1. Students: Amiran Divekar (131130105008) Ameedhara Hingrajiya (131130105013) Priyal Parikh (131130105037) Sal College of engineering Department of Chemical Engineering SEMESTER V Topic: Gas Absorption Faculty: Prof. H R Shah

2.  In an absorption column or tower, a gas is fed from the bottom of an absorption tower. The tower is packed with packing to increase contact time and removal efficiency. For dilute gases, the equilibrium relationship can be described by Henry' law. A typical mass balance over a column is given as

3.  where L, and G are molar flow rates per unit cross section of the tower for liquid, and gas respectively. x and y are concentrations of absorbing constituents expressed in mole fraction. Subscript 1 represents the bottom of the tower where gas enters the column. We can find minimum amount of liquid required to result the desired removal of solute from the gas as described below. Assume that the liquid exiting from the bottom of the tower is in complete equilibrium with entering gas then the solute absorbed by liquid is equal to the solute released from gas.

4.  Where superscript represents equilibrium condition. The quantity x 1 * is given by y 1 / m, where m is Henry's law constant. The quantity of liquid used in achieving the desired absorption level is 20 % to 30 % higher than the minimum value. We can find concentration of the solute in liquid exiting the tower as

5.  The height of the absorption tower can be calculated by a number of ways. If the height of a gas- and liquid-phase units (H G, H L ) are provided then height of packing required is given by

6.  Where H G is the height of a transfer unit based upon resistance in the gas phase, H OG is the height of a transfer unit based upon overall resistance in the gas phase, and H ETP is the height of a unit equivalent to a theoretical plate. H OG is given as

7.  And H ETP is given as

8.  The number of units based on the overall resistance in the gas phase can be calculated as  Where A is absorption factor and is defined as A = L /( mG ).

9.  The concept of an ideal solution is fundamental to chemical thermodynamics and its applications, such as the use of colligative properties. An ideal solution or ideal mixture is a solution in which the enthalpy of solution ( Δ Hsolution =0) is zero; with the closer to zero the enthalpy of solution, the more "ideal" the behavior of the solution becomes. Since the enthalpy of mixing (solution) is zero, the change in Gibbs energy on mixing is determined solely by the entropy of mixing ( Δ Ssolution ).  Raoult's Law  Henry's Law

10.  Raoult's law states that the vapor pressure of a solvent above a solution is equal to the vapor pressure of the pure solvent at the same temperature scaled by the mole fraction of the solvent present:  Psolution = XsolventPosolvent

11.  Raoult's Law only works for ideal solutions. "An ideal solution shows thermodynamic mixing characteristics identical to those of ideal gas mixtures [except] ideal solutions have intermolecular interactions equal to those of the pure components." 2 Like many other concepts explored in Chemistry, Raoult's Law only applies under ideal conditions in an ideal solution. However, it still works fairly well for the solvent in dilute solutions. In reality though, the decrease in vapor pressure will be greater than that calculated by Raoult's Law for extremely dilute solutions. 3

12.  Figure 0 : Positive non-ideal behavior of the vapor pressure of a solution follows Henry's Law at low concentrations and Raoult's Law at high concentrations (pure).

13.  Henry's law is one of the gas laws formulated by William Henry in 1803 and states: "At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid." An equivalent way of stating the law is that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid:

14.  C = kPgas  where  C is the solubility of a gas at a fixed temperature in a particular solvent (in units of M or mL gas/L)  k is Henry's law constant (often in units of M/atm)  Pgas is the partial pressure of the gas (often in units of Atm)

15. Figure 1 : Positive non-ideal behavior of the vapor pressure of a solution follows Henry's Law at low concentrations and Rault law at high concentrations (pure).

