Physical and Chemical Processes Final

electroneutrality

principle that in any given system the total positive charge must always equal the total negative charge

Alkalinity

a measure of the acid-neutralizing capacity of water. Volume of acid consumed (mL) × Molarity of acid (M) × 50 × 1000 / Volume of water sample (mL)

E(t)

exit age distribution. rate at which molecules are exiting a system

F(t)

cumulative age distribution. fraction of fluid with residence time less than or equal to a given value

Mean hydraulic detention time

tau = V/Q

Alkalinity: for pH between 6 and 9

CO3

Alkalinity: for pH less than 9

CO3 and OH can be ignored **don't ignore if given though

E(t) of a CFSTR for pulse input tracer

F(t) of CFSTR for pulse input tracer

E(t) in a PFR for pulse input

F(t) of a PFR for pulse input

relationship between F(t) and E(t)

E(t) = dF(t)/dt

F(t) =∫E(t)dt (from 0 to t)

PFR Mass Balance, no diffusion/dispersion and no reaction

Rate of change of mass stored in control volume = Rate of input of mass to cv − Rate of output of mass from cv

∂c/∂t = -v_x∂c/∂x

CFSTR Mass Balance for pulse input, no diffusion/dispersion and no reaction

Rate of change of mass stored in control volume = Rate of input of mass to cv − Rate of output of mass from cv

𝑐_p(t) = 𝑐₀𝑒^−𝑡/𝜏

CFSTR Mass Balance for step input, no diffusion/dispersion and no reaction

Rate of change of mass stored in control volume = Rate of input of mass to cv − Rate of output of mass from cv

𝑐_s(t) = 𝑐_in(1 - e^(-t/τ))

F(t) equation for a CFSTR with step input tracer

F(t) = 1 − 𝑒^−𝑡/𝜏

E(t) for a CFSTR with step input tracer

E(t) = 1/𝜏 (e^−𝑡/𝜏)

Relationship between effluent concentration and detention time for CFSTR with irreversible first order reaction

Freundlich isotherm

q = k_Fcⁿ

log transformed freundlich isotherm

logq = logk_F + nlogc

Logarithmic plot of equilibrium concentration data that can be used to obtain the Freundlich parameters

equation for time to ½ concentration in a batch reactor for a first order reaction

t_1/2 = ln2/k₁

fraction of liquid-phase resistance (percent of the gas transfer resistance that’s in the liquid phase) equation

equation for finding the effluent concentration after a first-order reaction in a series of 30 CFSTRs

1 cubic meter equals

1000 liters

concentration of adsorbate (i.e. PAC) equation

c_PAC = (c₀ — c_eq)/(q_eq — q₀)

Formula for time to breakthrough

t_bt = N_{BV, bt} x EBCT

Number of bed volumes at breakthrough equals

N_{BV, bt} = (p_b x q_in)/c_in

EBCT equals

EBCT = V_r/Q

Mass of adsorbent (usually carbon) at breakthrough equals

M_adsorbent = p_b x V_r

adsorption

molecules adhere to the surface of the phase

adsorbate or sorbate

molecule (liquid or gas) that adsorbs

adsorbent or sorbent

solid on which adsorption occurs is called

adsorption density

Amount of material (adsorbate) adsorbed per unit of adsorbent

mass sorbate/mass sorbent

concentration adsorbed

c_{i, adsorbed} = q_ic_{solid, sorbent}

E(t) curve for pulse input of a non-reactive tracer to the series of 𝑁 CFSTRs

(the orange curve)

F(t) curve for a pulse input of a non-reactive tracer to the series of 𝑁 CFSTRs

(the orange curve)

E(t) curve for a pulse input of a non-reactive tracer if you were modeling the reactor system as a PFR

(the black curve)

F(t) curve for a pulse input of a non-reactive tracer if you were modeling the reactor system as a PFR

(the black curve)

mass balance for oxygen transfer for a single droplet from a surface aerator, assume no diffusion/dispersion

(have to integrate and solve in some cases)

area of sphere

4πr²

a_L equals

a_L = A/V_L

Volume of a sphere

4/3πr³

Based on the Average WQ graph, where do the different types of WTP design occur.

1. Direct Filtration

2. DAF

3. DAF or Settling

4. Settling

What conditions (TOC, Turbidity, and True Color) are Direct Filtration best suited for under average water quality?

TOC: 0-3 mg/L

Turbidity: 0-5 NTU

True Color: 0-20 c.u.

What conditions (TOC, Turbidity, and True Color) are DAF best suited for under average water quality?

TOC: 0-14 mg/L

Turbidity: 0-10 NTU

True Color: 0-100 c.u.

What conditions (TOC, Turbidity, and True Color) are DAF or Settling best suited for under average water quality?

TOC: 0-14 mg/L

Turbidity: 10-100 NTU

True Color: 0-100 c.u.

What conditions (TOC, Turbidity, and True Color) are Settling only best suited for under average water quality?

TOC: 0-14 mg/L

Turbidity: 100+ NTU

True Color: 0-100 c.u.

Based on the Max WQ graph, where do the different types of WTP design occur.

1. Direct Filtration

2. DAF

3. DAF or Settling

4. Settling

What conditions (TOC, Turbidity, and True Color) are Direct Filtration best suited for under max water quality?

TOC: 0-5 mg/L

Turbidity: 0-25 NTU

True color: 0-35 c.u.

What conditions (TOC, Turbidity, and True Color) are DAF only best suited for under max water quality?

TOC: 0-14 mg/L

Turbidity: 0-50 NTU

True Color: 0-100 c.u.

What conditions (TOC, Turbidity, and True Color) are DAF or settling best suited for under max water quality?

TOC: 0-14 mg/L

Turbidity: 50-200 NTU

True Color: 0-100 c.u.

What conditions (TOC, Turbidity, and True Color) are Settling only best suited for under max water quality?

TOC: 0-14 mg/L

Turbidity: 200+ NTU

True Color: 0-100 c.u.

What graph is this?

Rapid Equilibrium Breakthrough Graph

Breakthrough curve for GAC columns