UNITED STATES DEPARTMENT OF THE INTERIOR GEOLOGICAL SURVEY Water Resources Division Washington 25, D.C. February 1, 1955 Code No. 45030 GROUND WATER BRANCH MEMORANDUM NO. 55.28 To: Field offices of the Ground Water Branch From: Chief, Ground Water Branch Subject: Redefinition of coefficient of storage. It has been evident for a long time that some of the hydrologic concepts used widely in ground-water investigations have not been clearly understood or consistently applied. The resultant confusion that has existed in the minds of many of us too frequently has been reflected in the way our field studies have been carried on and analyzed and in the way our investigative reports have been written and reviewed. There has been a growing desire, therefore, to put our house in better order, to refine our appreciation and understanding of certain important hydrologic concepts, and so to improve the effectiveness with which we examine, analyze, and report on problems of ground-water occurrence and movement. Paramount among the concepts needing reappraisal is that of the coefficient of storage, and the results of work directed toward this objective are the basis of this memorandum. Additional memoranda will follow as promptly as other concepts can be scrutinized and reappraised. It should be made clear that the redefinition given here, and the others that may follow, are not to be regarded as sacrosanct and incapable of further change. Any and all of our definitions and concepts are subject to change in the light of new information. Each redefinition, therefore, is to be regarded as a carefully thought cut interim term which is to be used until and unless restudy warrants a further change. In the use of the term coefficient of storage there has been uncertainty as to whether the term applied to an aquifer only, or to the aquifer and the adjacent confining beds; there has been uncertainty also as to whether it applied to artesian aquifers only or to water-table aquifers as well. As you will see, the proposed new definition applies to the aquifer only, and it applies to both artesian and water-table aquifers. Detailed explanations, complete with diagrams, of its application to artesian and to water-table situations have been prepared for inclusion in the summary of John G. Ferris' hydraulics lectures, to be duplicated for internal distribution in the near future. These explanations will indicate, among other things, why the specific yield is essentially equal, but not exactly equivalent, to the coefficient of storage for water-table conditions. The proposed definition of the coefficient of storage follows. The first paragraph beneath it constitutes explanatory material which, in this or some modified form, may appropriately be included in most reports in which the term coefficient of storage is defined. The paragraphs beyond are additional explanatory material for your information. "The coefficient of storage of an aquifer is the volume of water it releases from or takes into storage per unit surface area of the aquifer per unit change in the component of head normal to that surface." A simple way of visualizing this concept is to imagine an artesian aquifer which is elastic and is uniform in thickness, and which is assumed, for convenience, to be horizontal. If the head of water in that aquifer is decreased there will be released from storage some finite volume of water that is proportional to the change in head. Because the aquifer is horizontal, the full observed head change is evidently effective perpendicular to the aquifer surface. Imagine further a representative prism extending vertically from the top to the bottom of the aquifer, and extending laterally so that its cross-sectional area is coextensive with the aquifer-surface area over which the head change occurs. The volume of water released from storage in that prism, divided by the product of the prism's cross-sectional area and the change in head, results in a dimensionless number which is the coefficient of storage. If this example were revised slightly, it could be used to demonstrate the same concept of coefficient of storage for a horizontal water-table aquifer or for a situation in which the head of water in the aquifer is increased. As with almost any concise definition of a basic concept, it is necessary to develop its full significance, its limitations, and its practical use and application through elaborative discussion. The coefficient of storage is not exception in this respect, and the following discussion will serve to bring out a few ideas that are important in applying the concept to artesian and water-table aquifers in horizontal or inclined attitudes. Observe that the statement of the storage-coefficient concept first focuses attention on the volume of water that the aquifer releases from or takes into storage. Identification and measurement of this volume poses no particular problem but it should be recognized that it is measured outside the aquifer under the natural local conditions of temperature and atmospheric pressure; it is not the volume that the same amount of water would occupy if viewed in place of the aquifer. Although the example used to depict the concept of the storage coefficient was arbitrarily developed around a horizontally disposed artesian aquifer, the concept applies equally well to water-table aquifers and is not compromised by the attitude of the aquifer. This flexibility of application relies importantly, however, an relating the storage-coefficient concept to the surface area of the aquifer and to the component of head change that is normal to that surface. In turn, this relationship presupposes that the particular aquifer prism involved in the movement of water into or out of storage is that prism whose length equals the saturated into or out of storage is that prism whose length equals the saturated thickness of the aquifer, measured normal to the aquifer surface, and those cross-sectional area equals the area of the aquifer surface over which the head change occurs. Furthermore, water moves into or out of storage in this prism in direct proportion only to that part of the head change that acts to compress or distend the length of the prism. In other words, the component of the head change to be considered in the release or storage of water is that which acts normal to the aquifer surface. The mathematical models devised for analyzing ground-water flow usually require uniform thickness of aquifer. However, the storage coefficient concept, as defined here, applies equally well to aquifers