16.  If the principal purpose of the absorption operation is to produce a specific solution, as in the manufacture of hydrochloric acid, for example, the solvent is specified by the nature of the product, i.e. water is to be the solvent. If the principal purpose is to remove some components (e.g. impurities) from the gas, some choice is frequently possible.  The factors to be considered are:

17.  The gas solubility should be high, thus increasing the rate of absorption and decreasing the quantity of solvent required. Generally solvent with a chemical nature similar to the solute to be absorbed will provide good solubility. A chemical reaction of the solvent with the solute will frequently result in very high gas solubility, but if the solvent is to be recovered for re- use, the reaction must be reversible.  For example, H2S can be removed from gas mixtures using amine solutions since the gas is readily absorbed at low temperatures and easily stripped at high temperatures. Caustic soda absorbs H2S excellently but will not release it in a stripping operation.

18.  The solvent should have a low vapour pressure to reduce loss of solvent in the gas leaving an absorption column.

19.  The materials of construction required for the equipment should not be unusual or expensive.

20.  The solvent should be inexpensive, so that losses are not costly, and should be readily available.

21.  Low viscosity is preferred for reasons of rapid absorption rates, improved flooding characteristics in packed column, low pressure drops on pumping, and good heat transfer characteristics.

22.  The solvent should be non-toxic, non- flammable and chemically stable.

24.  Notations : In terms of mole fraction and total flowrates  y : mole fraction of solute A in the gas phase x : mole fraction of solute A in the liquid phase G : total molar flowrate of the gas stream (gas flux), kg-moles/m2.s L : total molar flowrate of the liquid stream, kg- moles/m2.s

25.  Gy and Lx are the molar flowrates of A in the gas and liquid respectively (kg-moles A/m2.s) at any point inside the column.

26.  Inside the column, mass transfer takes place as the solute (component A) is absorbed by the liquid. The quantities of L and x (for the liquid side) and G and y (for the gas side) varies continuously: as we gradually move up the column, component A is continuously being transferred from the gas phase to the liquid phase. Thus, in going up the column, there is a decrease in the total gas flowrate, and a decrease in the concentration of A in the gas phase. At the same time, in going down the column, there is an increase in the total liquid flowrate, and an increase in the concentration of A in the liquid phase. Thus,

27.  The inlet gas has a solute mole fraction of y1. The solute mole fraction is reduced to y2 at the outlet. By material balance for the solute in the gas, the amount to be removed is G ( y1 - y2 ). The least amount of liquid Lmin that can remove this amount of solute is the minimum liquid rate, often expressed in terms of a liquid- to-gas ratio, Lmin/G. Understanding the effect of reducing liquid rate requires an analysis of the operating line equation. This is shown in the Figure below.

29.  The condition at the top of the column (point D) is known: x2 the mole fraction of entering liquid is known, and the mole fraction of gas leaving y2 is known. Hence point D is fixed.

30.  The mole fraction of gas entering y1 is known. The mole fraction of liquid leaving x1 obviously depends on the liquid rate used. For the same amount of solute to be removed, using a larger quantity of liquid will result in smaller value of x1, and vice versa. Hence, when the liquid rate is changed, the condition at the bottom of the column varies along the horizontal line through y1.

31.  Recall that the operating line has a gradient of L/G. By reducing the liquid rate, we are decreasing the slope of the operating line and increasing the exit concentration x1. Therefore the operating line rotates around point D as L is decreased, e.g. from line DE to DF. Notice that the operating line has moved closer to the equilibrium curve.  When this happens, the driving force for mass transfer is smaller, i.e. the absorption process becomes more difficult.

32.  At point M, the operating line intersects the equilibrium line, and we have a condition of operation at zero driving force. At this point, we cannot reduce the liquid rate anymore. Hence, the liquid rate at this point of equilibrium is known as the minimum liquid rate, Lmin. At minimum liquid, the outlet liquid concentration is a maximum, x1(max).

33.  The minimum liquid rate results in infinite column height: infinite number of trays or packed height required for separation (at zero driving force).  The minimum liquid rate, Lmin can be calculated from the gradient of the operating line:

34.  Note: x1(max) can also be calculated using. Henry’s law.  The actual liquid rate to be used is specified as multiples of the minimum liquid rate. If the liquid rate for absorption is initially unknown, then one must calculates the minimum liquid rate first.