Influence of temperature, effective stress and non-Darcy flow on the fracture flow capacity of propped fractures

Abstract This paper is concerned with the effect of propping-agent concentration on flow capacity of a fracture in the case in which there is embedment of the propping agent. Previous published studies have shown definitely that there is a relationship between fracture flow capacity and propping-agent concentration, and it has been shown that the theoretical results are confirmed by laboratory experiments. The problem of directly finding sand concentration for maximum flow capacity of a sand-propped fracture is solved, and formulas and charts are given to obtain this concentration under various conditions of effective overburden pressure, medium sand-grain diameter and rock properties. It is shown that, for the same effective overburden pressure and the same rock characteristics, optimum sand concentration in pounds per gallon does not depend on medium sand diameter. For conditions met in hydraulic fracturing operations, it is found that sand concentration in grains per square inch for maximum flow capacity varies within a wide range of values; this indicates the convenience of using data of fracturing pressure and rock characteristics for calculating sand concentration in order to achieve the best results in fracture treatments. Introduction It has been pointed out in the published literature that one important factor controls the success of a hydraulic fracturing operation - the propping of the fracture. The main effect of the propping agent is to hold the fracture open by means of the reaction forces that oppose the pressure due to the overburden. It is assumed in this paper that the propping agent is sand, that the grains are spherical and uniform in size, and that this sand is distributed in a monolayer in the fracture. The existence of a sand concentration value for maximum fracture flow capacity has been recognized since the publication of one of the first studies on the subject. In the reference cited, flow capacity was assumed to be proportional to the cube of the fracture volume per square inch not filled by sand.

Download Full-text

A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow

Journal of Computational Physics ◽

10.1016/j.jcp.2014.11.038 ◽

2015 ◽

Vol 283 ◽

pp. 205-223 ◽

Cited By ~ 46

Author(s):

B. Nœtinger

Keyword(s):

Steady State ◽

Darcy Flow ◽

Fracture Flow ◽

Quasi Steady State ◽

Steady State Method ◽

State Method

Download Full-text

Fracture Flow Capacity - A Key to Sustained Production after Hydraulic Fracturing

10.2118/6127-ms ◽

1976 ◽

Cited By ~ 1

Author(s):

A.R. Jennings ◽

D.L. Lord

Keyword(s):

Hydraulic Fracturing ◽

Fracture Flow ◽

Flow Capacity

Download Full-text

Effect of a Partial Monolayer of Propping Agent on Fracture Flow Capacity

Transactions of the AIME ◽

10.2118/1291-g ◽

1960 ◽

Vol 219 (01) ◽

pp. 31-37 ◽

Cited By ~ 13

Author(s):

S.R. Darin ◽

J.L. Huitt

Keyword(s):

Fracture Flow ◽

Flow Capacity

Download Full-text

The effect of temperature on high-resolution TEM image contrast

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100139573 ◽

1995 ◽

Vol 53 ◽

pp. 640-641

Author(s):

T. Geipel ◽

W. Mader ◽

P. Pirouz

Keyword(s):

Form Factor ◽

Inelastic Scattering ◽

Accurate Method ◽

Waller Factor ◽

Effect Of Temperature ◽

Specimen Thickness ◽

Influence Of Temperature ◽

Debye Waller Factor ◽

Influence Of Temperature On ◽

Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

Download Full-text