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ESTS0160 WELBORE.

WELBORE, Transient Wellbore Fluid Flow Model

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1. NAME OR DESIGNATION OF PROGRAM:  WELBORE.
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2. COMPUTERS
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Program name Package id Status Status date
WELBORE ESTS0160/01 Arrived 25-MAY-2001

Machines used:

Package ID Orig. computer Test computer
ESTS0160/01 CDC 7600
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3. DESCRIPTION OF PROBLEM OR FUNCTION

WELBORE is a code to solve transient, one-dimensional two-phase or single-phase non-isothermal  fluid flow in a wellbore. The primary thermodynamic variables used in solving the equations are the pressure and specific energy. An equation of state subroutine provides the density, quality, and temperature. The heat loss out of the wellbore is calculated by solving a radial diffusion equation for the temperature changes out- side the bore. The calculation is done at each node point in the wellbore.
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4. METHOD OF SOLUTION

The program uses a partially implicit method to solve by a finite-difference method the Navier-Stokes equations of mass, momentum, and energy. Terms that would impose severe time restrictions (e.g. compressibility effects) are evaluated implicitly while other terms are expressed in an explicit manner. The convec- tion effects are solved using a conserving upwind finite difference  formulation. Slip is assumed between the gas and liquid phase and is given by an empirical correlation. Any slip model could be used but  the one provided with the program is that given by Orkiszewski, 1967. The friction factor is also given as an empirical correlation  as specified by Chisholm, 1973. Again any other correlation could be substituted if desired. The equation of state provided with the program is that of pure water.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:  Maxima of -, 200 nodal points, 25 grid points
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6. TYPICAL RUNNING TIME

The sample problem requires about 27 CP seconds on a CDC7600 for execution.
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7. UNUSUAL FEATURES OF THE PROGRAM

Steady state is not assumed. The transient wellbore code has been coupled with a single-phase radial  flow reservoir model. One can essentially eliminate the behavior of  the fluid in the well as an unknown so that the actual reservoir flow can be determined even when wellbore storage is important. By knowing the actual reservoir flow, one can determine reservoir pro-  perties by using a multi-rate well test analysis. It may not be necessary to wait until wellbore storage is over. During this early  time of a well test, a steady-state model of the flow in the well is not appropriate because a steady-state model assumes that mass into  the well equals the mass out of the well. Also, one can solve the flow into the well during a complete shut in to determine the effects of phase redistribution which is not possible with a steady- state model.
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8. RELATED AND AUXILIARY PROGRAMS

WELBORE is one of a set of five geothermal codes. The others are: ANALYZE for multiwell, multirate welltest parameter determination (NESC Abstract 891); CCC for one- phase conduction, convection, and compaction (NESC Abstract 892); SHAFT79 for two-phase geothermal reservoir simulation (NESC Abstract 893); and TERZAGI for isothermal fluid flow and subsidence (NESC Abstract 894).
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9. STATUS
Package ID Status date Status
ESTS0160/01 25-MAY-2001 Masterfiled Arrived
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10. REFERENCES

- D. Chisholm,
  Pressure Gradients Due to Friction During the Flow of Evaporating
  Two-Phase Mixtures in Smooth Tubes and Channels,
International Journal of Heat and Mass Transfer, Vol. 16, pp. 347-    358, 1973.
- C.W. Miller,
  Wellbore Storage Effects in Geothermal Wells, paper SPE 8203,
  presented at the 54th Annual Fall Technical Conference and Exhi-
  bition of the Society of Petroleum Engineers of the American
  Institute of Minning, Metallurgical and Petroleum Engineers,
  Las Vegas, Nevada, September 23-26, 1979,
  LBL-8844, September 1979.
- J. Orkiszewski,
  Predicting Two-Phase Pressure Drops in Vertical Pipe, Journal of
  Petroleum Technology, Vol. 19, pp. 829-838, June 1967.
- WELBORE, NESC No. 895.7600, WELBORE Sample Problem Output, NESC
  Note 81-10, October 14, 1980.
ESTS0160/01, included references:
- Constance W. Miller:
  WELBORE User's Manual
  LBL-10910 (January 1980).
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11. MACHINE REQUIREMENTS:  55,000 (octal) words of SCM storage.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
ESTS0160/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  SCOPE 2.1.5.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHOR

C.W. MILLER
Earth Sciences Division
Lawrence Berkeley Laboratory
Berkeley, California 94720
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16. MATERIAL AVAILABLE
ESTS0160/01
source program   mag tapeWELBORE Source Program                     SRCTP
test-case data   mag tapeWELBORE Sample Problem Input               DATTP
report                   LBL-10910 (January 1980)                   REPPT
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17. CATEGORIES
  • H. Heat Transfer and Fluid Flow
  • R. Environmental and Earth Sciences

Keywords: convection, finite difference method, fluid flow, geothermal systems, pressure, reservoir engineering, temperature.