Coagulation Chemistry: Effects on the Acid/Base Balance Via chemical equilibrium reactions, consumption of H in the precipitation step has a domino effect on the concentrations of H +, H, H C, HC, and C. The net changes can be determined by solving the equations for acid/base equilibrium: + + 14.0 ( H ( HC 6. ( ( ( H ( C H + H = 10 = 10 ( HC ( HC ( ( ( H C + HC + C = TTC 10. = 10 Coagulation Chemistry: Effects on the Acid/Base Balance The exact results can be obtained numerically, but the approximate change is conversion of one HC to H C for each H consumed, while TTC remains constant: ( ( s + Al + H Al H + H H + H + HC + H HC + Al + HC + H Al( H ( s + H C Coagulation Chemistry: Effects on the Acid/Base Balance The al ph can be estimated from the initial conditions and the amount of HC converted to H C. The calculations are often presented in the context of alkalinity (Alk, which is the net capacity to bind H + : ( ( ( ( + ( Alk = H + HC + C H HC Coagulation Chemistry: Effects on the Acid/Base Balance Unlike the concentrations of individual chemical species that contribute to alkalinity, Alk is conservative. This means that if a chemical with a certain Alk is added to a solution, the new Alk is just the original Alk plus the amount added. Very convenient for calculations, as shown by the following example. where the approximation applies at ph <~ 9.0. Alk is reported in equivalents per liter, where one equiv/l corresponds to the concentration that yields one mol/l for any term on the right (e.g., one mol/l of H or 0.5 mol/l of C 1
Example: Coagulation Chemistry A water supply at ph 7. and containing 0.8 meq/l Alk is dosed with 40 mg/l FeCl. The reactions are rapid, so no C exchanges with the atmosphere. The al ph must be 6.0. Will addition of base be required? 1. Approximate (HC init as Alk init. Each mmole of HC contributes one meq of Alk, so (HC init 0.8 mmol/l. Then, (H C is computed as: ( + ( HC ( H ( 8.0x10 4 ( 10 7. 4 = = = 6.5 K a 1 10 H C 1.1x10. Compute Alk from Alk init and FeCl dose (40 mg/l FeCl. Each mol/l of FeCl added combines with mol/l of H, and so reduces Alk by equiv/l: equiv Alk destroyed moles FeCl added Alk = Alk init * mol FeCl added L 4 equiv Alk destroyed mg FeCl 1 mol FeCl = 8.0x10 40 mol FeCl added L 16,500 mg 5 equiv meq = 6.15x10 = 6.15x10 L L. Approximate (HC as Alk, compute (H C from TTC and (HC. Fraction as given species 1.0 0.8 H C HC 0.6 0.4 0. 0.0 5 7 9 11 ph C 4. Compute ph from (H C, (HC, and K a1. ( ( 4 6.5 ( ( HC K 8.51x10 10 H.6x10 + a1 6 = = = 4 ( HC 1.1x10 ( ( TTC = TTC H C + HC,, init = 1.1x10 + 8.0x10 = 9.1x10 4 4 4 ( HC TTC, ( HC = 9.1x10 6.15x10 = 8.51x10 4 5 4 init + 6 ( ( ph = log H = log.6x10 = 5.47 The ph is too low, and lime or some other base would have to be added to increase it to at least 6.0.
