Formula sheet

Solid Waste and Resource Recovery Systems Formula Sheet

Environmental engineering formula sheet for solid waste and resource recovery covering mass balance, diversion, contamination, collection, landfill airspace, leachate, gas, energy recovery, reliability, and validation.

Branch: Environmental Engineering
Content: Formula sheet
Updated: Jun 23, 2026
Revision: v1.0.0 · reviewed

This formula sheet collects first-pass calculations for solid waste and resource recovery systems. Use it for facility checks, route planning, recovery performance review, landfill operations, leachate and gas screening, energy recovery, and validation evidence.

Solid waste calculations must state the boundary, time basis, moisture basis, density basis, and downstream acceptance basis. A recovery claim is weak unless recovered products, rejects, residuals, emissions, leachate, gas, and stored inventory can be reconciled.

Basis and Units

Common units:

mass flow: kg/day, t/day, kg/h;
volume flow: m^3/day, m^3/h;
density: kg/m^3 or t/m^3;
moisture content: percent wet basis or dry basis, stated explicitly;
energy: MJ/kg, kWh, MWh/day;
gas flow: m^3/h or normal m^3/h, with methane fraction stated;
concentration: mg/L, kg/m^3, ppm by the stated basis;
uptime and availability: percent over the selected operating period.

Do not mix wet mass, dry mass, compacted volume, loose volume, and accepted recovered mass without conversion.

Solid Waste Mass Balance

For a facility boundary:

\Delta S=M_{in}-M_{out}+M_{gen}-M_{loss}

For steady reporting over a period:

M_{in}=M_{product}+M_{reject}+M_{residual}+M_{stored}+M_{loss}

where $M_{loss}$ may include moisture loss, gas, dust, combustion products, or unmeasured removal.

Worked Check

A recovery facility receives:

M_{in}=150\ \text{t/day}

It ships accepted recovered products:

M_{product}=58\ \text{t/day}

rejects:

M_{reject}=71\ \text{t/day}

and stores:

M_{stored}=6\ \text{t/day}

Unreconciled loss:

M_{loss}=150-58-71-6=15\ \text{t/day}

Engineering Comment

The $15\ \text{t/day}$ gap may be moisture loss, scale error, stockpile change, bypass, dust, informal removal, or reporting error. The balance should not be accepted until the cause is understood.

Composition by Mass

For category $i$ :

M_i=x_iM_{total}

where $x_i$ is mass fraction.

Composition fractions should sum to one:

\sum_i x_i=1

If fractions do not close, revise the sampling basis before using the data for equipment sizing or recovery claims.

Wet and Dry Mass

Wet-basis moisture content:

\displaystyle MC_w=\frac{M_{water}}{M_{wet}}

Dry mass:

M_{dry}=M_{wet}(1-MC_w)

Dry-basis moisture content:

\displaystyle MC_d=\frac{M_{water}}{M_{dry}}

Convert carefully:

\displaystyle MC_d=\frac{MC_w}{1-MC_w}

Moisture changes density, heating value, biological activity, leachate generation, odor, sorting performance, and buyer acceptance.

Density and Volume Conversion

Volume from mass:

\displaystyle V=\frac{M}{\rho}

Mass from volume:

M=\rho V

Compaction ratio:

\displaystyle CR=\frac{\rho_{compacted}}{\rho_{loose}}

Worked Check

A route collects:

M=9.2\ \text{t}

with compacted density:

\rho=0.46\ \text{t/m}^3

Vehicle volume used:

\displaystyle V=\frac{9.2}{0.46}=20.0\ \text{m}^3

Engineering Comment

Payload and volume must both pass. A truck can be volume-limited by bulky material or payload-limited by wet organics and dense residuals.

Reported Diversion and Accepted Recovery

Reported diversion:

\displaystyle D_{reported}=\frac{M_{shipped}}{M_{in}}

Accepted recovery:

\displaystyle D_{accepted}=\frac{M_{shipped}-M_{buyer\ reject}}{M_{in}}

Residual rate:

\displaystyle R_{residual}=\frac{M_{reject}+M_{buyer\ reject}}{M_{in}}

Worked Check

Incoming waste:

M_{in}=120\ \text{t/day}

Shipped recovered material:

M_{shipped}=72\ \text{t/day}

Buyer rejects:

M_{buyer\ reject}=9\ \text{t/day}

Reported diversion:

\displaystyle D_{reported}=\frac{72}{120}=60.0\%

Accepted recovery:

\displaystyle D_{accepted}=\frac{72-9}{120}=52.5\%

Engineering Comment

Accepted recovery is the stronger metric. Shipment alone can overstate performance if contamination or downstream rejection is high.

