Triangular coordinate system for Ternary system (two pair partially soluble)

IN PLACE & HEAP LEACHING

In place leaching

• In place leaching is also called solution mining in which minerals are recovered through boreholes drilled into the deposit.
• In this process, the solvent is pumped through the borehole into the ore body.
• Then the solvent is circulated through the porous rock of dissolving ore.
• Then the leach solution is extracted via the second borehole.

Example

• For salt deposit fresh water used as the solvent, for copper deposit acid used as the solvent and for uranium ores acid or sodium bicarbonates used as the solvent.

Heap Leaching

• Heap leaching is an industrial mining process. 
• In this process, precious metals are extracted from ore via a series of chemical reactions that absorb specific minerals and then reseparate them after their division from earth metal.
• In this process, mined ore is usually crushed into the small lump and heaped on an impermeable plastic or clay lined leached pad.
• Then the solvent is passed through it or sprinkled on it to dissolve valuable materials.
• Then the leach solution is percolated through the heap and then collected, treated in the process plant.

Example

• Copper has leached from pyritic ores.

FICKS LAW OF DIFFUSION

Fick's law of diffusion

• Mass transfer is the natural tendency to transfer a given component (species) in a mixture from a region of high concentration to a region of low concentration to bring about a uniform or equilibrium condition. 
• The mass transfer has three requirements: 

1. that transfer occurs only in a mixture,
2. that at least one substance within the mixture moves from region of high concentration to a region of low concentration,
3. that the rate of mass transfer—i.e., the “flux” of a given substance—be proportional to the concentration gradient of that substance. 

Fick's  law

• In 1855 FICK proposed a relation between the flux of the diffusing substance and concentration gradient as the first law of diffusion which named as Fick's law of diffusion.

Fick’s law states that the flux of a diffusing component A in the z-direction in a binary mixture of A and B is proportional to the molar concentration gradient.

• Hence Fick's law of diffusion for component A in a binary mixture of A and B for steady-state diffusion is

           Where

• The negative sign in the equation indicates that diffusion occurs in the direction of decrease in concentration. Hence the term dCA/dz is -ve and flux become positive
• JA = molar flux of A in the z-direction [kmol/(m2.s)]
• CA = molar concentration of A [ kmol/ m3]
• dCA/dz = concentration gradient in the z-direction
• DAB = proportionality constant, diffusion coefficient for component A diffusing through B [m2/s]
• Z = distance in the direction of diffusion

MOLECULAR DIFFUSION

Molecular diffusion

• Mass transfer process can take place in a gas or vapour or in a liquid, and it can result from the random velocities of the molecules (molecular diffusion) or from the circulating or eddy currents present in a turbulent fluid (eddy diffusion).
• Molecular diffusion occurs due to movement of individual molecule through a substance by virtue of their thermal energy
• The phenomenon of molecular diffusion ultimately leads to completely uniform concentration of substances throughout solution which may initially have been nonuniform.
• For example:-

1. If a drop of blue copper sulphate solution is placed in a beaker of water, the copper sulphate eventually permeate the entire liquid. the blue color in times everywhere uniform, and no subsequent changes occurs.
2. In a two phase system not at equilibrium, such as layer of ammonia and air as a gas solution in contact with a layer of liquid water, spontaneous alteration through molecular diffusion also occurs, ultimately bringing the entire system to a state of equilibrium, after that diffusion stops.

• Hence in molecular diffusion ,if solution is not uniform everywhere in concentration of its constituents, the solution is spontaneously brought to uniformity by diffusion.
• It means that molecular diffusion is the mechanism of mass transfer in stagnant fluids or in fluids which are moving in laminar flow and the mass transfer takes place from a place of high concentration to low concentration.
• The rate at which a solute moves at any point in any direction must therefore depend upon concentration gradient at that point and in that direction.
• rate = molar flux [mol/ (area)(time)]
• The area is measured in the direction normal to the diffusion

EXAMPLES OF MASS TRANSFER

Example of mass transfer

Mass transfer operations

The operation carried out for separating the component of the mixture, involving the transfer of (mass) material from one homogeneous phase to another, due to the difference in vapor pressure, solubility or diffusivity and in which driving force for transfer is a concentration the difference is called mass transfer operations

Example:- Distillation, Gas absorption, Liquid Extraction, Drying

Example of mass transfer operations

• Depending upon phase contact between Gas, liquid and solid phase following are the classification of the mass transfer operations

Gas-gas phase contact

• The fragrance of incense sticks after lightning diffuse from one room to another room. 

