Continuity equation is a equation that explain the transport of a conserved quantity. Since, mass, energy, momentum are conserved under respective condition, a variety of physical phenomena may be describe using continuity equations. By using first law of thermodynamics, energy cannot be created or destroyed. It can only transfer by continuous flow. Total continuity equation (TCE), component continuity equation(CCE) and energy equation(EE) is applied to do mathematical model. Total continuity equation is the principle of the conservation of mass when applied to a dynamic system. The unit of this equation is mass per time. In overall balance, only one TCE can be written. CCE is based on component balance. Unlike mass, chemical components are not conserved. If reactions occur on a system, the number of moles of an individual component will increase if it is a product and will decrease if it is a reactant. The unit of CCE is moles of component per unit time. While EE, the first law of thermodynamics puts forward the principle of conservation of energy. The unit of EE is energy per time.
General balance equation:
Input+ generation- output-consumption= accumulation Rate law ra-1 = rb-1 = rc11 =r1r1= k1CA rc2-1= rd0.5= re0.5 =r2r2= k2 CC
F0 , ρF , ρCA
Total continuity equation
[ mass flow into system] – [mass flow out from the system] = [time rate of change of mass inside the system]dVρdt=F0ρ0- FρdVdt=F0ρ0ρ- FComponent continuity equation
[ Flow of moles of component into system ] – [ flow of moles of component out from system] + [rate of information from chemical reaction] = [time rate of change of moles of component inside system]Component A -ra=kCAdVCAdt=F0CA0- FCA- Vk1CAComponent B -rb=-ra=kCAdVCBdt=F0CB0- FCB- Vk1CAComponent C rc1=-ra=kCA , - rc2= r2= k2 CC dVCCdt=- FCC+ Vk1CA-Vk2CCComponent D rd= 0.5 rc2 = 0.5 k2 CC dVCDdt=- FCD+
References: Pedlosky, Joseph (1987). Geophysical fluid dynamics. retrived at 31 may 2013 from (http://en.wikipedia.org/wiki/Continuity_equation) William L. Luyben (1990). Process Modelling and Control for Chemical Engineers. 2rd edition. McGraw Hill International Edition Fogler, H.Scott, (1999). Elements of Chemical Reaction Engineering, 4th edition. Ame and Chaterine Vennema Professor ofChemical Engineering. Atkinson, Kendall A. (1989), An Introduction to Numerical Analysis (2nd ed.), New York. Retrieved at 25 may 2013 from (http://en.wikipedia.org/wiki/Euler_method)