Yew / Weng Mechanics of Hydraulic Fracturing

2. Auflage 2014
ISBN: 978-0-12-420011-1
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 244 Seiten

Revised to include current components considered for today's unconventional and multi-fracture grids, Mechanics of Hydraulic Fracturing, Second Edition explains one of the most important features for fracture design - the ability to predict the geometry and characteristics of the hydraulically induced fracture. With two-thirds of the world's oil and natural gas reserves committed to unconventional resources, hydraulic fracturing is the best proven well stimulation method to extract these resources from their more remote and complex reservoirs. However, few hydraulic fracture models can properly simulate more complex fractures. Engineers and well designers must understand the underlying mechanics of how fractures are modeled in order to correctly predict and forecast a more advanced fracture network. Updated to accommodate today's fracturing jobs, Mechanics of Hydraulic Fracturing, Second Edition enables the engineer to: - Understand complex fracture networks to maximize completion strategies - Recognize and compute stress shadow, which can drastically affect fracture network patterns - Optimize completions by properly modeling and more accurately predicting for today's hydraulic fracturing completions - Discusses the underlying mechanics of creating a fracture from the wellbore - Enhanced to include newer modeling components such as stress shadow and interaction of hydraulic fracture with a natural fracture, which aids in more complex fracture networks - Updated experimental studies that apply to today's unconventional fracturing cases

Autoren/Hrsg.

Yew, Ching H.

Weng, Xiaowei

Inhaltsverzeichnis

1;Front Cover;1
2;Mechanics of Hydraulic Fracturing;4
3;Copyright;5
4;Contents;6
5;Preface to the First Edition;8
6;Preface to the Second Edition;10
7;Chapter 1: Fracturing of a wellbore and 2D fracture models;12
7.1;Introduction;12
7.2;Fracturing of a wellbore;12
7.3;Constant height fracture models;16
7.3.1;The KGD model;17
7.3.2;The PKN model;19
7.4;Circular fractures;22
7.5;Energy consideration;25
7.6;Poroelasticity and filtercake;27
8;Chapter 2: Three-dimensional fracture modeling;34
8.1;Introduction;34
8.2;Fluid motion inside the fracture;34
8.3;Fracture opening equation;39
8.4;Propagation of a hydraulic fracture;41
8.4.1;Discretization of Eq.(2-14) in the time domain;42
8.4.2;Procedure for solving eqs.(2-24) and (2-29);43
8.4.3;Movement of fracture front;43
8.5;Mesh generation;45
8.5.1;Node generation on fracture front;45
8.5.2;Interior node generation;47
8.5.3;Insertion of nodes inside the domain;48
8.5.4;Construction of elements;50
8.5.5;Interpolation between meshes;51
8.6;Results and discussion;52
9;Chapter 3: Proppant transport in a 3D fracture;60
9.1;Introduction;60
9.2;The governing equations;60
9.3;Proppant transport;64
9.4;Finite element formulation;66
9.5;Analysis of shut-in;68
9.6;Results and discussion;69
9.7;Pseudo 3D models;76
10;Chapter 4: Deviated wellbores;80
10.1;Introduction;80
10.2;Stress distribution and initiation of a hydraulic fracture;81
10.3;Cased hole and perforation strategy;89
11;Chapter 5: Link-up of mini-fractures from perforated holes;100
11.1;Introduction;100
11.2;Formulation of the problem;100
11.3;Solution method;103
11.4;Fracture growth and link-up;105
11.5;Results and discussion;107
12;Chapter 6: Turning of fracture from a deviated wellbore;116
12.1;Introduction;116
12.2;Nonsymmetric growth of a 2D fracture from a horizontal wellbore;117
12.3;The turning of a hydraulic fracture;123
12.4;Results and discussion;128
12.5;Fracturing of a horizontal well;133
13;Chapter 7: Fracture propagation in a naturally fractured formation;144
13.1;Introduction;144
13.2;Interaction of a HF with a NF;144
13.3;Modeling of complex fracture networks;150
13.4;Impact of NFs on HF pattern;155
13.4.1;Example #1: Simple fracture network;155
13.4.2;Example #2: Complex fracture network;160
13.4.3;Effect of NF distribution on HF network;164
13.5;Propagation of shear slip along a NF;167
13.5.1;Theoretical development;170
13.5.1.1;Continuity of fluid mass in the fracture;172
13.5.1.2;Pressure drop in the fracture;172
13.5.1.3;Change of permeability due to pressure change and shear slip;172
13.5.1.4;Frictional law;173
13.5.1.5;Fracture opening equation;174
13.5.1.6;Boundary conditions;174
14;Chapter 8: Stress shadow;188
14.1;Introduction;188
14.2;Formulation of the problem;188
14.3;Interaction between parallel fractures;195
14.3.1;Two parallel fractures;195
14.3.2;Multiple transverse fractures in horizontal wells;197
14.4;Interaction among complex fractures;201
15;Chapter 9: Experimental studies;208
15.1;Introduction;208
15.2;Experiments carried out in laboratory;208
15.2.1;Breakdown pressure of an open hole;209
15.2.2;Fracture propagation and Its containment;210
15.2.3;Fracture initiated from deviated or horizontal wellbores;211
15.2.4;The shape of the hydraulic fracture near the tip region;212
15.2.5;Testing of fracture crossing criterion;214
15.2.6;Simulation of a massive hydraulic fracture;216
15.2.7;Similitude analysis;218
15.3;Experiments carried out in the field;219
15.3.1;Measurement of In situ stresses;220
15.3.2;Application of the measured downhole pressure curve;222
15.3.3;Measurement of fracture width and pressure;224
15.3.4;Hydraulic impedance method;226
15.3.5;Estimation and mitigation of near-wellbore tortuosity;226
16;Notations;232
17;Author Index;234
18;Subject Index;238

