A LINEAR RELATIONSHIP BETWEEN LIQUID PRODUCTION AND OILFIELD SUiBSIDENCE
WILMINGTON OIL FIELD
The well-known Wilmington oil field, located along the south coastal section of the Los Angeles basin, is one of the few additional fields for which the data permit a comparison between liquid production and subsidence. Owing, however, to the absence of offshore control and the presence of interfering subsidence domains, it has not been possible to measure or calculate, other than very roughly, the cumulative subsidence volumes over successive production intervals. Thus, although no attempt is made here to compare liquid production with successive volumes of subsidence, we may compare various aspects of liquid production with subsidence at a point (fig. 5).
According to records of the Long Beach Department of Oil Properties (D. R. Alien, 1969, written communication), the ratio of V, to Vp was about 0.62 for the period between 1936 (when production began) and 1956 (immediately preceding the initiation of full-scale water flooding). Our own crude estimate, as derived from the addition of three successive volumes of subsidence whose configurations are assumed to have approximated inverted elliptical cones, indicates that the maximum value of V, to Vpfor the period 1936 through mid-1957 was no more than about 0.7; subjective correction for the changing configu- ration of the subsidence bowl between 1946 and 1951 would reduce this ratio to about 0.55-0.60, a figure in reasonable agreement with that suggested by the Department of Oil Properties data.
R. O. Castle, R. F. Yerkes and F. S. Riley
Production in millions of bbls
0 200 W O 600 800 IMK) 1200 1400
*Net liquid production 30 I
FIGURE 5. Cumulative oil, gross-liquid, and net-liquid production from the Wilmington oil field plotted against cumulative subsidence near the center of the Wilmington subsidence bowl. Prepared from production statistics and subsidence data compiled by the California Division of Oil and Gas, and subsidence data presented by Gilluly and Grant (1949, pp. 471-473, 527), and Hudson (1957, table V).
HUNTINGTON BEACH OIL FIELD
The Huntington Beach field, which is also located along the south coastal section of the Los Angeles basis, is the only other field for which available data permit a comparison between liquid production and subsidence. W e have, however, been unable to develop any reliable estimates of successive changes in the volume of subsidence through all or even part of the production period of the Huntington Beach field. Although subsidence between 1920 (when production began in the Huntington Beach field) and 1933 has not been reliably determined at any bench mark within the zone of differential subsidence, w e can compare the post-1933 subsidence at selected bench marks with various aspects of liquid production (fig. 6).
GENERAL O B S E R V A T I O N S
Several conclusions emerge from direct comparisons between the various measures of liquid production and subsidence in the six fields examined above:
(1) All show at least a crudely developed linear relationship between cumulative net- liquid production and one or more measures of subsidence. Plots of subsidence against only oil or gross-liquid production are generally far less linear in character. Data from the Inglewood field suggest that subsidence at a point provides at least a rough index of the changing volume of subsidence.
(2) Departures from linearity seem to have characterized the early production stages in at least five of the six fields. Subsidence rates in the Bolivar Coast and Wilmington fields were, in proportion to their production rates, relatively low during the early years of development; whereas subsidence rates over the Inglewood field (and probably the Hun- tington Beach field) are believed to have been relatively high during the early production years.
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(3) VJV,, whether derived from the full period of observation or the slopes of the linear portions of the subsidence-production curves, ranged over nearly an order of magni- tude- that is, from 0.08 or 0.10 in the Inglewood field to nearly 1 over the clearly linear parts of the curves for two of the Bolivar Coast fields.
Production in millions of bbls
A Gross liquid production ( A )
FIGURE 6. Cumulative oil, gross-liquid, and net-liquid production from the Huntington Beach oil field plotted against subsidence at bench marks located (A) near the center of subsidence, and (BI midway up the southeast limb of the subsidence bowl. Prepared from production statistics of the California Division of Oil and Gas and elevation data of the US Coast and Geodetic Survey and the Orange County Ofice of County Surveyor and R o a d Commissioner. Easily related elevation meas- urements have been available only since 1933; estimates of subsidence since I920 shown by dashed lines.
E X P L A N A T I O N
The general theory advanced in explanation of reservoir compaction and resultant oil- field subsidence (Gilluly and Grant, 1949) is, in its broad outlines, beyond challenge. Thus Terzaghi’s principle, which relates increased effective stress directly to fluid-pressure decline, probably is validly applied to the multifluid-phase system. Yet in seeming oppo- sition to this generalization, measured reservoir pressure decline within the Vickers zone was disproportionately high with respect to surface subsidence during the early production years (fig. 2a and d); a similar situation is believed to have prevailed in the Wilmington field (City of Long Beach, 1967, unpublished data). Whatever the relationship, then, be- tween measured reservoir pressure decline and compaction, the two are certainly not directly proportional.
The most likely explanation for the poor correlation between reservoir-pressure decline and subsidence (or compaction) is that pressure decline as measured at individual producing wells is generally non-representative of the average or systemic decline over the field as a whole. Thus in examining this problem in the Wilmington field, Miller and Somerton (1955, p. 70) observed that “reductions in average pressure in the reservoir are virtually impossible to determine with a satisfactory degree of accuracy. ” This deduction, coupled with the observed linearity between net-liquid production and subsidence, sug-
R. O. Castle, R. F. Yerkes and F. S. Riley
gests that the liquid production may constitute a better index of average reservoir-pressure decline than that obtained through down-hole measurements.
