Water and Wastewater Treatment

Ideal reactor design (PFR vs CFSTR)

A plug flow reactor (PFR) is an ideal tubular reactor in which fluid moves as a plug with no axial mixing, so composition changes along the length but is uniform across any cross-section. A continuous flow stirred tank reactor (CFSTR, also called CSTR) is an ideal vessel in which the contents are perfectly mixed, so the effluent composition equals the composition inside the tank. For the same inlet concentration, flow rate and outlet concentration, the required volume depends on the reaction order.

For a first-order reaction with rate -r_A = kC and space time \tau = V/Q, the design equations are k\tau_{PFR} = \ln(C_0/C) for the PFR and k\tau_{CSTR} = (C_0 - C)/C for the CFSTR. With y = C/C_0, the volume ratio is V_{CSTR}/V_{PFR} = (1-y)/[y(-\ln y)], which is always at least 1. A PFR therefore never needs more volume than a CFSTR for first-order kinetics.

For second-order kinetics, -r_A = kC^2, the same integration gives V_{CSTR}/V_{PFR} = C_0/C. The gap between the two reactors widens rapidly as the required conversion increases.

The PFR is not always superior. Statements that use the word 'always' fail for zero-order or autocatalytic kinetics, where a CSTR can give equal or higher conversion for the same volume. Reaction kinetics therefore governs the choice of reactor.

Both ideal reactors are normally operated at steady state. The CSTR is uniformly mixed, whereas the PFR has concentration variation along its length. For a steady-state CSTR, the mass balance Q(C_0 - C) = Vr gives the volume directly from the removal rate evaluated at the effluent concentration.

Reactor diagrams are matched by features. A PFR is an unstirred tube with continuous inflow and outflow, a CSTR is a stirred vessel with continuous inflow and outflow, and a batch reactor is a closed stirred vessel charged once.

In a batch reactor, no reactant is added and no product is withdrawn after start-up, and the run lasts for a pre-specified duration. Because composition changes with time, batch operation is unsteady (transient) and not steady state.

Activated sludge process design

The activated sludge process (ASP) is a suspended-growth aerobic process in which wastewater is mixed with recycled microorganisms in an aeration tank and the biomass is then separated in a secondary clarifier. Its design rests on a small set of standard parameters.

The food-to-microorganism ratio is F/M = QS_0/(VX), where Q is the influent flow, S_0 is the BOD_5 entering the aeration tank, V is the tank volume and X is the MLVSS concentration. It is expressed in kg BOD per kg MLVSS per day. The effluent BOD does not enter this definition.

The observed yield Y (g VSS produced per g BOD removed) gives the net biomass production as P_x = Y(S_0 - S)Q.

When endogenous decay is included, the net waste activated sludge is P_x = \dfrac{Y(S_0 - S)Q}{1 + k_d\theta_c}, where k_d is the decay coefficient and \theta_c is the mean cell residence time. Longer residence time lowers the net sludge yield.

At steady state, the net rate of microorganism formation over the whole system equals the biomass leaving through the effluent and the wastage minus the biomass entering with the influent, divided by the aeration volume. The internal recycle stays inside the system boundary and cancels out of this balance.

Unit conversion is the most common error. Flow in MLD must be converted to m^3/d, and mg/L equals g/m^3, so BOD load in kg/d is obtained by multiplying m^3/d by g/m^3 and dividing by 1000.

Sedimentation settling types

Particle settling is classified by how particles behave during settling. Type I (discrete) settling involves non-flocculating particles, such as sand or grit, that settle individually under gravity without interacting. Type II (flocculent) settling involves particles that coalesce and change size while falling, as in a primary sedimentation tank. Type III (hindered or zone) settling occurs at higher solids concentration, where particles settle as a mass with a clear interface, as in the lower part of a secondary clarifier. Type IV (compression) settling occurs when particles in a dense layer are supported by those above.

For discrete particles in laminar flow, Stokes' law gives the terminal settling velocity v = \dfrac{(\rho_p - \rho_w) g d^2}{18\mu}. For two particle types in the same water, v \propto (G_s - 1)d^2, where G_s is the specific gravity. A ratio of velocities therefore leads directly to a ratio of diameters.

In a grit chamber, settling is Type I, and in a primary sedimentation tank, settling is Type II. In a secondary sedimentation tank, settling is Type III.

Solids removal often combines chemical and physical steps. Coagulation, flocculation and sedimentation aggregate fine particles into settleable flocs, and slow sand filtration then removes the remaining suspended matter by straining and biological action in the schmutzdecke. Chlorination and aeration do not remove suspended solids.

Chlorination and disinfection

Chlorine disinfection depends strongly on pH because free chlorine exists as two species in equilibrium. Hypochlorous acid, \mathrm{HOCl}, is a much more effective biocide than the hypochlorite ion, \mathrm{OCl^-}. The equilibrium has a pKa of about 7.5 at 25 °C, so the fraction present as \mathrm{HOCl} is highest at low pH. Disinfection efficiency is therefore greatest in mildly acidic water, and it falls as pH rises toward alkaline values.