Leseproben

Chapter 1 Fracturing of a wellbore and 2D fracture models
Abstract
The early fracture models are reviewed. And, the effects of dry zone and filter-cake on the behavior of a hydraulically induced fracture are discussed in this chapter. Keywords Constant height fracture Breakdown pressure KGD model PKN model Circular fracture Energy method Dry zone Filter-cake Poroelasticity Introduction
The hydraulic fracturing process has been employed to enhance the production of oil and gas from underground reservoirs for many decades. In the process, the frac-fluid is pumped at a high pressure into a selected section of wellbore. This fluid pressure creates one or more fractures extending into the rock medium that contains oil or gas. Since the fracturing operation is conducted at a great depth, the minimum compressive in situ stress is typically in horizontal direction, the hydraulically induced fracture is a vertical fracture. The dimension and propagation characteristics of a hydraulic fracture are important information in design of fracturing operations. Knowing the properties of reservoir rock, frac-fluid, and the magnitude and direction of in situ stresses, one seeks an accurate prediction of the dimension (opening width, length, and height) of the hydraulically induced fracture for a given pumping rate and time. Many fracture models have been developed for this purpose. The initiation of a hydraulic fracture from a vertical wellbore and two-dimensional fracture models are discussed in the following sections. Fracturing of a wellbore
Consider an uncased vertical wellbore (or an open hole) under the action of horizontal in situ stresses smin and smax as shown in Fig. 1-1. Figure 1-1 Horizontal section of a vertical wellbore under the action of in situ stresses and borehole pressure. Assume that the rock is an elastic medium and has a tensile failure stress sT. The breakdown pressure pb for introducing a fracture at the surface of borehole can be calculated by applying elasticity theory [1] to give b=3smin-smax+sT   (1-1) where smin is the minimum in situ stress, smax the maximum in situ stress, and sT the tensile failure stress of the rock. The hydraulically induced fracture is a vertical fracture and the fracture plane is perpendicular to the minimum horizontal in situ stress smin as shown. Note that the above equation is independent of hole size and the elastic moduli of rock medium. For a wellbore section at a depth of 10,000 ft, the typical values for the horizontal minimum and maximum in situ stresses are in the order of 5000-7000 psi, respectively. The rock has a tensile failure stress on the order of 500-1500 psi. Equation (1-1) clearly shows that the rock tensile failure stress sT has a small effect on the magnitude of breakdown pressure, and the hole breakdown pressure is mainly to overcome the compressive circumferential hoop stress produced by in situ stresses. It is clear that the applied wellbore pressure first balances the reservoir pressure (or pore pressure), then overcomes the compressive circumferential hoop stress, causing a tensile stress on the hole surface. A fracture is initiated when this surface stress reaches the tensile failure stress of the rock medium. The hydraulically induced fracture propagates from the wellbore into reservoir as pumping continues. A typical downhole pressure record (i.e., the pressure measured inside the hole near the opening of hydraulic fracture) is sketched in Fig. 1-2. Figure 1-2 A down-hole pressure record. The hydraulically induced fracture propagates into the reservoir as pumping continues, and at the same time the frac-fluid leaks off from the fracture surface into the surrounding rock medium. It is important to observe that the opening of the fracture is maintained by the net pressure (fluid pressure minus the minimum in situ stress), while the fluid leak-off rate from the fracture surface is caused by the differential between fluid pressure and reservoir pressure. Referring to Fig. 1-2 again, the maximum pressure is the initial breakdown pressure pb. The pressure drops, but not always in the field, when a fracture is initiated at the borehole surface. The near constant portion of