A single, deep, literature-grade model of a subcritical binary (Organic Rankine Cycle) geothermal power plant — from working-fluid selection through cycle thermodynamics, evaporator pinch analysis, resource-coupled energy and exergy balances, evaporation-temperature optimization, the balance-of-plant that turns gross power into net-to-grid (parasitic fans and pumps, ambient-set condensing, seasonal output), off-design operation as the resource cools, cycle-fidelity layers (recuperation, pressure drops, the pinch/area trade-off) and advanced configurations (zeotropic mixtures with temperature glide, and transcritical cycles), and the two real-world constraints that bound binary plant design: silica scaling and reservoir thermal decline.
Built on CoolProp for equation-of-state property data, with SciPy for the root-finding and optimization.
Most teaching ORC scripts stop at a per-kilogram cycle efficiency. Real geothermal binary design is dominated by things a per-kg cycle never sees:
- the pinch inside the evaporator, which sits at the working-fluid bubble point rather than at either terminal, so a log-mean-ΔT check is not enough;
- the resource coupling that ties working-fluid flow to the brine stream and decides how much power the field can actually support;
- the parasitic loads and ambient heat sink that separate turbine gross power from net-to-grid, and make output breathe with the seasons;
- the off-design behaviour of fixed installed hardware as the resource cools, which differs from re-optimizing a fresh plant each year;
- the silica chemistry that sets a floor on how cold the brine may be reinjected;
- the thermal decline that erodes output over field life.
This package models all of them, and checks itself against published numbers and against first-law / second-law balance closure.
git clone https://github.com/khb-git/geothermal-orc.git
cd geothermal-orc
python -m venv .venv && source .venv/bin/activate # Windows: .venv\Scripts\activate
pip install -e ".[dev]"Requires Python 3.10+. Core dependencies: CoolProp, numpy, scipy,
matplotlib, pandas. The [dev] extra adds pytest, jupyter, and
nbconvert for the test suite and demo notebook.
from geothermal_orc import ORCCycle, GeothermalResource, optimize_evaporation_temperature
# A subcritical isobutane cycle, 120 C evaporation / 30 C condensation.
cyc = ORCCycle("Isobutane", T_evap_C=120.0, T_cond_C=30.0,
eta_pump=0.75, eta_turbine=0.80)
# Couple it to a 150 C brine at 100 kg/s; size the plant to a 5 K pinch.
res = cyc.solve_with_resource(m_brine=100.0, T_brine_in_C=150.0, pinch_evap=5.0)
print(res.summary())
print("energy residual:", res.energy_balance_residual) # ~1e-16
print("exergy residual:", res.exergy_balance_residual) # ~1e-13
# Find the evaporation temperature that maximizes net power for this resource.
resource = GeothermalResource(T_reservoir_C=150.0, mass_flow=100.0)
opt = optimize_evaporation_temperature("Isobutane", resource, T_cond_C=30.0)
print(f"optimum: {opt.T_evap_opt_C:.1f} C -> {opt.W_net_opt/1e6:.2f} MW")For deliverable power, the plant layer adds parasitics and an ambient-set heat
sink:
from geothermal_orc import evaluate_plant
pr = evaluate_plant("Isobutane", resource, ambient_C=10.0) # ~30 C condensing
print(f"gross {pr.W_gross/1e6:.2f} MW -> net-to-grid {pr.W_net_plant/1e6:.2f} MW "
f"({pr.net_gross_ratio*100:.0f}% of gross)")And the economics layer turns net power into a cost of electricity:
from geothermal_orc import levelized_cost
econ = levelized_cost("Isobutane", resource, ambient_C=10.0, T_evap_C=95.0)
print(f"LCOE {econ.lcoe:.0f} USD/MWh | {econ.specific_capex:,.0f} USD/kW "
f"| wells {econ.capex_wells/econ.capex_total*100:.0f}% of CAPEX")…and the finance layer turns that cost into an investment decision:
from geothermal_orc import project_cashflow, ProjectAssumptions, monte_carlo
pr = project_cashflow(econ, ProjectAssumptions(ppa_price=120.0))
print(f"NPV ${pr.npv/1e6:.1f}M | IRR {pr.irr*100:.0f}% | payback {pr.payback_yr:.0f} yr")
mc = monte_carlo(econ, ProjectAssumptions(ppa_price=110.0))
print(f"P(NPV>0) = {mc['p_npv_positive']*100:.0f}%")The full walkthrough — a fourteen-act story from "what is a binary plant" to a
design verdict, advanced cycles, the cost of a megawatt-hour, and whether to
build it, with the plant schematic, T–s and T–Q diagrams, an
exergy-destruction breakdown, the gross-to-net waterfall and seasonal output,
fluid screening, silica curves, a re-optimized-vs-fixed-hardware decline, the
recuperator/pressure-drop/pinch-area refinements, the zeotropic and transcritical
advanced cycles, the CAPEX breakdown and cost-optimal-vs-power-optimal pinch, and
the NPV/IRR and Monte-Carlo risk analysis, plus an interactive design explorer —
is in
notebooks/demo.ipynb (executed, with plots embedded).