Contamination Rate

Contamination fraction in a product stream:

\displaystyle C=\frac{M_{contaminant}}{M_{sample}}

Clean product fraction:

P_{clean}=1-C

Use representative sampling. A single grab sample from a bale, windrow, bin, or conveyor may miss segregation and time variation.

Capture Efficiency

For a target material:

\displaystyle \eta_{capture}=\frac{M_{target,\ recovered}}{M_{target,\ incoming}}

Loss to residue:

M_{target,\ lost}=M_{target,\ incoming}-M_{target,\ recovered}

Capture efficiency should be reported by material type. A plant can have high total diversion while failing one high-value or high-risk stream.

Collection Route Capacity

Route volume:

V_{route}=N_h v_h

where $N_h$ is number of households or stops and $v_h$ is average set-out volume per stop.

Route mass:

M_{route}=\rho_{vehicle}V_{route}

Payload check:

M_{route}\leq M_{payload}

Vehicle volume check:

V_{route}\leq V_{vehicle}

Include seasonal peaks, missed pickups, density variation, compaction setting, and transfer distance before final routing.

Throughput and Residence Time

For a process with stored mass $M_S$ and throughput $\dot{M}$ :

\displaystyle t_R=\frac{M_S}{\dot{M}}

where $t_R$ is average residence time.

High residence time may increase odor, fire risk, vectors, product degradation, floor congestion, and stormwater contact.

Landfill Airspace Consumption

Airspace volume used:

\displaystyle V_{airspace}=\frac{M_{placed}}{\rho_{in-place}}

Remaining life:

\displaystyle t_{life}=\frac{V_{remaining}\rho_{in-place}}{\dot{M}_{placed}}

where $\dot{M}_{placed}$ is mass placement rate.

Worked Check

Remaining permitted airspace:

V_{remaining}=450{,}000\ \text{m}^3

In-place density:

\rho_{in-place}=0.82\ \text{t/m}^3

Annual waste placement:

\dot{M}_{placed}=95{,}000\ \text{t/year}

Remaining life:

\displaystyle t_{life}=\frac{450{,}000(0.82)}{95{,}000}=3.88\ \text{years}

Engineering Comment

This screen ignores settlement, cover soil, intermediate cover, operational slopes, unusable geometry, diversion changes, and permit constraints. Use it for planning, not final landfill life certification.

Leachate Water Balance

Leachate generation screen:

Q_L=P_{contact}+M_{waste}+Q_{runon}-E-Q_{recirc}-Q_{diverted}

where terms must be expressed as flow or volume over the same period.

Storage balance:

S_{t+\Delta t}=S_t+(Q_{in}-Q_{out})\Delta t

Emergency free storage:

S_{free}=S_{capacity}-S_t

Leachate estimates require cover condition, exposed waste area, stormwater separation, pump availability, recirculation, treatment limits, and wet-weather access.

Leachate Pollutant Load

Mass loading rate:

\dot{M}=QC

Total mass over a period:

M=\sum_i Q_iC_i\Delta t_i

where $Q$ is leachate flow and $C$ is concentration.

Concentration alone does not define treatment burden. A low concentration at high wet-weather flow can exceed the daily mass load from a high concentration at low flow.

First-Order Landfill Gas Generation Screen

A simple first-order methane generation screen is:

Q_{CH4}(t)=L_0Mk e^{-kt}

where:

$Q_{CH4}$ is methane generation rate;
$L_0$ is ultimate methane potential per mass of waste;
$M$ is waste mass represented by the model;
$k$ is decay rate constant;
$t$ is time since placement.

Use consistent time units. The model is a screen; real landfill gas depends on waste composition, moisture, temperature, cover, compaction, oxygen intrusion, settlement, collection system balance, and staged placement.

Worked Check

Use:

L_0=85\ \text{m}^3/\text{t}

M=100{,}000\ \text{t}

k=0.05\ \text{year}^{-1}

t=5\ \text{years}

Methane generation:

Q_{CH4}=85(100{,}000)(0.05)e^{-0.05(5)}

Q_{CH4}=330{,}971\ \text{m}^3/\text{year}

Engineering Comment

This value is generated methane, not necessarily collected methane. Collection efficiency, wellfield balance, downtime, air intrusion, condensate, cover cracks, and lateral migration control actual recovery.

