Reference · v0.9

Methodology

Every equation, parameter, and assumption powering the four feasibility calculators. Built so investors, engineers, and regulators can audit any number on any tab back to its source.

EPA LandGEM v3.02Arps hyperbolicGWP-100 = 28×Subpart WNPV / IRR

§ 01

Overview & scope

The MCF.DIGITAL feasibility calculators model a single project site converting waste methane (landfill gas, associated petroleum gas, anaerobic digester biogas, or coal-mine methane) into Bitcoin via on-site reciprocating-engine generators driving ASIC miners. Each calculator runs the same six-tab pipeline:

Gas spec → engine derate → net kW → miner count → hashrate.
Year-by-year flow projection (decline curve).
Methane abated → tCO₂e/yr.
Carbon-credit revenue (decline-aware NPV).
Mining revenue (hashprice × hashrate × uptime).
Deal structure (capex, opex, royalty).

Out of scope

No grid-export modeling, no CHP heat sales, no monte-carlo on hashprice or BTC, no portfolio rollup across sites, no FX risk, no curtailment / interruptibility modeling. Hashprice is held flat through the project horizon (sensitivity analysis is on the roadmap).

§ 02

Units & conventions

Gas flow	scfm (standard ft³/min) at 60 °F, 14.7 psia
Volumetric conversion	1 scfm ≈ 14,884 m³/yr
Methane content	vol-% CH₄ at the wellhead / engine inlet
Mass	Mg (metric tonnes) — never short tons
Energy	kW (electrical, after derate)
GHG basis	GWP-100 = 28× for CH₄ (IPCC AR5, WG1 Ch. 8)
Currency	USD, nominal (not inflation-adjusted)
Discount rate	10% real default; user-tunable 0–25%
Project horizon	20 years default; range 5–30

All conversions use NIST-standard factors. Energy content is reported on an LHV basis (the convention for reciprocating engine specs published by Caterpillar, Waukesha, Jenbacher, and MWM). HHV-based vendor sheets are converted on read.

§ 03

Tab 1 — Gas-to-power

3.1 Energy content of fuel gas

\text{BTU/scf} = 1{,}012 \cdot \frac{\%\text{CH}_4}{100}

1,012 BTU/scf: LHV of pure methane at standard conditions
CH₄ %: User-entered methane fraction at engine inlet

Other combustibles (C₂H₆, etc.) are negligible for the four feedstocks modeled and are folded into the methane fraction for simplicity. For >5% non-methane combustibles, increase CH₄ % to compensate.

3.2 Gross electrical output

kW_{\text{gross}} = \frac{\text{scfm} \cdot \text{BTU/scf} \cdot 60 \cdot \eta_{\text{elec}}}{3{,}412}

η_elec: Engine electrical efficiency (default 38% LHV — typical for 1–4 MW spark-ignition gen-sets)
3,412: BTU/h per kW conversion

3.3 Derate stack

kW_{\text{net}} = kW_{\text{gross}} \cdot (1 - d_{\text{alt}}) \cdot (1 - d_{\text{amb}}) \cdot (1 - d_{\text{H}_2\text{S}}) \cdot (1 - d_{\text{silox}}) - P_{\text{parasitic}}

d_alt: 3% per 1,000 ft above 500 ft elevation
d_amb: 1% per 10 °F above 77 °F intake air
d_H₂S: Step penalty above 500 ppm (amine-treatment capex add)
d_silox: Step penalty above 5 mg/Nm³ (carbon-bed scrubber capex add)
P_parasitic: Compressor + chiller + miner-room HVAC; default 8% of net

3.4 Mining capacity

n_{\text{miners}} = \left\lfloor \frac{kW_{\text{net}}}{kW_{\text{per-miner}}} \right\rfloor

kW_per-miner: Antminer S19 XP: 3.0 kW @ 140 TH/s default

Hashrate scales linearly with miner count. Mixed fleets are not modeled — pick the modal miner.

§ 04

Tab 2 — Decline curves

Three decline models cover the four sources. All return a unitless multiplier rebased to year 1 = 1.0, which then drives every downstream tab.

4.1 LandGEM v3.02 (landfill)

Q(t) = \sum_{i} k \cdot L_0 \cdot M_i \cdot e^{-k(t - i)}

Q(t): Methane generation at year t (m³ CH₄/yr)
k: First-order decay constant (1/yr) — 0.02 arid, 0.05 conventional, 0.7 wet
L₀: Methane potential (m³ CH₄/Mg waste) — 96 (inventory) to 170 (CAA)
M_i: Waste accepted in year i (Mg)
t − i: Age of cohort i (yrs)

We don't ask for waste-acceptance history. We back-solve an implied flat M from your current measured wellhead flow, then forward-decay each cohort. EPA defaults shipped as presets.

