Process Comments Constituents effected
Adsorption/
desorption
Many chemical constituents tend to attach or sorb onto solids. The implication for wastewater discharges is that a substantial fraction of some toxic chemicals are associated with the suspended solids in the effluent.
Adsorption combined with solids settling results in the removal from the water column of constituents that might not otherwise decay.
Metals, trace organics, NH41, PO432
Algal synthesis The synthesis of algal cell tissue using the nutrients found in wastewater. NH41, NO32, PO432, pH, etc.
Bacterial conversion
Bacterial conversion (both aerobic and anaerobic) is the most important pro- cess in the transformation of constituents released to the environment. The exertion of BOD and nitrogenous oxygen demand (NOD) are the most com- mon examples of bacterial conversion encountered in water-quality manage- ment. The depletion of oxygen in the aerobic conversion of organic wastes is also known as deoxygenation. Solids discharged with treated wastewater are partly organic. Upon settling to the bottom, they decompose bacterially either anaerobically or aerobically, depending on local conditions. The bacterial transformation of toxic organic compounds is also of great significance.
BOD5, nitrification, denitrification, sulfate reduction, anaerobic fer- mentation (in bottom sediments), conversion of priority organic pollutants, etc.
Chemical reactions
Important chemical reactions that occur in the environment include hydrolysis, photochemical, and oxidation-reduction reactions. Hydrolysis reactions occur between contaminants and water.
Chemical disinfection, decomposi- tion of organic compounds, specific ion exchange, element substitution
Filtration Removal of suspended and colloidal solids by straining (mechanical and
chance contact), sedimentation, interception, impaction, and adsorption.
TSS, colloidal particles
Flocculation Flocculation is the term used to describe the aggregation of smaller
particles into larger particles that can be removed by sedimentation and filtration. Flocculation is brought about by Brownian motion, differential velocity gradients, and differential settling in which large particles overtake smaller particles and form larger particles.
Colloidal and small particles
Gas absorption/
desorption
The process whereby a gas is taken up by a liquid is known as absorp- tion. For example, when the dissolved oxygen concentration in a body of water with a free surface is below the saturation concentration in the water, a net transfer of oxygen occurs from the atmosphere to the water.
The rate of transfer (mass per unit time per unit surface area) is propor- tional to the amount by which the dissolved oxygen is below saturation.
The addition of oxygen to water is also known as reaeration. Desorption occurs when the concentration of the gas in the liquid exceeds the satura- tion value, and there is a transfer from the liquid to the atmosphere.
O2, CO2, CH4, NH3, H2S
(continued )
For example, bacterial conversion is considered in Chap. 2 in the analysis of the BOD reaction, and in greater detail in the chapters dealing with biological treatment. Because all of the processes summarized in Table 1–10 are rate dependent, representative rate expressions used to model these processes are presented in Table 1–11. The important thing to note about Table 1–11 is the variety of different rate expressions that have been used to model constituent conversion and separation processes.
Conversion Processes. Rate expressions have been used to describe the conversion of wastewater constituents in treatment processes and the fate of constituents released in the environment. For example, the first order reaction, Eq. (1–48), expressed as (rc52kC ) is used to model the exertion of BOD and bacterial decay, as discussed subsequently in Chap. 2. Although Eq. (1–51) is second order overall, it is first order with respect to CA
and CB, individually. Equation (1–52), known as a saturation type of equation (also known as a Monod type equation), is illustrated on Fig. 1–7. As shown on Fig. 1–7, when the concentration, C, is large the rate of reaction is zero order, and when the concentration is low, the rate of reaction is first order.
1–10 Introduction to Process Kinetics 35
Process Comments Constituents effected
Natural decay In nature, contaminants will decay for a variety of reasons, including
mortality in the case of bacteria and photooxidation for certain organic constituents. Natural and radioactive decay usually follow first-order kinetics.
Plants, animals, algae, fungi, pro- tozoa, eubacteria (most bacteria), archaebacteria, viruses, radioac- tive substances, plant mass
Photochemical reactions
Solar radiation is known to trigger a number of chemical reactions. Radia- tion in the near-ultraviolet (UV) and visible range is known to cause the breakdown of a variety of organic compounds.
Oxidation of inorganic and organic compounds
Photosynthesis/
respiration
During the day, algal cells in water bodies will produce oxygen by means of photosynthesis. Dissolved oxygen concentrations as high as 30 to 40 mg/L have been measured. During the evening hours algal respiration will consume oxygen. Where heavy growths of algae are present, oxygen depletion has been observed during the evening hours.
Algae, duckweed, submerged macrophytes, NH14, PO432, pH, etc.