Viewing it: GitHub renders the notebook with all plots inline; if its viewer ever hiccups (the occasional "An error occurred" page), the nbviewer badge above always renders it. To move the explorer's sliders, click Open in Colab and run all cells — Colab installs the package and gives you a live kernel.
| module | what it does |
|---|---|
thermo |
State wrapper over CoolProp; flow-exergy relative to a dead state; saturation/critical helpers. |
fluids |
14-fluid library with ASHRAE-34 safety, ODP, GWP100, and a wet/dry/isentropic classifier; environmental screen(). |
heat_exchanger |
LMTD, and counterflow_profile — a duty-swept T–Q profile that resolves the internal pinch through phase change. |
cycle |
ORCCycle: the four-point cycle (solve) and the resource-coupled plant with full energy/exergy balances (solve_with_resource); optional recuperator and heat-exchanger pressure drops. |
geothermal |
Fournier–Rowe silica solubility (amorphous & quartz), the quartz geothermometer, the reinjection-temperature floor, and a GeothermalResource with a thermal-decline model. |
optimization |
optimize_evaporation_temperature (net-power maximization under subcritical/pinch/silica constraints) and screen_fluids (multi-fluid ranking). |
plant |
Balance of plant: parasitic loads (air-cooled-condenser fans, brine pumping), ambient-set condensing, evaluate_plant (gross → net-to-grid), seasonal_performance, off-design operation (design_plant, off_design_operation, decline_curves), and the pinch_area_tradeoff. |
mixtures |
Zeotropic working-fluid mixtures with temperature glide: MixtureCycle (built on P-T/P-Q flashes since CoolProp lacks mixture P-H/P-S), glide helpers, and screen_compositions. |
transcritical |
TranscriticalCycle: supercritical heat addition (no evaporation plateau) with subcritical condensing, for resources whose hot end a subcritical fluid cannot reach. |
economics |
Techno-economics: Turton module costing of every component (CEPCI-updated), geothermal well costs, and levelized_cost → LCOE, plus pinch_lcoe_tradeoff (cost-optimal vs power-optimal design) and lcoe_sensitivity. |
finance |
Project finance and risk: a discounted-cash-flow model (project_cashflow → NPV, IRR, payback, break-even PPA) with optional debt, tax, and depreciation, and a monte_carlo layer that turns the point LCOE into a distribution and a probability of positive NPV. |
State-point numbering follows DiPippo (2016): 1 condenser outlet / pump inlet, 2 pump outlet, 3 evaporator outlet / turbine inlet, 4 turbine outlet / condenser inlet.
pytest -qThe suite is 156 tests and targets correctness rather than coverage theatre:
energy- and exergy-balance closure on resource-coupled solves, pinch behaviour
across phase change, silica-correlation values against the literature, the
classifier's wet/dry/isentropic verdicts, optimizer feasibility/ranking,
parasitic and off-design plant behaviour, recuperator/pressure-drop/mixture/
transcritical physics, techno-economic LCOE in the published range with the
right cost structure, the break-even-equals-LCOE finance identity, and a
test_benchmarks.py suite that pins headline numbers to published values.
Performance note:
solve_with_resourceprecomputes the (flow-independent) working-fluid side of the evaporator profile once and runs the pinch root-find over the brine side only, which keeps the optimizer and fluid screen fast without changing the full-resolution result.
This package is honest about what is validated versus what is merely plausible:
Hard validations (matched to published values):
- Amorphous-silica and quartz solubilities reproduce Fournier & Rowe (1977) to within a few mg/kg (e.g. amorphous ≈ 117 mg/kg at 25 °C vs. a literature 115–120; quartz ≈ 48.1 mg/kg at 100 °C vs. 48–52).
- The quartz geothermometer round-trips: 200 °C → 265 mg/kg → 201 °C.
- Energy and exergy balances on every resource-coupled solve close to machine precision (residuals ~1e-16 and ~1e-13).
- Wet/dry/isentropic fluid classes agree with the standard literature consensus (e.g. water/ammonia/R134a wet; isobutane/pentanes/R245fa dry; R1234yf/R1234ze(E) near-isentropic).