4.2 Arps hyperbolic (flare gas, CMM)

q(t) = \frac{q_i}{(1 + b \cdot D_i \cdot t)^{1/b}}

q_i: Initial rate (year 1, normalized to 1.0)
D_i: Initial nominal annual decline (1/yr) — APG 25%, CMM 15%
b: Hyperbolic exponent — 0 = exponential, 0.5 = typical Arps, 1 = harmonic
terminal: Floor decline; switches to exponential at this rate (APG 5%, CMM 3%)

Industry-standard 'Arps with terminal switch' to avoid the unphysical fat tail of pure hyperbolic decline at long horizons.

4.3 Flat-with-trend (biogas)

q(t) = q_1 \cdot (1 + g)^{t - 1}

g: Annual feedstock growth/decline (1/yr); default 0%, bounded ±5%

Anaerobic digesters are steady-state — output tracks influent feedstock volume. Use g > 0 for a growing herd or expanding intake; g < 0 for a contracting operation.

§ 05

Tab 3 — Emissions & abatement

5.1 Methane mass flow

\text{kg CH}_4/\text{yr} = \text{scfm} \cdot 60 \cdot 8{,}760 \cdot \rho_{\text{CH}_4} \cdot \frac{\%\text{CH}_4}{100}

ρ_CH₄: 0.6556 kg/m³ at standard conditions
8,760: Hours per year (uptime applied separately for net abatement)

5.2 CO₂-equivalent abatement

\text{tCO}_2\text{e/yr} = \frac{\text{kg CH}_4/\text{yr}}{1{,}000} \cdot \text{GWP}_{100} \cdot (1 - \varepsilon_{\text{baseline}})

GWP_100: 28 (IPCC AR5, AR6 raised this to 27.9 — kept at 28 for parity with most registries)
ε_baseline: Counterfactual destruction efficiency: vented = 0%, flared = 98%

If the baseline is an existing flare (98% destruction efficient), abatement credit is only the marginal 2% plus the displaced grid emissions. Vented sources (open landfill cells, unflared CMM) get the full GWP credit.

§ 06

Tab 4 — Carbon credits

Carbon revenue is the most uncertain line in the stack. Voluntary-market prices for methane abatement have ranged from $3/t (over-the-counter ARB-pre-compliance) to $40/t (high-quality VCS+CCB). Compliance markets (CCA, RGGI) trade $20–$90/t. The calculator defaults to $15/t — a conservative voluntary midpoint — and is fully tunable.

6.1 Discounted carbon NPV

\text{NPV} = \sum_{t=1}^{N} \frac{\text{tCO}_2\text{e}_t \cdot P_{\text{credit}} \cdot (1 - h)}{(1 + r)^t}

tCO₂e_t: Decline-adjusted annual abatement at year t
P_credit: User-tunable credit price ($/t)
h: Verification haircut + buffer-pool contribution (default 15%)
r: Discount rate (default 10%)
N: Project horizon (default 20 yr)

The 15% haircut accounts for issuance lag (registries take 6–18 months), validation/verification cost, and the mandatory buffer pool that most methodologies require to insure against reversal.

§ 07

Tab 5 — Revenue

7.1 Mining revenue (annualized)

\$/\text{yr}_{\text{mining}} = \text{TH/s} \cdot \text{hashprice} \cdot 365 \cdot u \cdot (1 - f_{\text{pool}})

TH/s: Total fleet hashrate from §3.4
hashprice: $/TH/day — user input (current ~$50/TH/day @ $95k BTC)
u: Uptime fraction (default 95% — reciprocating-engine industry standard)
f_pool: Pool fee (default 2%)

7.2 Total revenue stack

\$/\text{yr}_{\text{total}} = \$/\text{yr}_{\text{mining}} + \$/\text{yr}_{\text{carbon}}

The lifetime-revenue chart in the Revenue tab shows year-by-year totals using the decline multiplier from §4. Year-1 numbers anchor; subsequent years scale by q(t)/q(1).