Conditions in typical natural waters. Lots of dissolved NM. High doses of Fe + or Al + generate new surfaces to which the NM can bind. Coagulation and NM Low doses of Fe + or Al + partially neutralize the charge on the NM. The NM exerts a coagulant demand. HC H H -C C Fe + Fe + - H H H - H CH C - The Enhanced Coagulation Rule Requires NM removal from many surface waters Removal requirement depends on NM conc n (quantified as Total rganic Carbon, TC and Alkalinity Escape clause available if a point of diminishing returns is reached Enhanced coagulation is a BAT. If it doesn t work, you are off the hook TC (mg/l ALK (mg/l CaC 0-60 >60-10 >10 < N/A N/A N/A -4 5* 5 15 4-8 45 5 5 >8 50 40 0 *Required percentage reduction in TC Flocculation Theory: Particles Flocculate by Three Mechanisms The Rate of Collisions by Each Mechanism Can be Predicted from Theory Sh β = 1 G d + 6 ( d ij i j Fluid shear: Particles collide by traveling on different streamlines at different velocities Differential sedimentation: Particles collide due to different settling velocities The rate of reaction by all mechanisms is expected to be first order with respect to each type of particle second order overall: r Brownian motion: Particles collide due to random motion = β nn =+ ( ij i j k i j Br kt B 1 1 β = + + μ di d j ( d d ij i j DS π β = v v d + d ( 4 ( ρ ρ ( ij i j i j π g = d + d d d 7μ p w i j i j
Different mechanisms dominate for different size ranges. The only controllable mechanism is shear, by controlling the shear rate, G. Conventional Surface Water Treatment for Drinking Water From: Water on Tap, USEPA pamphlet accessed on 01/04/09 at http://www.epa.gov/safewat er/wot/pdfs/book_wateronta p_full.pdf 4
(From pflow, November 005 Headloss 90 80 10 gpm/ft Filter backwash water flowing into (above and out of (right launders Photos by Dan Gallagher From: Virginia Tech Water Treatment Primer, accessed on 01/04/09 at http://www.cee.vt.edu/ewr/environmental/teach/wtprimer/backwash/backwash.html Headloss (inches of water 70 60 50 40 0 0 10 8 gpm/ft 0 0 10 0 0 40 50 60 70 80 Time (hour 6 gpm/ft 4 gpm/ft Coagulant = FeCl (0 mg/l Temperature = 10 ο C 5
Effluent particle counts Filter effluent particle counts (1-150 µm (#/ml 100000 10000 10 gpm/ft 8 gpm/ft 1000 6 gpm/ft 100 4 gpm/ft 10 Coagulant = FeCl (0 mg/l Temperature = 10 ο C 1 0 10 0 0 40 50 60 70 80 Time (hour Granular Media Filtration Filtration Complexity 10 μm 0.8 mm Two dependent variables of importance Headloss Effluent particle concentration Never at (long-term steady state Two different modes of operation (filtration and backwashing Numerous independent variables (hydraulic loading rate, influent particle concentration and distribution, media size, backwashing frequency and operation, etc. Particle removal is clearly not primarily by sieving 6
Modeling Particle Removal ( L,CV d NV dt ( L,CV ( p = QN Q N + dn V r d( NV,CV Assume pseudo-steady state, so L Q= Av 0 = Av dn+ V r 0 0 L,CV p Av dn= V r 0 L,CV p dt = 0 V L,CV p Rate of Removal of Particles Number of r = by a Single Collector Collectors in Layer Rate of Approach of Removal Efficiency of Number of = Particles to a Collector a Single Collector Collectors in Layer V L,CV p Rate of Approach of Removal Efficiency of Number of r = Particles to a Collector a Single Collector Collectors in Layer π d Ac = 4 c Rate of Approach of = Nv π d c 0 Particles to a Collector 4 Removal Efficiency of η a Single Collector Total Volume of Number of Collector Media AdL 1 = = Volume of a Single Collector ( ε Collectors in Layer π dc /6 ( 1 ( 1ε π d AdL c = Nv0 [ η] 4 π dc /6 = ε η Nv0 AdL d c Single Collector Removal Efficiency 7
Av dn= V r 0 L,CV p ( 1ε η Av 0 dn = N v0 AdL d c ( 1 dn ε η = dl =λdl N d c N ln N out in =λl N = N exp( λl out in Filter coefficient Summary: Mass Balance Analysis of Particle Removal in a Granular Filter Removal modeled based on interactions of influent particles with isolated collector grains Assuming short-term, pseudo-steady state, removal of each type of particle is predicted to decline exponentially with depth Coefficient for the exponential loss rate depends on the particle characteristics (size, density, etc. If we could predict η for a given type of particle, we could predict N out /N in for that particle Approach: Predict η by treating filter as a tightly packed flocculation basin, where incoming particles flocculate with filter grains η Br kt B = 0.905 μddv c p 0 / 8
B=Backwash required c=concentration; h=headloss; S=Standard length bed; L=longer bed B=Backwash required; c=concentration; h=headloss; S=Standard size grains; d=larger diameter grains 9
Summary: Rapid Rate Filtration Based on relative sizes of particles and collectors, sieving is unimportant and removal can be modeled based on interactions (flocculation with isolated collector grains Particle removal by clean grains predicted to be least efficient for particles ~1 μm Actual particle removal tends to improve over time due to particle capture by previously captured particles (filter ripening Run terminated and filter backwashed when either effluent particle concentration or filter hydraulic headloss exceeds specified criterion Acceptable length of run can be modified by design and operational decisions (grain size, filtration rate, coagulant dose, etc. 10