the pressure curve is the propagation pressure pprog. This is the pressure that causes the propagation of hydraulic fracture into the reservoir. When pumping stops, the pressure drops instantly to a lower value, due to the vanishing frictional pressure loss in the pipe, perforation entrance and near-borehole area, and then continues to decrease slowly to the reservoir pressure due to fluid leaking off from the fracture and borehole as shown in the figure. The transition point is called the shut-in pressure psi (or the instantaneous shut-in pressure, ISIP). However, fluid continues to leak off from fracture surface and the fracture opening width continues to decrease. The fluid pressure inside the fracture eventually reaches to an equilibrium with the minimum in situ stress and at this point the hydraulic fracture closes. The fracture closure pressure, which can be determined from the pressure decline analysis, is taken as a measure of the minimum in situ stress. Although the ISIP is somewhat higher than the fracture closure pressure, the ISIP can be easily identified from the measured pressure-time curve. Field engineers often use ISIP to estimate the magnitude of the minimum horizontal in situ stress. Unfortunately, the situation is somewhat more complicated in field conditions. The underlying control factors for this pressure drop are discussed by McLennan and Roegiers [2]. Equation (1-1) is derived from the assumption that the rock is an elastic medium. However, most reservoir rocks are porous medium through which fluid can flow. The pressure difference between fracture and reservoir causes the fluid to flow from the fracture into reservoir, that is, fluid leak off. The experimental study carried out by Haimson and Fairhurst [3,4] and Medlin and Masse [5] have demonstrated that the porosity and pore fluid have an influence on the hole breakdown pressure. By applying the poroelasticity theory, Schmitt and Zoback [6] have modified Eq. (1-1) to the form as follows: For a formation impermeable to frac-fluid, b=3smin-smax+sT-ßpb   (1-2) For a formation permeable to frac-fluid, b=3smin-smax+sT-app1-2v1-v1+ß-a1-2v1-v   (1-3) where pp is the pore pressure; ß the pore pressure factor in tensile failure criterion, 1 = ß = 0; v the Poisson’s ratio of dry rock; and =1-bulkmodulusofdryrockbulkmodulusofskeletonmaterial,1=a>0. Parameter a is known as the Biot’s poroelastic parameter which approaches the upper limit of 1.0 for a compliant rock and less for a stiff low-porosity rock. Schmitt and Zoback [6] have demonstrated that Eqs. (1-2) and (1-3) give a better agreement with experimental data. The above equations clearly show that the effect of rock porosity and pore pressure is to lower the hole breakdown pressure. They also suggest that the breakdown pressure of the hole is dependent on the filtercake-forming capability of the fluid. Most wellbores that need fracturing are cased wellbores. To fracture a cased wellbore, the wellbore is first perforated with shaped charges to form a series of perforated holes spiraling along the wellbore surface as shown in Fig. 1-3. Figure 1-3 A cased vertical wellbore with perforated holes. The perforations are typically made at spacings of 4-6 shots per foot and at a phase angle of 60° or 120° as shown in the figure. When the wellbore is pressurized, the perforated holes in (or near) the direction of maximum horizontal in situ stress (smax) will be fractured first. The breakdown pressure can be calculated from Eq. (1-1) by replacing the maximum horizontal in situ stress smax with the vertical stress sVert. The mini-fractures initiated from the perforations may or may not link up to form a large hydraulic fracture perpendicular to the minimum in situ stress along the direction of the wellbore axis. In practice, it is desirable for the mini-fractures to link up forming a large fracture along the wellbore. The linking up of mini-fractures will be discussed in Chapter Five. Constant height fracture models
Since the wellbore is often fractured at a great depth (> 5000 ft) where the minimum in situ stress is in the horizontal plane, the fracture is a vertical fracture whose plane is perpendicular to the minimum in situ...