Sedimentation The suspended solids discharged with treated wastewater ultimately settle
to the bottom of the receiving water body. This settling is enhanced by flocculation and hindered by ambient turbulence. In rivers and coastal areas, turbulence is often sufficient to distribute the suspended solids over the entire water depth.
TSS
Sediment oxygen demand
The residual solids discharged with treated wastewater will, in time, settle to the bottom of streams and rivers. Because the particles are partly organic, they can be decomposed anaerobically as well as aerobically, depending on conditions. Algae which settle to the bottom will also be decomposed, but much more slowly. The oxygen consumed in the aerobic decomposition of material in the sediment represents another dissolved oxygen demand in the water body.
O2, particulate BOD
Volatilization Volatilization is the process whereby liquids and solids vaporize and
escape to the atmosphere. Organic compounds that readily volatilize are known as VOCs (volatile organic compounds). The physics of this phe- nomenon are very similar to gas absorption, except that the net flux is out of the water surface.
VOCs, NH3, CH4, H2S, other gases
Table 1–10 (Continued )
The rate expression given by Eq. (1–53) is known as a retarded first order rate expres- sion because the rate constant changes with distance or time, as illustrated on Fig. 1–8, or with the degree of treatment which, in turn, can be related to distance or time. The term,
rt, in the denominator is the retardation factor. In wastewater treatment applications, the exponent n in Eq. (1–53) is related to the particle size distribution (see Fig, 1–8).
For example, if all of the particles are the same size and composition, the value of the exponent n is equal to one, and the retardation factor rt is equal to zero. The retarded rate expression is also applied to the removal of organic matter from mixtures where the
Table 1–11
Examples of rate expressions for selected conversion and separation processes given in Table 1–10a
Process Rate expression Comments
Conversion processes
Bacterial conversion rc 5 2kC rc 5 rate of conversion, M/L3 T
k 5 first order reaction rate coefficient, 1/T C 5 concentration of organic material remaining, M/L3
Chemical reactions rc56k nC n rc5 rate of conversion, M/L3 T
k n5 reaction rate coefficient, (M/L3)n21/ T
C 5 concentration of constituent, (M/L3)n
n 5 reaction order (e.g. for second order n 5 2) Natural decay rd 5 2kdN rd 5 rate of decay, no./T
kd 5 first order reaction rate coefficient, 1/T
N 5 amount of organisms remaining, no.
Separation processes
Gas absorption/
desorption rab5 kab
A V (Cs2 C )
rde52kde
A V (C 2 Cs )
rab 5 rate of absorption, M/L3 T
rde 5 rate of desorption, M/L3 T
kab 5 coefficient of absorption, L/T
kde 5 coefficient of desorption, L/T
A 5 area, L2 V 5 volume, L3 Cs 5 saturation concentration of constituent in liquid, M/L3 (see Eq. 2–49)
C 5 concentration of constituent in liquid, M/L3
Sedimentation rs 5 ys
H (SS ) rs5 rate of sedimentation, 1/T
ys5 settling velocity, L/T
H 5 depth, L
SS 5 settleable solids, L3/L3 Volatilization rv 5 2kv (C 2 Cs ) rv 5 rate of volatilization per unit time per unit volume, M/L3T
kv 5 volatilization constant, 1/T
C 5 concentration of constituent in liquid, M/L3 Cs 5 saturation concentration of constituent in liquid, M/L3 (see Eq. 2–49)
a Adapted in part from Ambrose et al. (1988), Tchobanoglous et al. (2003).
biodegradability of the individual constituents comprising the organic matter is different (Tchobanoglous et al., 2003).
Separation Processes. Unlike conversion processes where constituents are removed through transformation, separation processes bring about removal by the physical transfer of constituents from a diluted state to a concentrated state. Separation processes exploit particular characteristics of constituents to bring about removal. The removal methods for particulate and dissolved constituents are considered below.
Particulate Constituents. The removal of particulate constituents depends on the nature
and size of the constituent but is brought about primarily through the application of grav- ity and pressure forces. For example, large coarse solids in wastewater, greater than about 6 mm (0.25 in.), are removed by screening (i.e., sieving). The force of gravity is used to bring about the separation (removal) of grit and other settleable material. Very light con- stituents such as oils and grease are also removed by the force of gravity and by flotation because their density is less that that of water. Smaller particulate constituents that cannot
Reaction rate, r
Concentration, C, mg/L 0.2
0 0.4 0.6 0.8 1
10 20 30 40 50
0
r kC
K C with k 1 and K 1
Figure 1–7
Rate of reaction versus concentration for a saturation type expression. Beyond about 20 mg/L the rate of reaction is essentially zero order.
