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BULLETIN OF THE AMERICAN ASSOCIATION OF PETROLEUM GEOLOGISTS

VOL. 37, NO. 8 (AUGUST, 1953), PP. 1954-2026. 44 FIGS.

ENTRAPMENT OF PETROLEUM UNDER

HYDRODYNAMIC CONDITIONS'

M. KING HUBBERT2

Houston, Texas

ABSTRACT

The anticlinal or so-called "gravitational" theory, despite its effectiveness as a basis for petroleumexploration, represents but a special case of oil and gas accumulation, and is valid only when the associatedground water is in hydrostatic equilibrium. Since this need not be the case, a more general formulation,valid for both hydrostatic and hydrodynamic conditions, is required.

Oil and gas possess energy with respect to their positions and environment which, when referred tounit mass, may be termed the potential at any given point of the fluid considered. When the potential ofa specified fluid in a region of underground space is not constant, an unbalanced force will act upon thefluid, driving it in the direction in which its potential decreases. Hence, oil and gas in a dispersed stateunderground migrate from regions of higher to those of lower energy levels, and come ultimately torest in positions which constitute traps, where their potentials assume locally minimum or least values.In nearly all cases traps for petroleum are regions of low potential which are enclosed jointly by

regions of higher potential and impermeable barriers.Oil and gas migration occurs through a normally water-saturated environment. If the water is at

rest, the oil and gas equipotential surfaces will be horizontal, the impelling forces will be directedvertically upward, and the traps will be the familiar ones of the anticlinal theory. If the water is inmotion in a non-vertical direction, the oil and gas equipotentials will be tilted downward in the flowdirection with those for oil inclined at an angle greater than those for gas. The impelling forces for oiland for gas will not be parallel and the two fluids will migrate in divergent directions to traps which ingeneral will not coincide and may, in fact, be separated entirely, a trap for oil being incapable ofholding gas, and vice versa.

Under hydrodynamic conditions accumulations of oil or gas will invariably exhibit inclined oil- or gas-water interfaces with the angle of inclination given by

d z d h tan = = -

dx ppodx

where dz/dx is the slope of the interface, p,,, the density of the water and pothat of the oil (or gas), anddh/dx the component of slope of the potentiometric surface of the water in the horizontal direction x,Stable oil and gas accumulations may be found in anticlines but they may equally well occur in struc -tural terraces, noses, monoclines, and other unclosed structures entirely devoid of lithologic barriers toupdip migration.

Not only are these effects theoretically expectable but they have been found to occur, with tilts rangingfrom tens to hundreds of feet per mile, in almost every major oil-producing area. If many suchaccumulations are not to be overlooked, we must supplement our customary knowledge of structure andstratigraphy with the three-dimensional ground-water hydrology of every petroliferous basin.

Publication No. 29, Exploration and Production Technical Division, Shell Oil Company, Houston,Texas.

Manuscript received, November 5, 1952.This paper was presented on March 26, 1952, before the American Association of Petroleum

Geologists at its annual meeting in Los Angeles, and also during October and November, 1952, as aDistinguished Lecture before the affiliated societies of the Association.

A study of this kind is necessarily a cooperative enterprise, and the writer expresses his indebted-ness to his many colleagues who in one way or another have assisted in its development. For specificassistance he is indebted to Henry Rainbow for the clarification of obscure mathematical points, toRobert Nanz and W. R. Purcell for information on capillary-pressure phenomena, and to Arne Junger,Charles H. Fay, and C. C. Templeton for critical discussions of the manuscript; but he is especiallyindebted to his research assistant, Jerry Conner, for performing the extensive series of confirmatoryexperiments cited, and to J. B. Woolley for invaluable editorial assistance in the final compilation ofthe paper.

Chief consultant (general geology), Shell Oil Company.