that thicken or thin substantially, if the "surface area" is measured in the plane that divides the aquifer into upper and lower halves that are symmetrical with respect to flow. The imaginary prism would then be taken perpendicular to this mean plane of flow. The Artesian Case Consider an artesian aquifer, in any given attitude, in which the head of water is changed, but which remains saturated before, during, and after the change. It is assumed that the beds of impermeable material confining the aquifer are fluid in the sense that they have no inherent ability to absorb or dissipate changes in forces external to or within the aquifer. Inasmuch as no dewatering or filling of the aquifer is involved, the water released from or taken into storage can be attributed only to the compressibility of the aquifer material and of the water. By definition the term "head of water" and any changes therein connotes measurements in a vertical direction with reference to some datum. In a practical field problem the change in head very likely would be observed as a change in water-level elevation in a well. The change in head is an indication of the change in pressure in the aquifer prism, and the total change in force tending to compress the prism is equal to the product of the change in pressure multiplied by the end area of the prism. Obviously this change in force is not affected by the inclination of the aquifer, inasmuch as a confined pressure system is involved and the component of force due to pressure always acts normal to the confining surface. Thus any conventional method of observing head change will correctly identify the change in pressure normal to the aquifer surface and may be considered as a component of head acting normal to that surface. Summary statement -- For an artesian aquifer, regardless of its attitude, the water released from or taken into storage, in response to a change in head, is attributed solely to compressibility of the aquifer material and of the water. The volume of water (measured outside the aquifer) thus released or stored, divided by the product of the head change and the area of the aquifer surface over which it is effective, correctly determines the storage coefficient of the aquifer. The Water-Table Case Application of the storage-coefficient concept to water-table aquifers is more complex, although reasoning similar to that developed in the preceding paragraphs can be applied to the saturated zone of an inclined water-table aquifer. Consider a water-table aquifer, in any given attitude, in which the head of water is changed. Obviously there will now be dewatering or refilling of the aquifer, inasmuch as it is an open gravity system with no confinement of its upper surface. Thus the volume of water released from or taken into storage must not be attributed not only to the compressibility of the aquifer material and the water, in the saturated zone of the aquifer, but also to gravity drainage or refilling in the zone through which the water table moves. The volume of water involved in the gravity drainage or refilling, divided by the volume of the zone through which the water table moves, is the specific yields. Except in aquifer of low porosity the volume of water involved in gravity drainage or refilling will ordinarily be so many hundreds or thousands of times greater than the volume attributable to compressibility that for practical purposes it can be said that the coefficient of storage equals the specific yield. The conventional method of measuring change in head by observing change in water level elevation in a well evidently identifies the vertical change in position of the water table. In other words, head change equals vertical movement of the water table. It can be seen that the volume of the zone through which the water table moves is equal to the area of the aquifer surface over which the head change occurs, multiplied by the head change, multiplied by the cosine of the angle of inclination of the water-table. The product of the last two factors is the component of head change acting normal to the aquifer surface. The importance of interpreting correctly the phrase "component of head change" which appears in the definition of the storage coefficient cannot be overemphasized. Summary statement -- For a water-table aquifer, regardless of its attitude, the water released from or taken into storage, in response to a change in head, is attributed partly to gravity drainage or refilling of the zone through which the water table moves, and partly to compressibility of the water and aquifer material in the saturated zone. The volume of water thus released or stored, divided by the product of the area of aquifer surface over which the head change occurs, and the component of head change normal to that surface, correctly determines the storage coefficient of the aquifer. Usually the volume of water attributable to compressibility is a negligible proportion of the total volume of water released or stored and can be ignored. The storage coefficient then is sensibly equal to the specific yield. Conclusion It should be understood that the numerical results obtained by substituting aquifer-test data in an appropriate mathematical model indicate the transmissibility and storage coefficients for an ideal aquifer. The hydrologist must judge how closely the real aquifer resembles this particular ideal. It is usually recognized that in short pumping tests under water-table conditions the water does not drain from the smaller openings in the unwatered portion of the aquifer in any manner even approximating the instantaneous release assumed in devising the mathematical model (the Theis nonequilibrium formula). Similarly, in testing artesian aquifers it is recognized that the aquifer skeleton does not adjust instantaneously to the change in head, that considerable water is often contributed by intercalated clay beds, and furthermore that water leaks through the confining beds which, in the mathematical model, have been assumed to be impermeable. These recognized departures from the ideal, however, do not constitute grounds for modifying the definition given for the coefficient of storage. The definition does not, and cannot assure anyone that any pumping test in any aquifer will result in establishing the correct coefficient of storage for that aquifer. Pertinent comments on the redefinition of the coefficient of storage are solicited. The form given above may be considered official, however, until further notice. (s) A. N. SayreRedefinition of coefficient of storage.