Disinfectants act by different mechanisms. Typical examples are:

• Ethanol — dissolves membrane lipids and denatures proteins, disrupting the cell membrane.
• Mercuric chloride — binds sulfhydryl (–SH) groups and inactivates enzymes that depend on them.
• Glutaraldehyde — cross-links and alkylates amino groups, which inactivates proteins.
• Isopropyl alcohol — an effective disinfectant at about 60 to 90 percent concentration, and therefore not unusable.

These examples show that a statement such as 'a disinfectant cannot be used' is generally false when the agent is a standard, effective chemical at a suitable concentration.

Coagulation mechanisms

Coagulation destabilizes colloidal particles so that they can aggregate. The main mechanisms are charge neutralization, adsorption of soluble hydrolysis species onto particle surfaces, compression of the electrical double layer (ionic layer compression), sweep coagulation and polymer bridging. The dominant mechanism depends on pH and on the coagulant.

Alum produces positively charged aluminium hydrolysis species at low pH. At pH 4, these species neutralize the negative surface charge of suspended colloids, adsorb onto them and compress the double layer, but an amorphous \mathrm{Al(OH)_3} precipitate for sweep coagulation does not form to any appreciable extent. Sweep coagulation requires near-neutral pH, and polymer bridging requires an added polymeric coagulant aid.

Flocculation is driven by particle collisions. Collisions caused by Brownian motion constitute perikinetic flocculation, while collisions caused by fluid motion from external mixing constitute orthokinetic flocculation.

In the electric double layer, the Stern layer is the compact inner layer of counter-ions next to the particle surface, and it is more compact than the diffuse layer that extends further into the solution. The zeta potential is measured at the slipping plane, which lies beyond the Stern layer, so it is not the same as the Stern potential.

Industrial effluent characteristics

Industrial effluents differ widely in pH, colour, organic load and toxicity, so general statements about a whole industry must be checked carefully. Molasses-based distillery spent wash is strongly coloured, dark brown owing to melanoidins, and it is acidic. Wood-based pulp and paper effluent from the kraft process is also dark, owing to lignin-derived compounds, but it is alkaline. Their pH values therefore do not both fall in the same range.

BOD values also vary between industries. Pulp and paper effluent generally has a BOD well below 15,000 mg/L, so a blanket BOD claim for both effluents is not correct. Toxicity is effluent-specific and cannot be assumed to be high for every effluent of a given type.

When two effluents are mixed, the resulting pH is found from the moles of hydrogen and hydroxide ions in each stream. The acid stream supplies [\mathrm{H^+}] \times Q in mol/d and the alkaline stream supplies [\mathrm{OH^-}] \times Q in mol/d. The two react to neutralize each other, and the excess ion determines the final pH after dividing by the total flow. Buffering and temperature effects are neglected in such problems.

Reverse osmosis recovery and mass balance

Reverse osmosis (RO) is a high-pressure membrane process that removes dissolved salts such as total dissolved solids (TDS). The feed is split into a permeate (product water) and a reject (concentrate). Recovery is the fraction of the feed flow that leaves as permeate, and rejection is the fraction of solute removed. Concentration in the reject rises as recovery increases, because the same salt mass is concentrated into a smaller stream.

A solute mass balance gives the reject concentration. For feed flow Q_f, permeate flow Q_p and reject flow Q_r, the balance is Q_fC_f = Q_pC_p + Q_rC_r. Here Q_p/Q_f equals the recovery and C_p = (1 - \text{rejection}) \times C_f. Solving for C_r gives the concentration of the reject.

RO membranes foul when deposits and adsorbed material form on the surface and reduce flux, and this occurs in microfiltration as well as in RO. Concentration polarization is an inherent feature of RO, because solutes accumulate in a boundary layer at the membrane surface. Ultrafiltration is commonly used as a pretreatment to remove colloids, bacteria and macromolecules and so protect RO membranes from fouling. Reverse osmosis itself is a final polishing step and is not a pretreatment for microfiltration.

Flocculation velocity gradient

In a flocculation tank, the velocity gradient G (s^{-1}) measures the intensity of mixing that brings particles together. The theoretical power needed to maintain a given velocity gradient is P = G^2\mu V, where \mu is the dynamic viscosity (Pa·s or N·s/m^2) and V is the tank volume (m^3). Power in watts is then divided by 1000 to obtain kilowatts. Dynamic viscosity of water near 20 °C is about 1.0\times10^{-3} Pa·s, so units must be consistent before substitution.

The equation shows that power rises with the square of the velocity gradient, so doubling G increases the power requirement four times for the same tank volume and viscosity.

Primary clarifier mass balance

A primary clarifier removes a fraction of the influent suspended solids that settle to the bottom as sludge. The solids mass balance states that the solids removed equal the influent solids load multiplied by the removal efficiency. The influent solids load in kg/d is the flow in m^3/d multiplied by the concentration in kg/m^3, which is numerically the same as mg/L multiplied by m^3/d divided by 1000.

The sludge mass is obtained by dividing the solids removed by the solids fraction of the underflow, M_{sludge} = M_{solids}/w, where w is the weight fraction of solids. The sludge volume then follows from the sludge density, V_{sludge} = M_{sludge}/\rho_{sludge}. A sludge with a low solids content has a much larger volume than one with a high solids content, so the solids fraction must be used rather than the solids load itself.