
Citation: | Kaiming Tian, Li Wan. Flow Deflection in Intersected Tubes. Journal of Earth Science, 2000, 11(4): 426-428. |
In order to verify the flow interference at the fracture intersections, a group of hydraulic simulations of crossing flow was carried out. The manifold interference effects at the intersection of fractures on water flow has been confirmed extensively either in the normal or in the oblique intersected tubes as well as in the intersected tubes of either equal or variant diameters. Consequently, suggest that the fissure network can no longer be taken as a set of solitary fractures, but as a set of elementary intersected fractures. The deflection effect at fracture intersections on the water flow should be taken into consideration when is dealt with any theory related to the water migration in fractures.
The theoretical calculations of water migration, whether in an individual fracture or in a fissure network, have all been based on the equation for viscous flow between parallel plates. Wilson and Witherspoon (1976) first accomplished a hydraulic simulation of fracture water crossing flow only in a normal intersected tube with equal diameters, with the aid of which they hoped to approach the flow interference effects at the fracture intersections. From such a hydraulic simulation, they reached the conclusion that even if the fracture system with different orientations intercept and connect one another, the flow in one fracture system will not be influenced by the flow in other fracture systems. This hypothesis were also shared by Louis (1974), Sharp (1970), Snow (1969), Romm (1966) and so on. Actually they all failed to give proper attention to the flow interference effect at the fracture intersections. Therefore, the total flow through the fracture rock is the vector sum of the contributions of all conduits. The fissure network is generally oversimplified as a set of solitary fractures.
It was Ollos (1963) who brought up certain special interference effects of tube-crossing on the water flow for the first time, but he admitted that the scientific basis of hydromechanics to study these effects was not yet provided. Chernyshev (1979) has recently laid special emphasis on the importance of starting the research on the fracture water crossing-flow.Judging by a vast amount of in-situ observations and analyses, Tian (1983) advanced another hypothesis of "flow deflection of fractures water". He suggested that the flow deflection would occur at the fracture intersections when the openings of fractures are unequal. Apparently, the two hypotheses are contrary to each other.
A series of laboratory experiments on crossing flow were conducted by Hull and Koslow (1986), who proposed that the streamlines through fracture junctions cannot cross, but neither addressed the flowrate deflection of crossing flow in fracture. However, the flowrate deflection is the most important hydraulic property of crossing flow.
To verify which hypothesis is the correct one, it is necessary to repeat not only the flow experiments that were made by Wilson and Witherspoon (1976) previously, but also a group of hydraulic simulations of crossing flow in intersected tubes.
The method of hydraulic simulation we had adopted oriented the crossing flow in an intersected tube, instead of in fractures. Four kinds of the simulator used for research were: (a) a normal intersected tube with equal diameters, (b) an oblique intersected tube with equal diameters, (c) a normal intersected tube with variant diameters, (d) an oblique intersected tube with variant diameters, whose sizes are shown in Fig. 1. Two crossing pipelines are bored through the center of each plexiglass square, and, consequently, divided into four pieces. The simulator of an intersected tube is symmetrical around the center of the intersection. Close to the center of the intersection, four piezometric tubes are attached to the four pieces of pipelines one by one which are used to observe the flow interference effects at the intersection.
The square is 5 cm long on each side, and 3 cm in thickness. With each mouth of the four pieces of pipelines, three consecutive cuboids 15 cm are connected together. Through the axis of these cuboids, a conduit of the same diameter is drilled. In this way, every piece of the crossing pipelines is 17.5 cm long. Also a pair of piezometric tubes has been fitted on each side of every cuboids connection. If any distinguishable disparity of water levels is absent between two pairs of these piezometric tubes, the magnitude of flowrate in the simulator may have been controlled within the allowable regime during flow experiments.
The structure of the experimental installation shown in Fig. 2 is fixed on a steel chassis. To each end of the conduit, an adjustable water tank of steady level is linked.
(1) Step one.The height of the adjustable water tanks in an intersected tube is adjusted to create different water head losses between the inlet and outlet of flow. At first, water is allowed to pass through only one of the pipelines, but the water flow in another pipelines is cut off at the same time. The flowrate Q1 versus the head loss Δh1, the relative equation is made, namely Q1=f (Δh1). Secondly an exchange is made to measure the flowrate Q2 versus the corresponding head loss Δh2 to obtain a similar equation, namely Q2=f (Δh2). Therefore, ΣQ=Q1+Q2=f (Δh1) +f (Δh2) is without any interference at the tube intersection.
(2) Step two.In the intersected tube, the water heads arekept at both inlets at an equally higher level whilst place the other water heads at both two outlets simultaneously kept at a similarly lower level. The difference between the higher level and the lower level is named the head loss
Under the condition of the crossing flow, in the intersected tubes with unequal diameters, the intake flowrate Qb in the bigger tube is not equal to its discharge flowrate Qb+Δq. In addition the intake flowrate Qs in the smaller tube is not equal to its discharge flowrate Qs-Δq. Consequently, occurs a flowrate deflection of Δq from the smaller tube into the bigger one.Nevertheless, in the intersected tubes with equal diameters, the flowrate deflection approaches to zero, i.e.Δq→0.
(3) Step three.During the crossing flow experiments, is first obtained the total flowrate of the two pipelines versus the head loss
All Δq and P of crossing flow in an intersected tube actually originate from the flow interference effects at the tube intersection for laminar flow. The manifold interference effects at the tube intersection on water flow have been ascertained extensively either in the normal or in the oblique intersected tubes, particularly in the oblique intersected tubes with variant diameters. Therefore whatever the scale of flow deflection atthe fracture intersection may be, its important effect on the natural fracture water migration should not be neglected.
In this sense, the authors suggest that the fissure network can no longer be taken just as a set of solitary fractures, but as a set of elementary intersected fractures. Any theory related to the migration of water in fractures shonld include the flow deflection effects of fracture intersections on the flow.
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