How are water vapor ratios and transformation rates calculated?
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How are the water vapor ratio and conversion rate calculated? Could anyone provide the calculation formulas and the derivation process? Thank you! ! ! ! ! ! !
Please note, OP: it’s the water vapor ratio, not something else. The water vapor ratio is the ratio of water vapor to the dry basis gas volume of the syngas. The conversion rate can be calculated based on the dry-basis CO content in the gas before and after the conversion: Y2 = (1×Y1－1×Y1×X) / (1＋1×Y1×X). From this, it can be derived that X = (Y1－Y2) / Y1(1＋Y2). Here, Y1 and Y2 represent the dry-basis concentrations of CO in the gas before and after conversion, while X is the conversion rate
To calculate the water vapor ratio, it is necessary to know the pressure and temperature of the system: Water vapor ratio = P_water / (P – P_water)； This formula is applicable to calculating the water-vapor ratio after the separation tank, as the water vapor is saturated at this point. P_water: The saturated vapor pressure of water vapor at this system temperature ； P: Total system pressure ； Wet basis conversion rate: X = (V_inlet CO – V_outlet CO) / V_inlet CO. Dry basis conversion rate: X = (V_inlet CO – V_outlet CO) / (V_inlet CO + V_inlet CO * V_outlet CO). The wet basis conversion rate is easy to understand, as it matches the formula given in textbooks ； Derivation of dry basis conversion rate: X=【V_inlet – (1+X*V_inlet)*V_outlet】/V_inlet ； CO + H2O === CO2 + H2 X*V inlet 0 X*V inlet X*V inlet
The reaction CO + H2O = CO2 + H2 is a reaction with constant volume; however, when the effect of water vapor is excluded, it is a reaction that results in an increase in the dry basis (the total amount of gas without water vapor). It can be assumed that before the reaction, the total amount of gas is 1 kmol, with CO present in an amount of akmol, H2O in n kmol, CO2 in b kmol, H2 in c kmol, and other gases in d kmol； The conversion rate is x, and the amount of CO that has been converted is ax kmol. Therefore, the amounts of each gas after the reaction are as follows: CO: (a-ax) kmol, H2O: (n-ax) kmol, CO2: (b+ax) kmol, H2: (c+ax) kmol, and other gases: dkmol. The total dry basis amount before the reaction is 1 kmol, and it is (1+ax) kmol after the reaction. Thus, the carbon monoxide content in the dry transformed gas is given by a2 = (a – ax)/(1 + ax). By rearranging this expression, we obtain x = (a – a2)/a(1 + a2); in other words, the conversion rate = XCO_in – XCO_out / XCO_in(1 + XCO_out)