Groundwater Flow and Contaminant Transport
Groundwater Flow and Contaminant Transport BSysE 595
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This 6 page Class Notes was uploaded by Haylie Rowe on Thursday September 17, 2015. The Class Notes belongs to BSysE 595 at Washington State University taught by Staff in Fall. Since its upload, it has received 50 views. For similar materials see /class/205960/bsyse-595-washington-state-university in Bioengineering at Washington State University.
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Date Created: 09/17/15
Mass Transport with Reaction 1 Mass Conservation Statement Mass conservation statement incorporates porous medium serving as source sink terms Mass in ow rate Mass out ow rate i Mass production rate Change in mass storage with time MT 1 1 2 Reaction Classification Homogeneous operating within a single phase Heterogeneous operating between two phases Equilibrium vs kinetic depending on reaction rate relative to mass transport rate 3 Rate Law and Reaction Order Rate law an equation that relates the rate of a reaction to the Cs of reactants and catalyst or products raised to various powers 1 Consider the reaction C aA bB gt ID eE C catalyst The rate law for reactants is Rate kA quot 3quot GP m n p often but not always integers must be determined experimentally have no relationship to the coefficients in the balanced equation Reaction order equals the exponent of the concentration of that species in the rate law 4 General Form of ld Equation With Vv 0 2 Da0aci 2 r mass produced or consumed per unit volume per unit time molesL3T 5 Equation for Firstorder Kinetic Reactions For firstorder decay r M m C 3 It A decay constant T l Substituting 3 into 2 gives 2 x vx ng 4 6x2 ax at 6 Equation for Sorption Reactions For sorption of mass from solution 6C r at C C of species on the solid phase or mass sorbed per unit medium volume M L 3 5 Substituting 5 into 2 yields D vaciacac quotax2 quotax net at For kinetic nonequilibrium sorption reactions 6 C C C at f 9 a function of both C of mass in solution and mass sorbed on the solid For equilibrium sorption reactions 6C a t fC a function of only C of mass in solution Given a linear equilibrium sorption a C GS 6 at p at pb bulk density or total mass of solids per unit volume of porous medium M L 3 S amount of mass sorbed on the solid per unit mass of solid moles M l mm0m D ps z 265gcm 393 is mineral particle density The linear F reundlz ch isotherm is SQC amp K d distribution coefficient L3 M l Differentiating 8 with time gives 6S 6C K 9 at d at U Combining Eq 6 7 and 9 leads to 6C 6C l n K 10 Substituting 10 into 2 gives 2 Dx vx 319 z E 11 6x2 6x n at at Rearranging 11 gives 12 2 Dxa Cvx E 1Mpst 3x2 6x at n The bracketed quantity is a constant termed retardation factor Rf Rf 1 1n pst Eq 12 is thus rewritten as l z 13 Rf 6x2 Rf 8x at The retardation factor serves to decrease the values of the transport parameters of D and v
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