The approximately linear relationship between net-liquid production and subsidence remains imperfectly understood; a general explanation may be offered, however, through simple analogy with a tightly confined artesian system of infinite areal extent. The artesian coefficient of storage m a y be defined as the volume of water released from storage within a column of aquifer underlying a unit surface area during a decline in head of unity. In an artesian system that is hydraulically isolated from any free-water surface, the volume of water represented by the storage coefficient will be derived entirely from the expansion of the confined water and compaction of the reservoir skeleton. Thus the total volume of reservoir compaction must be linearly related to cumulative production, provided only that the bulk modulus of elasticity of the water and the modulus of compression of the reservoir skeleton remain invariant over the relevant stress interval (see Jacob, 1940, p. 575-577). In the case of a well field in which the liquid-extraction flux is very high (that is, one characterized by closely spaced wells and high production rates) and hydraulic diffu- sivity' is very low, fluid-pressure decline will be expressed chiefly as mutually interfering cones of depression surrounding individual wells and will be largely confined to the main body of the well field. Thus production will be obtained chiefly from liquid expansion and reservoir compaction within the areal limits of the well field itself, rather than by extrac- tion (and consequent but almost unmeasureable subsidence) from an extensive peripheral region. Under these circumstances the average pressure decline at any location within the field (and the consequent increase in effective stress and resultant compaction) will tend with time to become approximately linearly related to cumultative production. More significantly, subsidence will be restricted to a well-defined area within which it can be measured with some degree of accuracy.
The system described above becomes directly comparable with an oil field if two res- trictions are imposed on the producing oil field: (1) the proportion of gas in the net fluid produced must remain constant so that the effect of adding the produced gas to the cumu- lative liquid production curve will uniformly change its slope but not its form (a restriction dictated by the presumption that the expansive effect of the gas is a function of its concen- tration in the fluid system); (2) the compressibilities of both brine and oil in the reservoir state must be sufficiently close as to be considered identical. The second required restric- tion is considered the most vulnerable feature of this model.
Liquid production from a petroleum system in which the reservoir solids are only slightly compressible and the reservoir fluids are relatively highly compressible, will con- sist of: (1) a relatively large volume attributable to fluid expansion; and (2) a relatively small volume attributable to compaction. Because the reservoir pressure decline, and thus the increased effective stress and the compaction, are directly proportional to liquid pro- duction, VJV, for this system should be constant and charaterized by values close to but greater than O. This model m a y be typified by the Inglewood field, which has been iden- tifìed as an essentially solution-gas-drive field (California Department of Water Resources, 1964, p. 16). Liquid production from a system in which the reservoir skeleton is highly compressible and the reservoir fluids are only slightly compressible, constitutes the oppo- site extreme, and will consist of: (1) a relatively large volume attributable to reservoir compaction; and (2) a relatively small volume attributable to fluid expansion. Because reservoir compaction due to increased effective stress is again directly proportional to liquid production, VJ V, for this system will again be constant, but characterized by values less than but close to 1. This system m a y be typified by some of the Bolivar Coast fields, which are thought to be driven by formation compaction (van der Knaap and van der Viis,
1. Hydraulic diffusivity, a term analogous to thermal diffusivity, is defined as the transmissivity of an aquifer (hydraulic conductivity times thickness) divided by its storage coefficient. This ratio determines the rate at which a head change propagates through the aquifer.
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1967, pp. 94-95). The Wilmington field may be an example of one intermediate between the two cited extremes.
Departures from linearity may be related to changes in fluid or skeletal compressibili- ties. It is likely, however, that the observed departures in the early parts of the curves (figs. 3, 4, and 5) are due chieflly to changes in the produced gas-net liquid ratio. Thus relatively low gas production from the Wilmington (as deduced from production statistics of the California Division of Oil and Gas) and Bolivar Coast fields (as inferred from the changing gas-oil ratio
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see Davila and others, 1951, p. 21 1) during their initial develop- ment, was associated with relatively low subsidence rates. The Inglewood field, on the other hand, was apparently characterized by both high gas production and relatively rapid subsidence during its early development (see fig. 2).C O N C L U S I O N
If linearity between net-liquid production and subsidence is indeed a general characteristic of subsiding oil fields, its recognition may supplement existing predictive techniques.
Because the older techniques have been based largely or exclusively on the Wilmington experience, the relationship described here may have broader applicability in estimating future subsidence over recognized examples of subsiding fields.
ACKNOWLEDGMENT
Partial support for this study was provided by the Division of Reactor Development and Technology, US Atomic Energy Commission.
REFERENCES
California Department of Water Resources (1964): Investigation of failure Baldwin Hills Reser- voir, California Dept. Water Resources, 64 p.
DAVILA, C.R., SMITH, A.N.L. and AUSTIN, H. (1951): Production ,in Text of papers presented at the National Petroleum Convention, Caracas, Venezuela, September 9-18, 1951, Tech. Ofice Hydrocarbons of the Ministery Mines and Hydrocarbons, U. S. Venezuela, pp. 201-275.
DRIVER, H.L. (1943): Inglewood oil field (California), California Diu. Mines Bull. 118, pp. 306-309.
GILLULY, James and GRANT, U.S., 4th (1949): Subsidence in the Long Beach Harbor area, HUDSON, F. S. (1957): Subsidence of Long Beach Harbor area, Report to the City of Long Beach JACOB, C. E. (1940): On the flow of water in an elastic artesian aquifer, Am. Geophys. Union Trans., MILLER, F.G. and SOMERTON, W.H. (1955): Operators eye heroic measures to halt Wilmington
sinking, Oil and Gas Jour., vol. 54, no. 33, pp. 66-72.
VAN DER KNAAP, W . and V A N DER VLIS, A. C. (1967): On the cause of subsidence in oil-producing areas, in Rock mechanics in oil field geology, drilling and production, World Petroleum Cong., 7th Mexico City, 1967, Proc., Voi. 3, pp. 85-105.
How did you compute the subsidence during its early stages?