Gas Collection and Energy Recovery

Collected methane:

Q_{CH4,collected}=\eta_{collection}Q_{CH4,generated}

Energy rate:

P_{thermal}=Q_{CH4}LHV

Electrical output:

P_e=\eta_e P_{thermal}

Use consistent units. If $Q$ is in m^3/h and $LHV$ is in MJ/m^3:

\displaystyle P_{thermal,kW}=\frac{Q LHV}{3.6}

because $1\ \text{kWh}=3.6\ \text{MJ}$ .

Worked Check

Collected methane flow:

Q=120\ \text{m}^3/\text{h}

Lower heating value:

LHV=35.8\ \text{MJ/m}^3

Electrical efficiency:

\eta_e=0.34

Thermal power:

\displaystyle P_{thermal}=\frac{120(35.8)}{3.6}=1193\ \text{kW}

Electrical power:

P_e=0.34(1193)=406\ \text{kW}

Engineering Comment

This screen excludes parasitic loads, gas cleaning, downtime, flare bypass, siloxanes, moisture, engine derating, and grid interconnection limits.

Waste-to-Energy Net Energy

Feed energy rate:

\dot{E}_{feed}=\dot{M}LHV_{waste}

Net electrical energy:

P_{net}=\eta_e\dot{E}_{feed}-P_{aux}

where $P_{aux}$ includes fans, pumps, conveyors, air pollution controls, ash handling, and facility loads.

Moisture, ash, chlorine, metals, heating value variability, and bypass fraction should be reviewed before using a single LHV value.

Equipment Availability

Availability:

\displaystyle A=\frac{T_{scheduled}-T_{down}}{T_{scheduled}}

For repairable equipment:

\displaystyle A\approx\frac{MTBF}{MTBF+MTTR}

where MTBF and MTTR must use the same time basis and failure definition.

Environmental performance can depend directly on availability. A down conveyor can force bypass, a down pump can raise leachate head, and a down flare can increase emissions.

Risk Priority Number

Risk priority number:

RPN=SOD

where severity $S$ , occurrence $O$ , and detection $D$ use defined scoring rules.

Use RPN to prioritize review, not to prove safety. High-severity fire, leachate, gas migration, slope, or exposure hazards may require controls even when occurrence is estimated as low.

Validation and Reconciliation Checks

Useful reconciliation checks include:

M_{in}-M_{out}-M_{stored}-M_{loss}\approx0

D_{accepted}\leq D_{reported}

Q_{leachate,wet}\geq Q_{leachate,dry}

Q_{gas,collected}\leq Q_{gas,generated}

A_{critical}\geq A_{required}

Any violation should trigger a data, boundary, instrumentation, or operations review before the metric is used for external reporting or engineering release.

Common Mistakes

Common solid waste calculation mistakes include:

reporting diversion based on shipped material instead of accepted recovered material;
using loose density for compacted landfill airspace;
ignoring moisture changes when comparing mass, heating value, and biological activity;
sizing collection routes by volume but missing payload limits;
treating generated landfill gas as collected gas;
using leachate concentration without flow to estimate treatment load;
averaging facility performance without accounting for downtime, bypass, stockpile growth, or buyer rejection;
relying on one sampling event for variable waste composition.

Validity Limits

These formulas are screening tools. They are useful for mass balance, route checks, preliminary storage, recovery quality, gas and energy plausibility, and operating diagnostics. Final design or compliance decisions require representative sampling, verified scale data, site hydrology, equipment curves, monitoring records, permit conditions, safety review, downstream acceptance records, and responsible engineering approval.

REF

Disciplines

Solid Waste and Resource Recovery Systems Formula Sheet

Basis and Units

Solid Waste Mass Balance

Worked Check

Engineering Comment

Composition by Mass

Wet and Dry Mass

Density and Volume Conversion

Worked Check

Engineering Comment

Reported Diversion and Accepted Recovery

Worked Check

Engineering Comment

Contamination Rate

Capture Efficiency

Collection Route Capacity

Throughput and Residence Time

Landfill Airspace Consumption

Worked Check

Engineering Comment

Leachate Water Balance

Leachate Pollutant Load

First-Order Landfill Gas Generation Screen

Worked Check

Engineering Comment

Gas Collection and Energy Recovery

Worked Check

Engineering Comment

Waste-to-Energy Net Energy

Equipment Availability

Risk Priority Number

Validation and Reconciliation Checks

Common Mistakes

Validity Limits

See also