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RECENT DEVELOPMENTS IN REACTIVE TRANSPORT

RECENT DEVELOPMENTS IN REACTIVE TRANSPORT. J esus Carrera Technical University of Catalonia (UPC) Barcelona, Spain In collaboration with Carlos Ayora, Maarten Saaltink, Xavier SánchezVila, Michela Desimoni …. Contents. Is Reactive transport needed? An example Can be understood?

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RECENT DEVELOPMENTS IN REACTIVE TRANSPORT

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  1. RECENT DEVELOPMENTS IN REACTIVE TRANSPORT Jesus Carrera Technical University of Catalonia (UPC) Barcelona, Spain In collaboration with Carlos Ayora, Maarten Saaltink, Xavier SánchezVila, Michela Desimoni … Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  2. Contents • Is Reactive transport needed? An example • Can be understood? • Can be solved efficiently? … and the answer is YES Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  3. Calcite dissolution in coastal aqf. Mixture of calcite equilibrated with salt and fresh waters can be under or oversaturated with respect to calcite (often under) To simulate this effect, consider 1D diffusion experiment freshwater calcite saltwater Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  4. Simple mixing (no transport) Mixing leads to maximum undersaturation for around 20% fresh water Saturation Index (SI) Reaction Rate Dissolution rate (controlled by diffusion) SI & r Dissolution rate proportional to Diff coeff. and maximum at the fresh water end Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  5. Speciation Dissolution causes diffusion of CO2 (acidity) at the freshwater end, which drives further dissolution Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  6. Reducing concentration of CO2 at the freshwater end, causes an increase in subsaturation. Therefore, one would expect an increase in dissolution rate However, dissolution rate is dramatically reduced Sensitivity to CO2 Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  7. Summary of 1D diffusion exp • The interplay between transport and reactions is non-trivial. • Saturation index calculations are needed but they fail to indicate • how much calcite is dissolved, which is controlled by mixing rate, • nor where (or under which conditions) dissolution rate is maximum. Simulating reactive transport is needed to understand the fate of reacting solutes! Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  8. K, T, S, recharge • B.C’s, geometry • Transport • Solute mass conservation • Advection • Diffusion/Dispersion • Dispersivity, porosity • Reactive transport • Chemical reactions • Equilibrium • Kinetic • Equilibrium and rate constants The ingredients of reactive transport • Flow • Momentum conservation • Water mass conservation Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  9. Chemical reactions: Stoichiometric matrix • Assume a chemical system • Stoichiometric Matrix • Reaction rate: Mass balance Let ri be the number of moles of reactants that evolve into products for the i-th reaction The columns of S can be viewed as the contribution of reactions to each species Primary Secondary Constant Ac. How to evaluate r? Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  10. Equilibrium reactions: Mass Action Law • Traditional notation • Matrix notation Notice that neither water nor calcite enter in the mass action law, as their activity is constant However, for equilibrium reactions, it is not possible to write the reaction rate explicitly Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  11. Formulation of Reactive transport problems ns transport equations nr algebraic equations Looks awful! (nr + nsunknowns at every point) Seek tricks and/or simplifications Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  12. The basic trick: components Choose component matrix U, such that Components: Linear combinations of species that remain unaltered by equilibrium reactions Then, ns-nr transport equations. (A good choice of U allows these equations to be decoupled!) Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  13. Example • Chemical system • Stoichiometric Matrix • Components matrix • Components Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  14. Procedure • Define chemical system and components • Solve transport equations for components (and/or primary species) • Speciation: Compute species concentrations from components (and/or primary species) • Substitute species back into transport equations to obtain reaction rates Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  15. Step 1: Chemical system Reaction Stoichiometric matrix Components: is conservative! Step 2: Solve transport of u Transport equations where (1) (2) (1)-(2) yields: Analytical solution for 2 species Assume 2 species (e.g. SO42- and Ca2+) in eq. with gypsum Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  16. Step 3: Speciation Solve Together with Step 4: Compute r Plugging C2 into We obtain Transport Chemistry Analytical solution for 2 species Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  17. u Distancefrom peak of u Spatial distribution of reaction rate reaction rate, r/f u r/f Spatial distribution of reaction rate is more controlled by mixing, than chemistry Distancefrom the peak of u Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  18. Step 4: Compute r Plugging C2 into We obtain Mixing of several waters Step 3: Speciation Can be very complex, but Where a is the mixing ratio (possibly a vector) That is, 1) Transport a 2) Use any code (e.g., PHREEQE, RETRASO,…) to compute speciation Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  19. (a) Dimensionless [SO42-] Dimensionless [Ca2+] c1 (e.g., SO42-) water1 mixture  (b) water2  reaction rate c2 (e.g., Ca2+) distance, Solution of binary system for pulse input Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  20. Dimensionless reaction rate Dimensionless y-distance x-distancefrom the plume centre Spatial distribution of reaction rate Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  21. -30 reaction rate -20 distancefrom plume centre Integrated reaction rate for varying initial pulse 40 30 Dimensionless reaction rate Dimensionless distancefrom the plume centre Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  22. 2.0 0.08 80 - 115 2.0 60 0.06 1.5 1.5 40 0.04 20 0.02 Vy/DT Vy/DT 1.0 1.0 0 0 0.5 0.5 0 0 0.50 0 0.50 0 Vx/DL Vx/DL Spatial distribution of total precipitate Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  23. Types of reaction Paradigm Homogeneous Heterogeneous Systems Fast (equilibrium) Slow (kinetic) Fast (equilibrium) Slow (kinetic) Tank * Canal * * River * * * Aquifer * * * * Chemical systems paradigms Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  24. (1) Primary species (2) Secondary species(1) first Ns-Ne columns of S last Ne columns of S Mobile (a) aqueous (primary) species (2) aqueous (secondary) first Ns-Ne-Nk columns of S (not specifically labeled) (f) kinetic aqueous species. solutes in the 2nd block of Sk Immobile (k) kinetic minerals (& gases) (q) minerals (& gases) in equilib. minerals (& gases) in the 2nd block of Sk Classification os chemical species Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  25. Conclusions • Is Reactive transport needed? • Reaction (rate , where, when, under which conditions) are controlled by transport. • Can be understood? • All it takes is to understand components • The difficult part is to choose the relevant species and reactions. • Can be solved efficiently? • Similar effort as conservative transport Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  26. But Reactions are driven by disequilibrium Disequilibrium is driven by actual mixing We need to know how to evaluate actual mixing! Current stochastic transport theories fail to do so! Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  27. Water mass balance Flow Equation _ = Solute mass balance Adv. form Tpt. Eqn Flow Eqn. x Ck+1 Div. form Tpt. Eqn _ = + _ = = _ = _ _ Mass Final Initial Mass Mass balance mass mass In out = Reverse time weigthing Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  28. infiltration case (INF). Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  29. evaporation case (EVA). Recent developments in Reactive Transport, Alicante, Spain. October, 2005

  30. alternating evaporation-infiltration case (ALT) Recent developments in Reactive Transport, Alicante, Spain. October, 2005

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