Straightforward approximate formulas are presented for the estimation of flow rates of air (gas) and water (incompressible liquid) from a cavern in a permeable mass; the cavern acting as a source or a sink. The mass may be soil or fractured rock and the cavern may be a drill "vole, a tunnel or a compressed air surge chamber among others. The idealized geometry of the cavern and the distance to a boundary equipotential, which may be the groundwater table, determines the value of a geometry factor appearing in the flow rate formulas. One formula applies to water flow in completely water saturated media and a slightly different formula to air flow in dry media. Special emphasize is given to the application of the formulas in questions regarding design of unlined compressed air surge chambers in jointed rock.
Vereinfachte, approximative Formeln sind fuer die Bestimmung der Stömungsgeschwingigkeit von Luft (Gas) and Wasser (unzusammendrueckbarer Fluessigkeit) aus einer Kaverne in durchlassiger Materie prasentiert, wo die Kaverne als eine Quelle oder Senke fungiert. Die Materie könnte Erde oder klueftiger Fels sein, and die Kaverne könnte ein Bohrloch, ein Tunnel oder ein geschlossenes Wasserschloss das mit Druckluftpolster arbeitet sein, u.a. Der in den Strömungsformeln auftretende Geometriefaktor wird durch die ideale Geometrie der Kaverne and durch den Abstand von einem Randàquipotential (z.B. dem Grundwasserspiegel) bestimmt. Die eine Formel ist fuer die Wasserströmung in wassergesattigten Böden anwendbar, and eine àhnliche Formel fuer die Luftstrimung in trockenen Baden. Besondere Betonung wird our die Anwendung der Formeln in den Fragen der Konstruktion unausgekleideter geschlossener Wasserschlösser mit Druckluftpolstern in zerklueftetem Fels gelegt.
Des formules approximatives et directes pour estimer les vitesses d''ecoulement de l''air (gaz) et de l''eau (liquide incompressible) à partir d''une caverne dans une masse permeable sont presentees; la caverne agissant comme source ou comme drain. La masse peut être un sol ou un roc fracture et la caverne peut être un trou de fourage, un tunnel ou une chambre d''equilibre a air comprime entre autres. La geometrie idealisee de la caverne et la distance à une equipotentielle limite, qui peut être la nappe d''eau souterraine, determine la valeur d''un facteur de geometrie apparaissant dans les formules de vitesse d''ecoulement. Une première formule s''applique à l''ecoulement de l''eau dans un medium complètement sature d''eau et une autre formule, legèrement differente, à l''ecoulement de l''air dans un medium sec. Un accent special est mis sur l''utilisation des formules en question pour le calcul des chambres d''equilibre à air comprime sans recouvrement interieur dans un roc comprenant des joints. Fig. 2. Geometry in an idealized flow problem(figure in the paper).
INTRODUCTION The planning of closed air surge chambers in Norway in the early seventies called for methods to predict air loss from caverns located in fractured rock. The work undertaken by the- present authors (1973) was directed towards the development of appropriate formulas for estimating rock mass permeability from borehole tests(Lugeon tests) and measurements of water flow into tunnels and caverns. Furthermore to develop formulas for estimating water and air flow from a cavern knowing the effective permeability of the rock mass. Fig. 1(Figure in the paper). Closed air surge chamber in a fractured rock mass (not in scale). Fig. 1 shows the typical problem; an air surge chamber partially filled with compressed air. Under air pressure higher than, or even slightly below the original water pressure at the chamber location, compressed air will migrate into the rock joints intersecting the chamber. The air loss must be compensated for by compressors. One crucial question is the compressor capacity needed. The analysis of flow problems in fractured rock is difficult for several reasons. The flow taking place in hard rock suitable for the location of air surge chambers is exclusively limited to fissures and joints. The spacing, distribution and openings of such are likely to be most irregular. Considering even a single joint parallel plate theory may not be correct as the flow may take place in channels. In the theory to be presented the medium in which flow takes place is considered homogenous. Thus the theory itself is not developed particularly for flow problems in fissured rock. The flow equations to be presented applies to soils and other permeable media as well. In the present paper emphasize is, however, given to the application of the flow equations to inhomogenous rock. The combined flow of air and water (two fluid system) is hard to analyse. Much easier is the analysis of water (liquid) flow in a completely water saturated porous medium and the analysis of air (gas) flow in a dry porous medium. When able to handle the latter problem at least an upper limit of the air flow in a mixed air-water flow problem is given. The theory to be presented is limited to single fluid flow, but some emphasis is given to the application of the results to the mixed flow problem of an air surge chamber.
