Göran Rehbinder

The double packer permeameter with narrow packers. Analytical solution for non steady flow

The hydraulic diffusivity and permeability of a rock mass can be measured with a double packer permeameter, placed in a long bore hole. If the flow is steady, the relation between supply pressure and flux is a measure of the permeability whereas if the flow is transient, the relation is a measure of both the hydraulic diffusivity of the rock and the elasticity of the equipment. If the equipment is effectively rigid and the distance between the packers is much bigger than the size of the packers, an approximate closed solution is characterized bytwo parameters: the distance between the packers divided by the radius of the hole and the width of the packers divided by the radius of the hole. The flow is fully 3-D if the hydraulic diffusion distance far exceeds the distance between the packers. If the elasticity of the equipment is not negligible, the transient solution is characterized byone parameter including the elasticity coefficient of the equipment the conductivity of the rock and the radius of the hole. The relations between pressure and flux is given as a closed formula, suitable for engineering practice.

Measurement of the relaxation time in Darcy flow

The inertia of a liquid flowing through a porous medium is normally ignored, but if the acceleration is great, it may be important. The relaxation time, defined so that it alone accounts for the inertia, has been determined experimentally with a simple oscillator. A U-Tube is provided with a porous plug and filled with a liquid. During pendulation of the liquid, the frequency and the damping define the relaxation time. The measured value of the relaxation time is about 10 times the theoretical estimate derived from Navier-Stokes equation.

Darcyan flow with relaxation effect

The equation for the flow of a liquid through a porous medium is either elliptic or parabolic which implies that a disturbance in pressure or head is transmitted with infinite velocity. This is unsatisfactory from a physical viewpoint, although not necessarily from a practical one. If Darcys law is completed with an inertial term the flow equation becomes a strongly damped wave equation. The proposed additional term can be identified from experiments with confined flow and free surface flow when the pressure or head varies harmonically with time.

The Drag Force on the Grains in a Permeable Medium Subjected to a Water Jet

SummaryA theory for destruction of rock with a high speed water jet is derived on the basis of viscous flow through porous media. The theory yields that a grain in the rock exposed to a water jet is subjected to a hydraulic force proportional to the water pressure gradient in the rock and to the volume of the grain. If a semi-space of a presaturated rock is hit by a water jet of sufficient pressure the theory predicts the initial stage of the crater to be an annular crater the radius of which is twice the radius of the jet. In the case of a dry rock the theory predicts that the typical ring structure of the initial stage of the crater should not occur. The conclusion is that in destruction of rock with a high-pressure water jet the permeability is a very important parameter in contrast to the case of mechanical destruction.ZusammenfassungEine Theorie über Gesteinsdestruktion mit Hochdruckwasserstrahl gründet sich auf die Theorie viskoser Strömung durch poröse Medien. Die Theorie besagt dass eine Partikel im Gestein durch einwirken eines Wasserstrahls einer hydraulischen Kraft ausgesetzt wird die proportional zum Gradienten des Wasserdruckes im eigentlichen Gestein und proportional zum Volumen der Partikel ist. Wenn ein Halbraum eines wassergesättigten Gesteins von einem Wasserstrahl mit ausreichend hohen Druck getroffen wird, sagt die Theorie, so soll das Anfangsstadium des sich bildenden Kraters ringförmig sein mit einem Radius doppelt so gross als der Radius des Wasserstrahls. Im Falle trockenen Gesteins, erklärt die Theorie, soll die typische Ringstruktur im Anfangsstadium des Kraters nich auftreten. Zusammenfassend kann man sagen die Permeabilität ist ein bedeutend wichtiges Parameter bei Gesteinsdestruktion mit Hochdruck wasserstrahl im Gegensatz zum Fall mechanischer Destruktion.

The Double Packer Permeameter with Long Packers. An Approximate Analytical Solution

The hydraulic diffusivity and permeability of a rock mass can be measured with a double packer permeameter, placed in a long bore hole. If the flow is steady, the relation between supply pressure and flux is a measure of the permeability whereas if the flow is transient, the relation is a measure of both the hydraulic diffusivity of the rock and the elasticity of the equipment. If the equipment is effectively rigid and the axial extent of the packers is much bigger than the radius of the hole the solution is characterized byone parameter viz. the ratio between the distance between the packers and the radius of the hole and by a dimensionless time. An approximate closed transient solution for engineering purpose can be derived for a given supply flux but not for a given supply pressure.

Theory of single well tests in a leaky aquifer. Analytical solution for non steady flow

The evaluation of a pump test or a ‘slug’ test in a single well that completely penetrates a leaky aquifer does not yield a unique relation between the hydraulic properties of the aquifer, independent of the testing conditions. If the flow is transient, the drawdown is characterized by a single similarity parameter that does not distinguish between the storativity and the leakage factor. If the flow is quasi stationary, the drawdown is characterized by a single similarity parameter that does not distinguish between the transmissivity and the leakage factor. The general non steady solution, which is derived in closed form, is characterized bythree similarity parameters.

Sediment removal with a siphon at critical flux

Non cohesive sediment at the bottom of a water reservoir can easily be removed with a siphon. Theoretical analysis and experiments show that the mechanism that initiates the removal the grains of the sediment is due not only to the horizontal viscous shear at the top of the sediment, but also to the flow in the sediment it self. The lift, acting at the grains, is proportional to the square of the flux and at least to the square of the submersion of the mouthpiece of the siphon. Since the flux is limited, the submersion is the most important parameter. The theory says that right below the mouthpiece, the sediment is not exposed to any lift, but to compression. Simple experiments confirm the theoretical conclusions.

Investigation of water jet pulses generated by an impact piston device

High speed water pulses for destruction of rock, concrete etc. have been studied for more than a decade. The high speed pulses can be created in different ways and some investigations have been published about supersonic pulse generators. In this paper a device called impact pipe is studied theoretically as well as experimentally. In an impact pipe the impact velocity of a piston is transferred to pressure in a pressure chamber provided with a small nozzle through which a jet comes out. It is shown that theoretically the maximum pressure of 400 MPa is achieved if the length of the impacting piston is sufficiently long. Pressure measurements and high speed photography show that the water pulse coming out through the nozzle has violent radial bursts due to the pressure waves in the pressure chamber.

Relaxation of pore pressure in a slender core of a rockfill dam

The relaxation of pore pressure in the core of a rockfill dam, that is caused by a rapid discharge of the water from the reservoir, is controlled by two different time scales. The time scale due to de-consolidation is irrelevant, whereas the time scale due to the displacement rate of the phreatic surface is equal to the ratio between the conductivity and the porosity. If the core is vertical and slender, the motion of the phreatic surface is governed by an ordinary first order differential equation. If the discharge is instantaneous, the equation is separable and has been solved. Experiments with a Hele Shaw cell show that the agreement between theory and experiment is not too good. The explanation is that the discharge of liquid from the reservoir in the Hele Shaw cell is not effectively instantaneous. The practical result implies that the relaxation time is approximately 1 year for a core of a real dam composed of soil whose height and width are 50 and 4 meters, respectively.

Critical damping for well oscillations. A theoretical investigation

The oscillations of water in a well in a leaky aquifer might be subcritically or supercritically damped. The theory of well oscillations has turned out to be a special case of a general theory of damped motion of pendulums. In the case of a well in a leaky aquifer, the criterion for critical damping is a simple power expression that relates the leakage factor and the storativity of the aquifer and where the exponent is a function of the transmissivity of the aquifer. If the damping is critical and the leakage is extremely small, so the storativity has to be. If the aquifer is non leaking, the damping cannot be supercritical.