Static analysis of fluids in ore heap

Figure 1 represents any section of a bottomed ore heap or waste rock pile.

Figure 1 Type of space partition in ore or waste rock heap

V, solid rock block area; c-breaking rock crack;

V 1 - water filling area; V 2 - air filling area

When filling the liquid at a lower flow rate until the lower part of the non-mineral space is filled with liquid, we can observe the following phenomenon:

First, due to the influence of surface tension (or interface energy), when the liquid flows through the surface of the ore, the liquid is adsorbed by the surface of the ore to form a very thin liquid film. That is to say, when the liquid moves downward, it does not move directly downward in the non-mineral space, but as shown by the arrow in the figure, moves downward along the surface of the ore in the form of a liquid film.

Second, due to the effect of the capillary force, when the liquid flows through the ore fissure, it gradually penetrates into the pores of the ore.

Third, the liquid gradually occupies the lower gap, and the upper part of the gap is still occupied by air.

4. The air is expelled from the pores or spaces occupied by the liquid. The competition for liquid and air to enter the space is almost independent of the upper feed flow rate, but is controlled by the capillary force in the mine.

The rise or fall of liquid in the so-called capillary tube caused by the action of capillary force is a common phenomenon of liquid in porous media and is a widely studied problem of seepage statics. The rise or fall height of the liquid in a porous medium can be derived from the Laplace equation according to the Mao management theory:

h r =2rcosθ/Rρg (1A)

Where, h r - the rise or fall height of the liquid in the capillary;

Θ-average infiltration angle;

R-capillary radius;

R-surface tension;

The density of the ρ-liquid (flow) body;

G-gravity acceleration.

Due to the inconvenient use of the capillary radius, it can be expressed by the average diameter de of the capillary tube, then the formula (1A) is rewritten as

Hr=4rcosθ/deρg (1B)

There are also many scholars who advocate the use of the equivalent particle size d ρ of the particles. The relationship between the average diameter of the capillary and the particle equivalent particle size is

De=0. 8d ρ . Formula (1B) can be expressed as

Hr=5rcosθ/d ρ ρg (1C)

Some people have used the heap immersion test to test the validity of this formula. As a result, the theoretical calculations are basically consistent with the experimental measurements. The conditions and results of the test are as follows:

HEAP porosity of 37%, the leaching solution density 1.08g / cm 3, a surface tension measured value r = 7.3 × 10 - 4 N / cm 2. Simplified, calculated


The table below shows the results of experimental and theoretical calculations.

Relationship between the rise of capillary fluid and the size of ore

Ore size (mesh)

Particle equivalent particle size (cm)

Capillary fluid elevation (cm)

measured value






















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