Distance, x or time, t Original particle size distribution
Assumed particle size distribution after distance, x or time, t
Idealized particle removal rate coefficient
TSS particle size distribution
k1 > k2 > k3 > k4 > k5
k0 >
0
Figure 1–8
Definition sketch to illustrate the change that can occur in the removal rate coefficient with distance or time when an influent wastewater with a particle size distribution such as shown is applied to a granular medium filter or a constructed wetland.
1–10 Introduction to Process Kinetics 37
be removed by gravity can be removed by filtration, in which wastewater is passed through a filtering medium by the application of force in the form of pressure.
Dissolved Constituents. Dissolved constituents can also be removed from water by con-
centration on a solid surface (e.g., activated carbon adsorption and ion exchange). An important consideration in the modeling of adsorption-type separation processes is that because the reaction is assumed to be instantaneous after the constituent reaches the rele- vant surface, the reaction rate is controlled by the transport of the constituent to the point of reaction. The transfer of mass by molecular diffusion in stationary systems can be rep- resented by the following expression, known as Fick’s first law:
r5 2Dm
0C 0x (1–54)
where r 5 rate of mass transfer per unit area per unit time, ML22T21
Dm5 coefficient of molecular diffusion in the x direction, L2T21
C 5 concentration of constituent being transferred, ML23
x 5 distance, L
The negative sign in Eq. (1–54) is used to denote the fact that diffusion takes place in the direction of decreasing concentration. Also, it should be noted that the concentration gradi- ent (0C/0x) is assumed to be constant. In the chemical engineering literature the symbol J
is used to denote mass transfer in concentration units whereas the symbol N is used to denote the transfer of mass expressed as moles.
The coefficient of molecular diffusion is related to the frictional coefficient of a par- ticle as given by the Stokes-Einstein law of diffusion. For spherical particles the coeffi- cient of diffusion is given by the following expression (Shaw, 1966).
D5 kT
6pmrp
5 RT
6pmrpN (1–55)
where D 5 coefficient of diffusion, m2/s
k 5 Boltzmann constant 1.3805 3 10223 J/K
T 5 temperature, K 5 273.15 1 °C
R 5 universal gas law constant, 8.3145 J/mole?K m5 dynamic viscosity, N?s/m2
rp5 radius of particle, m
N 5 Avogadro’s number, 6.02 3 1023 molecules/gãmole
The terms in the denominator in Eq. (1–55) correspond to the coefficient of friction for a particle as defined by Stokes law. The coefficient of diffusion for a particle with a radius of 1027 m (0.01 mm), which corresponds to the size of the smallest bacteria, for the fol- lowing conditions is:
T 5 20°C m5 1.002 3 1023 N?s/m2
D5 kT
6pmrpA 5 (8.3145 J/mole?K)(293K)
6(3.14)(1.00231023 N?s/m2)(1027m)(6.0231023/mole) 5 21.43 3 10213 m2/s 5 2.143 3 1028 cm2/s
From the above computation it is easy to see that as the particles get smaller the coefficient of molecular diffusion increases. Depending on the fluid regime, the coefficient of molecular diffusion in Eq. (1–55) will be replaced by the turbulent coefficient of dispersion, as described further in Appendix I.
Many important separation processes used in wastewater treatment involve mass transfer across the gas-liquid interface (e.g., aeration) or the removal of undesirable con- stituents (e.g., stripping). For example, the rate of flux of a slightly soluble gas from the gas to the liquid phase (liquid film controls transfer rate; see discussion in Sec. 5–10), based on Fick’s first law, can be approximated as follows:
r 5 KL(Cs2 Ct) (1–56)
where r 5 rate of mass transferred per unit area per unit time, ML22T21
KL5 overall liquid mass transfer coefficient, LT21
Cs5 concentration in equilibrium with gas as given by Henry’s Law, ML23
Ct5 concentration in liquid bulk phase at time t, ML23 The mass transfer coefficient depends on the characteristics of the wastewater and the treatment process design and is, therefore, unique for each situation. The application of mass transfer for aeration is considered in Secs. 5–10 and 5–11. Other treatment processes that depend on mass transfer including carbon adsorption, gas stripping, and ion exchange are considered in Chap. 11.
Analysis of Reaction Rate Coefficients
Typically, reaction rate coefficients are determined using the results obtained from batch experiments (i.e., no inflow or outflow), from continuous flow experiments, and from pilot and field scale experiments. Using the data from batch experiments, the coefficients can be determined using a variety of methods including (1) the method of integration and (2) the differential method (see Table 1–12).
1–10 Introduction to Process Kinetics 39
Table 1–12