Gas-liquid contact

• A cup of water left in a room eventually evaporate as a result water molecules diffusing into the air. This is liquid to gas diffusion.
• Gas absorption:- If a mixture of ammonia and air is contacted with liquid water, a large portion of ammonia will dissolve in the liquid, and in this way air ammonia mixture can be separated.
• Desorption or stripping:- If air is brought into contact with an ammonia-water solution, some of the ammonia leaves the liquid and enters the gas phase.
• If the liquid phase is a pure liquid, containing one component while the gas contains two or more, the operation is humidification or dehumidification depending upon the direction of transfer
• Humidification of the air: - When dry air contacted with liquid water result in evaporation of some water into the air
• Dehumidification: - When very moist air contacted with pure liquid water may result in condensation of part of moist air in the air. 

Gas-liquid contact

• A piece of solid CO2 ( dry ice ) will also get smaller and smaller in time as the CO2 molecules diffuse into the air. This is a solid to gas transfer example.
• Fractional sublimation: - If a solid solution is partially vaporized without the appearance of the liquid phase, the newly formed vapor phase and residual solid each contains all the original components, but in different propositions
• Drying or Desorption:- If solid which is moistened with a volatile liquid is exposed relatively dry gas, the liquid leaves the solid and diffuses into the gas
• Adsorption: - If diffusion takes place from solid to gas phase is called adsorption.
• For example:- If a mixture of water vapor and the air is brought into contact with activated silica gel, the water vapors diffuse to solid, which retains it strongly, and the air is thus dried.

Liquid-liquid contact

• Liquid extraction operations:- This separation involving contact of two insoluble liquid phases.
• for example - Acetone water solution is shaken in separating funnel with carbon-tetra chloride and the liquid allowed to settle, a large portion of acetone will be found in the carbon chloride-rich phase and will thus have been separated from the water.
• Fractional extraction:- a solution of acetic acid and acetone can be separated by adding it to the insoluble mixture of water and carbon tetrachloride. After shaking and setting, both acetone and acetic acid will be found in both liquid phases, but in different proportions.

Liquid-solid contact

• If a spoon of sugar is added in a cup of coffee will eventually sweeten the coffee because sugar molecule diffuses into the coffee.
• Leaching:- In this process diffusion is from solid to liquid phase takes place.
• For example- Leaching of gold from its ore by cyanide solutions. Another example is the leaching of cottonseed oil from the seeds by hexane.
• Adsorption:- In this process diffusion is from liquid to solid phase takes place
• For example:- The colored material which contaminates impure cane sugar solutions can be removed by contacting liquid solutions with activated carbon.

Solid-solid contact

• The diffusion rate is very slow
• If metallic gold and metallic are placed in intimate contact, over a period of time molecules of lead will diffuse into the gold and vise versa. but the rate of diffusion is very slow.

MASS TRANSFER AND MASS TRANSFER OPERATIONS

Mass transfer

• Mass transfer means the transfer of substance through another on a molecule scale.
• The net movement of mass from one location usually by a stream, phase, fraction, or component, to another.
• This mass transfer occurs due to the concentration difference or gradient.

Hence The process of transfer of mass as a result of the concentration difference of a component in a mixture or two-phase which are in contact is called mass transfer

• Example:- evaporation of water from a pool of water into a stream of air flowing over the water surface

Mass transfer operations

The operation carried out for separating the component of the mixture, involving the transfer of (mass) material from one homogeneous phase to another, due to the difference in vapor pressure, solubility or diffusivity and in which driving force for transfer is a concentration difference is called mass transfer operations

• In the mass transfer operations, neither equilibrium phase consists of only one component. 
• Hence when two-phase is initially contacted, they will not be of equilibrium compositions. 
• The system then attempts to reach equilibrium by a relatively slow diffusive movement of the constituents, which transfer in part between the phases in the process. 
• Separations are therefore never complete, although they can be brought as near completion as desired. 
• Mass transfer occurs in many processes such as absorption, evaporation, adsorption, drying, precipitation, membrane filtration, and distillation. 

In mass transfer operations, the Mass transfer may occur

• In one direction (gas absorption)
• In both direction (distillation)
• With simultaneous heat transfer( drying and crystallization)
• With simultaneous chemical reaction (Absorption of CO2 in an aqueous solution of KOH)
• With the exchange of one or more components
• Isothermally and non-isothermally