractured well with an asymmetric fracture

2000 ◽  
Vol 25 (1-2) ◽  
pp. 49-58 ◽  
Author(s):  
Sergio Berumen ◽  
Djebbar Tiab ◽  
Fernando Rodriguez
Keyword(s):  
Constant Rate ◽  
Fractured Well
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