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R.D. Carter

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Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*J Pet Technol*31 (03): 362–372.

Paper Number: SPE-6838-PA

Published: 01 March 1979

Abstract

This paper discusses how to analyze past performance and predict futureperformance of tight gas wells stimulated by massive hydraulic fracturing (MHF)using finite fracture flow-capacity type curves. The limitations ofconventional pressure transient analysis and other methods of evaluating MHFtreatment are discussed. A set of constant well-rate and wellbore-pressure typecurves is presented. Introduction Because of the deteriorating gas supply situation in the U.S. and theincreasing demand for energy, the current trend is to consider seriously theexploitation and development of low-permeability gas reservoirs. This has beenpossible because of changes in the economic climate and advances in wellstimulation techniques, such as massive hydraulic fracturing (MHF). It nowappears that MHF is a proven technique for developing commercial wells inlow-permeability or "tight" gas formations. As the name implies, MHF isa hydraulic fracturing treatment applied on a massive scale, which may involvethe use of at least 50,000 to 500,000 gal treating fluid and 100,000 to 1million lb proppant. The purpose of MHF is to expose a large surface area ofthe low-permeability formation to flow into the wellbore. A low-permeabilityformation is defined here as one having an in-situ permeability of 0.1 md orless. Methods for evaluating a conventional (small-volume) fracturing treatmentare available, but the evaluation of an MHF treatment has been a challenge forengineers. To evaluate the success of any type of fracture stimulation, prefracturing rates commonly are compared with postfracturing production rates.These comparisons are valid qualitatively if both pre- and postfracturing ratesare measured under similar conditions (that is, equal production time, samechoke sizes, minimal wellbore effects, etc.). Unfortunately, to evaluate thesuccess of different kinds of fracturing treatments, pre- and postfracturingproduction rates often are measured pre- and postfracturing production ratesoften are measured and compared using not only the same well tested underdissimilar conditions, but also the same kind of comparisons between differentwells that may even have different formation permeabilities. Thus, resultsoften are invalid and may cause misleading conclusions. Moreover, suchcomparisons do not help predict long-term performance. To predict long-termperformance for MHF wells, reliable estimates of fracture length, fracture flowcapacity, and formation permeability are needed. Pressure transient methods for analyzing wells with small-volume fracturingtreatments are based on the concept of infinite or high fracture flow capacityand are used to determine the effectiveness of a stimulation by estimating thefracture length. Our experience indicates that these methods are not adequatefor analyzing wells with finite flow-capacity fractures. Such methods provideunrealistically short fracture lengths for MHF wells provide unrealisticallyshort fracture lengths for MHF wells with finite flow-capacity fractures.Furthermore, fracture flow capacities cannot be determined. Includes associated paper SPE 8145, "Type Curves for Evaluation andPerformance Prediction of Low-Permeability Gas Wells Stimulated by MassiveHydraulic Fracturing."

Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*J Pet Technol*15 (06): 651–658.

Paper Number: SPE-400-PA

Published: 01 June 1963

Abstract

A method based on theoretical considerations is presented for estimating stabilized performance of gas wells from data obtained from short-term flow tests. Calculated results are presented for 11 gas wells evaluated with four- to five-hour flow tests. For seven wells on which comparison was available, satisfactory agreement between measured and calculated performance was obtained. Although the final results are favorable, differences in flow capacity k(g)h obtained from flow tests conducted at different rates were observed. This inconsistency did not seriously affect the calculated results in the test wells. Introduction In order to negotiate the sale of gas from newly drilled gas wells and to plan otherwise for the orderly exploitation of gas reserves, it is necessary to predict the long-term withdrawal rates physically possible for each well. Since low permeability gas wells do not stabilize except after a lengthy period of flow, the operator is unable, without wasting large amounts of gas, to measure directly the stabilized performance prior to contracting for sale of the gas and connecting the well to a pipeline. This problem is not new, but is one which has recently received considerable attention because of the rising importance of natural gas in the economy and new emphasis on the development of gas reserves. Thus, a method is needed for estimating stabilized performance from information obtained from short-flow tests in which stabilized flow is not attained. Such short tests would be suitable for wells not connected to a pipeline since the tests require only small amounts of time, labor and production of gas. Other requirements of such a method are short calculation time and use of a model of the gas well and is reservoir drainage area which is as consistent as possible with present theoretical, experimental and field knowledge. The method presented herein was developed in an effort to meet these requirements. It has been named the "two-flow method".In addition to the section on the development and description of the method, a description of field application of the method and a discussion of well test results are included. Finally, there is a section on an additional consideration prompted by some of the test results. The Appendix contains certain details of the derivation of the two-flow method and a sample calculation for Test Well 1. MATHEMATICAL DEVELOPMENT AND DESCRIPTION OF THE METHOD The method is based upon the following assumptions: The system can be described as a finite cylindrical gas reservoir produced by a single cylindrical well located at the center of the reservoir. Flow is strictly radial. Flow obeys Darcy's law except very near the well where a quadratic flow law is assumed. The system is also characterized by a laminar flow skin factor. The use of a quadratic or turbulent flow term is more fully justified in Refs. 1 and 2.When such a system is opened at the wellbore to constant rate flow from an initial condition of uniform pressure distribution, the radius or drainage quickly passes through the nondarcy flow and "skin effect" region immediately surrounding the well. After the drainage radius or "transient" has passed beyond this region and before it reaches the external boundary, drawdown can be expressed by ( ) = [ ] + Bq ......................................(1) After the drainage radius reaches the external boundary, stabilized flow exists and drawdown is given by ( ) = [ ] ...................................(2) Eqs. 1 and 2 form the basis for the method. The validity of these equations will now be examined in the light of some well test data previously available. It has been found by actual measurements on gas wells that the relationship between drawdown and flow rate, that is the performance curve, is closely approximated by q = C ( ) ...............................(3) Eq. 3 is a straight line on log-log graph paper. JPT P. 651^

Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*J Pet Technol*14 (05): 549–554.

Paper Number: SPE-108-PA

Published: 01 May 1962

Abstract

Numerical solutions are presented to some problems of unsteady-state radial flow of gas in which Darcy's law holds. These solutions are intended to aid in explaining the observed behavior of gas wells during drawdown tests. The variation of viscosity and Z-factor with pressure is accounted for in the solutions. Results are presented for three types of problems: unfractured wells producing at a constant rate, fractured wells producing at a constant rate and unfractured wells producing through a critical flow prover. In the critical-flow-prover solutions, a correction of the calculated wellbore pressure to account for non-Darcy flow is made. A good correlation is shown between the solutions to the problem of Type 1 and the corresponding diffusivity-equation solution. Using this correlation, the diffusivity solution may be used to obtain gas-well solutions. The solutions to the problems of Type 2 illustrate the difference in drawdown-curve behavior to be expected between fractured and unfractured gas wells. Methods for estimating fracture radius and flow capacity are presented and verified from solutions of Type 2. The solutions to the problems of Type 3 illustrate the differences to be expected between critical-flow-prover drawdown tests and constant-rate tests. A equation is presented for correcting critical-flow-prover data to constant-rate conditions. A description of the methods used in obtaining the solutions appears in the Appendix. Introduction It is necessary for many engineering purposes, such as predicting future deliverability performance, to be able to relate bottom-hole flowing pressure, formation pressure and flow rate for conditions of stabilized flow in gas wells. This information is customarily given as a plot of (p -p ) vs q on logarithmic coordinates. It is desirable to be able to predict stabilized performance curves for gas wells based on data obtained from drawdown tests of short duration. Tests of long duration may be wasteful of gas, and low-permeability wells do not stabilize in a short-duration test. Although it is now commonly recognized that non-Darcy flow plays a significant part in gas-well behavior, it is believed that an understanding of transient behavior of systems obeying Darcy's law is still important in the interpretation of short-term test data, and the prediction of stabilized performance curves there from. In this connection, an equation for correcting Darcy flow solutions for non-Darcy flow effects has existed in the literature for some time. This equation is ......................................(1) It seems likely that solutions of the type presented herein, combined with the non-Darcy flow correction of the type of Eq. 1 and the usual laminar-flow skin factor, could provide a model which would adequately explain transient gas-well behavior for times after the non-Darcy flow region (which should be confined to a small area surrounding the well) has been established. The solutions presented in this paper are for three types of problems: unfractured wells producing at a constant rate, fractured wells producing at a constant rate and unfractured wells producing through a critical flow prover. In the problems of Types 1 and 2, no corrections for non-Darcy flow were made in the results presented, since it was reasoned that the constant-rate boundary condition would facilitate such a correction if it was desired later. For the problems of Type 3, however, a condition of varying flow rate required that a non-Darcy flow correction of the type of Eq. 1 be included. This was done. Based on the numerical results presented, a number of approximations and a correlation are presented which may be useful in analyzing gas-well test data. TYPE 1 PROBLEMS-UNFRACTURED WELL, CONSTANT FLOW RATE It is assumed that the system can be described as a finite cylindrical gas reservoir produced by a single cylindrical well located at the center of the reservoir. Flow is strictly radial. When the flow obeys Darcy's law, the governing differential equation is ..........(2) where M(p) = (2,703 x 10(–6) x 520), and f(R) =. Boundary and initial conditions are: ...................(3) JPT P. 549^