By E. J. Hoffman
The ever present examples of unsteady-state fluid move pertain to the construction or depletion of oil and fuel reservoirs. After introductory information regarding petroleum-bearing formations and fields, reservoirs, and geologic codes, empirical equipment for correlating and predicting unsteady-state habit are awarded. this is often by way of a extra theoretical presentation in response to the classical partial differential equations for stream via porous media.Whereas those equations may be simplified for the move of (compressible) fluids, and idealized recommendations exist when it comes to Fourier sequence for linear move and Bessel features for radial stream, the movement of compressible gases calls for laptop strategies, learn approximations. An research of computing device recommendations exhibits, luckily, that the unsteady-state habit could be reproduced by way of steady-state density or strain profiles at successive occasions. this may demark draw down and the transition to long term depletion for reservoirs with closed outer limitations.
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Additional info for Unsteady-State Fluid Flow: Analysis and Applications to Petroleum Reservoir Behavior
I . . . " ~ 30 i- ~ zc i " ~ ?. I. 8 61 it tO It |Z Fig. 1. The ordinate is expressed as the percentage of daily production for the first year, and starting at year one. 3 Thus at point 2, representing the end of year 2, the daily production may be construed as 50% of that at point 1, which represents the end of year 1. The points so represented would therefore constitute the relative daily production rate on that day of the year: wheren = 1, 2, 3 , . . years. 2, with slope of---1. Hence 1 --~--1 C or C-- 1 This line can in fact be determined approximately from the first three points' 1, 2, and 3.
As previously derived, values greater than unity are not admissible. Therefore, for C ~ 1, say at points 1 and 2, C=l a - Ro +12 Ro +11 or a - 100 Ro +2 50 R o +1 and Ro-- 0 . 57. The calculations may be refined by using a b- where - at~ 1 t 2 1 t 3 - bt 2 -- 64 UNSTEADY-STATE FLUID FLOW a _ L), b_ O_~j provided C is not greater than unity. S7 + 2 Unfortunately, We would be mdetemamate. Cumulative Solution It has previously been derived that 1-C ~ l- 1+ (34) 01-C or W-a 1- [ c,l 1-C 1+ Ro where a is a constant defined by the above substitution.
REFERENCES Muskat, Morris, Physical Principles o f Oil Production, McGraw-Hill, New York, 1949. Reprinted as the second edition by Intemational Human Resources Development Company, Boston, 1981. 40 2. UNSTEADY-STATE FLUID FLOW Fertl, W. , Abnormal Formation Pressures. Implications to Exploration, Drilling, and Production of Oil and Gas Resources, Elsevier, Amsterdam, 1976. With contributions by G. V. Chilmgarian and H. H. Rieke. 3. Hoffman, E. , Phase and Flow Behavior in Petroleum Production, Energon, Laramie, WY, 1981, Chapter 14.
Unsteady-State Fluid Flow: Analysis and Applications to Petroleum Reservoir Behavior by E. J. Hoffman