Pressure loss in open fractures at near wellbore reservoir conditions is measured in the laboratory. The fractures were made artificially in 1.5 Inc. cores which were flowed with nitrogen gas in a Hassler core holder.
Forchheimer's flow equation describes the pressure loss behavior at the entire rate interval investigated. Empirical functions for the permeability and the inertial flow coefficient are derived.
The greatest challenge to this work has been to measure the very small fracture widths accurately.
This thesis is a laboratory study on high velocity flow in open rock fractures.
1.1 Reservoir fractures improve productivity
In low permeability oil and gas reservoirs, conductive fractures may increase the production rate considerably. Fractures can either exist naturally in the reservoir (as for the Ekofisk reservoir) or they can be artificially made from existing wells. The artificial fractures are created hydraulically by injecting fluid at high rate and high pressure until the formation fractures. Proppant agents in the fracturing fluid keep the fracture open when the pressure is released and the well is put on production. Because of stronger, bigger, lighter and rounder proppants and higher fluid viscosities with less formation fluid loss, very high conductivity fractures can now be created.
Today the productivity of even high permeability reservoirs may be improved by hydraulic fracturing. Due to higher production rates, the field develop- ment costs are paid back much faster and rents are saved. By creating very high conductivity fractures, relative to the reservoir permeability, even more marginal reservoirs can become profitable to develop.
1.2 Known fracture parameters
During hydraulic fracturing several parameters such as volume injected, pressure and time are recorded. From these data we know the average approximate width, height, length and proppant coverage of the fracture. For natural fractures, the width can be determined by open hole well logging. Then rough estimates of fracture permeability can be made after shut in for transient pressure build up testing.
To manage more accurate simulation of the reservoir without expensive well tests, and to plan future hydraulic fractures, we want to know how the fracture geometry and fluid properties affect the pressure loss. How these parameters affect the pressure loss during production, especially at high rates, is today far from fully understood.
1.3 Earlier work on flow in fractures
During the literature search no references to experiments on propped fractures were found. However, some experiments have been executed on open fracturesl and on packed proppant agents /2-4/ They all indicated that non linear high velocity flow is common in both open fractures and in packed proppants. The article on open fractures refer to weak inertial (Cubic) flow and the others on packed proppants refer to strong inertial (Forchheimer) flow:/2-4/
dp/dx = vµ/k + (Beta)(rho)v^2 (1-1)where µ is the viscosity, k is the permeability, (Beta) is inertial resistance, (rho) is density, v is velocity and x is the coordinate in the flow direction.
The permeability does not deserve much attention because most of the pressure loss in hydraulic fractures is caused by the high velocity term/2/ which is proportional to the inertial resistance coefficient, (Beta). Experiments indicate that Beta is dependent on only rock properties /5/. Different expressions for Beta in proppants and porous media are suggested. They all express oB as a function of either permeability and porosity /3,4/ or only as a function of permeability./2/ Some experiments show even that the Beta-factor in packed sand changes at higher Reynolds numbers, probably due to inhomogeneous permeability in the media/2/.
1.4 Earlier work at NTNU
Research on flow in open fractures is going on at our university, NTNU, in Norway. Skjetne (1995)/6/ has simulated open fractures numerically. He has also set up the core flow apparatus used in this thesis. Bentzen (May 1996)/7/ and Trygve Kløv (Dec. 1996)/12/ have developed methods of creating artificial fractures in 1.5 Inc. diameter rock cores. The fractures look very similar to what we could expect to have in a real hydraulic induced fracture.
The core is parted longitudinally and the fracture between the two halves is kept open with a spacer mattress on the edges in between. The fractured core is placed in a Hassler core holder and flowed with nitrogen gas. The flow rate and pressure loss are recorded and fed into a computer program (1) which calibrates and calculates solutions to equations for different flow regimes (Darcy, Weak Inertial (Cubic) and Strong Inertial (Forchheimer flow)). Then the solutions of the flow equations are plotted to determine the acting flow regime and to find parameters such as the permeability (k) and the inertial flow coefficient (Beta) after curve fitting.
1.5 The goals of this thesis
The object of this thesis is to improve the general understanding of pressure loss in fractures, measure pressure loss on open fractures in the laboratory and to find out:
- if the pressure loss in open fractures at near reservoir conditions follows
Forchheimer's equation 1-1
- how fracture width (w) and roughness act on the permeability
- how permeability (k), width (w), and roughness act on the Cofactor
- if the Beta-factor changes at different Reynolds numbers
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(1)Programmed by Erik Skjetne and Trygve Kløv at NTNU
1. Forchheimer's equation describes the flow in open near wellbore rock fractures at reservoir conditions.
2. The pressure loss is at reservoir conditions a function of both the per- meability and the inertial flow coefficient (Beta). Neither the inertial flow coefficient nor the permeability may with reasonable feasibility be ne- glected.
3. Both permeability and the inertial flow coefficient are functions of frac- ture width, and roughness. The roughness may be divided into an in- ertial roughness (n) and an viscous roughness (R). Empirical functions are derived.
4. The inertial flow coefficient is constant over the entire measured Reynolds number interval (Reynolds numbers from 2.5 to 1850).
5. Wall slip is not observed in this laboratory study.
/2/ J.P. Martins, D. Milton-Tayler,H.K. Leuag: "The Effects of Non-Darcy Flow in Propped Hydraulic Fractures", SPE paper 20709, Sept. 1990
/3/ D.A Pursell, S.A. Holditch, D. Blakeley: "Laboratory Investigation of Inertial Flow in High-Strength Fracture Proppants", SPE paper 18319, Oct 1988
/4/ D.R Maloney, B.L. Gall, C.J. Raible: "Non-Darcy Gas Flow Through Propped Fractures: Effects of Partial Saturation, Gel Damage, and Stress", SPE paper 16899, Sept. 1987
/5/ David Milton-Tayler: "Non-Darcy Gas Flow: From Laboratory Data to Field Prediction", SPE paper 26146, June 1993
/6/ E. Skjetne: "High-Velocity Flow in Pororus Media", Doctoral-Engineer Thesis at Norwegian Institute of Technology, 1995
/7/ T. Bentzen: "High Velocity Flow in Fractures", project at Norwegian University of Science and Technology, 1996
/8/ Ze Su : "Pressure Drop in Perforated Pipes For Horizontal Wells", Doctoral-Engineer Thesis at Norwegian Institute of Technology, 1996
/9/ K.O. Temeng and R.N. Horne: "The Effect of High-Pressure Gradients on Gas Flow", SPE paper 18269, Oct. 1988
/10/ Frank M. White: "Viscous Fluid Flow", Second Edition, Mc Graw-Hill International Editions
/11/ T. Kløv: "Comressible Flow Between Paralell Plates", paper, Norwegian University of Science and Technology, Dec. 1996
/12/ T. Kløv: "High Velocity Flow in Fractured Cores", paper, Norwegian University of Science and Technology, Dec. 1996
/13/ T. Kløv: "Properties of Induced Fractures in Vertical and Deviated Wells", paper, Norwegian University of Science and Technology, July 1996
/14/ E. Skjetne: "User manual for High-Velocity Flow Setup", Norwegian University of Science and Technology, Feb. 1995
Last modified: Wed Feb 26 16:52:19 NFT 1997