§ 08

Tab 6 — Deal structure

Capex line items (defaults reflect 2024-2025 EPC quotes for 1–4 MW skid-mounted installations):

Gen-set + balance of plant	$1,200/kW installed
Gas treatment (H₂S + siloxane)	$80k–$300k step (gated by spec)
ASIC fleet	$25/TH (S19 XP MSRP, used market 2024)
Electrical infra + miner shed	$200/kW installed
Permitting + interconnection	$150k flat
Royalty to host	5–25% of mining + carbon revenue, post-opex

Opex covers O&M ($0.018/kWh), miner replacement at year 4 (sinking fund), gas treatment consumables, and overhead. Royalty is modeled as a top-line revenue share to keep the waterfall linear.

§ 09

IRR & payback

9.1 Internal rate of return

0 = \sum_{t=0}^{N} \frac{CF_t}{(1 + \text{IRR})^t}

CF_0: Negative — capex outlay at t=0
CF_t: Net cash flow year t (revenue − opex − royalty)

Solved via Newton-Raphson with 50-iteration cap, bracketed [-99%, 1000%]. Returns null if cash flows never turn positive.

9.2 Simple payback

T_{\text{simple}} = \min \left\{ t : \sum_{i=0}^{t} CF_i \geq 0 \right\}

9.3 Discounted payback

T_{\text{disc}} = \min \left\{ t : \sum_{i=0}^{t} \frac{CF_i}{(1 + r)^i} \geq 0 \right\}

Discounted payback is always ≥ simple payback. Both are linearly interpolated within the crossing year for sub-annual precision.

9.4 Sensitivity sweep (tornado chart)

The Revenue-tab tornado chart re-runs the IRR equation in §9.1 with each of {BTC price, hashprice, capex, decline rate} shocked to (1 − s) and (1 + s) of its current value in turn, all other inputs held at base. The shock magnitude s is user-controlled via the slider above the chart (default 20%, range 5–50%). The bar width equals the absolute IRR swing in percentage points (pp); rows are sorted by impact magnitude so the most influential driver sits on top.

BTC price & hashprice — both scale mining USD revenue linearly; cash flows in §9.1 are multiplied by 0.80 / 1.20.
Capex — the t=0 outlay CF₀ is multiplied by 0.80 / 1.20. Painted inverted (capex up ⇒ IRR down) so red always means "IRR-down".
Decline rate — the source-specific decay parameter is shocked: k for LandGEM, D_i for Arps, growth g for flat-with-trend. For biogas at g ≈ 0, we fall back to a ±2 pp shock so the bar isn't degenerate. The shocked decline curve is fed back through §4 → §7 → §9.1 to re-derive cash flows.

This is a one-at-a-time (OAT) local sensitivity — it does not capture interaction effects. For correlated swings (e.g. BTC × hashprice tend to co-move) treat the bars as upper bounds on isolated risk; the real combined swing is typically larger. To stress-test all four feedstocks simultaneously under the same shock, use the side-by-side compare page.

§ 10

Known limitations

Single-site only — no portfolio rollup or fleet-level optimization.
Hashprice held flat across the horizon. Use sensitivity sweeps manually until tornado charts ship.
BTC price held flat. Mining revenue is hashprice-driven, so this matters less than for HODL strategies.
No FX risk (USD-denominated throughout).
No curtailment, interruptibility, or seasonal flow variation. LandGEM and Arps both assume monotonic decline.
No tax treatment, depreciation schedules, or 45V/45Q credit modeling. Pre-tax economics only.
GWP-100 chosen for registry parity; switch to GWP-20 (84×) if your buyer requires it — not exposed in UI yet.

§ 11

Sources & citations

U.S. EPA (2005). Landfill Gas Emissions Model (LandGEM) Version 3.02 User's Guide. EPA-600/R-05/047.
Arps, J.J. (1945). Analysis of Decline Curves. Trans. AIME 160, 228–247.
IPCC (2014). Fifth Assessment Report (AR5), Working Group I, Chapter 8 — Anthropogenic and Natural Radiative Forcing.
U.S. EPA. Subpart W — Petroleum and Natural Gas Systems, 40 CFR Part 98.
U.S. EPA. AP-42, Chapter 2.4: Municipal Solid Waste Landfills.
Caterpillar / Waukesha / Jenbacher / MWM gen-set technical data sheets (2023–2024 editions).
Hashrate Index. Hashprice methodology and historical series.
Verra VCS Methodology VM0041, ACR Methodology for Coal Mine Methane (for buffer-pool and verification haircut conventions).

Spotted an error?

Methodology corrections are taken seriously — every equation on this page is open to challenge. Email hello@mcf.digital with a citation and we'll update.

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