- Benchmarked against the ORC literature (
tests/test_benchmarks.py): subcritical thermal efficiency at 100 °C/30 °C lands at ~11–12% (the ~10% consensus of Saleh et al. 2007 and Su et al. 2018), ideal-cycle efficiency ~15%, and the 150 °C fluid screen tops out on isobutane/propane — matching Augustine et al. (NREL), who found isobutane optimal for 140–170 °C binary. - Advanced cycles preserve balance closure and match the literature direction: recuperated, pressure-drop, mixture, and transcritical solves all keep energy/exergy balances closed; zeotropic mixtures help low-enthalpy resources (~5% at 120 °C, per Heberle/Chys) and transcritical propane helps at 150 °C (~5%, per Astolfi), while neither beats a well-matched pure fluid where one already fits.
- Techno-economics in range: Turton module costing plus geothermal wells gives ~$90/MWh and ~$6,700/kW for the 150 °C base case (inside the published band for medium-temperature binary; Lazard/IRENA), with wells the dominant (~60%+) share of CAPEX.
- Finance reproduces the LCOE: under all-equity, no-tax, matching-discount assumptions the break-even PPA equals the Tier 3 LCOE to within rounding and the IRR at that price equals the discount rate — the cash-flow model is internally consistent with the cost model before debt, tax, escalation, and Monte-Carlo risk are layered on.
Plausibility checks (right physics, right ballpark — not matched to a named plant):
- Absolute net-to-grid power, utilization (second-law) efficiency, and brine outlet temperature fall within ranges DiPippo reports for comparable ~150 °C binary resources, but are not calibrated to a specific operating unit.
- Parasitic-load defaults (fan air-side ΔT and Δp, brine-loop pressure) are documented, site-independent starting points; a real project substitutes measured values.
- The off-design model uses a reduced Stodola + fixed-UA + part-load-turbine representation; the part-load curve is illustrative, not a specific machine map.
- Decline rates use the Snyder et al. (2017) averages (~0.5 %/yr binary, ~0.8 %/yr flash, predominantly linear); an individual field can differ.
The core cycle now spans subcritical and transcritical operation, pure fluids and zeotropic mixtures, with an optional recuperator, heat-exchanger pressure drops, a reduced balance-of-plant, off-design behaviour, a techno-economic LCOE layer, and a project-finance/risk layer. What it models:
- Subcritical and transcritical cycles; pure fluids and zeotropic mixtures (temperature glide); optional recuperator; heat-exchanger pressure drops; the pinch/area (UA) trade-off.
- Parasitics and ambient-set condensing (gross → net-to-grid), seasonal output, and fixed-hardware off-design decline.
- Techno-economics: component sizing and Turton module costing, geothermal well costs, LCOE, and the cost-optimal vs power-optimal design question (how much heat-exchanger area is worth buying).
- Project finance & risk: discounted cash flow with optional debt, tax and depreciation → NPV, IRR, payback, break-even PPA, and a Monte-Carlo distribution of LCOE/NPV with the probability of a positive return.
Deliberate simplifications that remain:
- First-order costing. Turton module costing with material/pressure factors held at a carbon-steel, low-pressure baseline; well count, well cost, O&M, and finance terms are documented, adjustable assumptions, not a bankable model.
- Monte-Carlo holds the plant design fixed. Uncertainty is propagated through the economic/financial drivers (PPA, well cost, capacity factor, cost of capital); resource-temperature uncertainty enters only through the deterministic sensitivities, not a re-solved thermodynamic sample.
- Reduced off-design. A Stodola swallowing law plus fixed UA and an illustrative part-load turbine curve, not a manufacturer's component map.
- Mixture comparison anchored on mean condensing temperature (a fair proxy); a full cooling-water-matched condenser with floating pressure is not yet built.
- Brine as pure water; calcite/CO₂/H₂S chemistry beyond silica is not modelled (binary's pressurized, no-flash operation does suppress calcite).
- Empirical decline; reservoir-scale thermal breakthrough is out of scope.
Roadmap status: parasitics, ambient/seasonal, and off-design (Tier 1), the fidelity layer — recuperation, pressure drops, mixtures, transcritical (Tier 2) — the techno-economic LCOE layer (Tier 3), and the project-finance/risk layer (Tier 4) are done; a fully cooling-water-matched condenser with floating condensing pressure, and Monte-Carlo over a re-solved thermodynamic model (resource-temperature uncertainty), are the natural next steps.
- R. DiPippo, Geothermal Power Plants: Principles, Applications, Case Studies and Environmental Impact, 4th ed., Butterworth-Heinemann, 2016.
- B. Saleh, G. Koglbauer, M. Wendland, J. Fischer, "Working fluids for low-temperature organic Rankine cycles," Energy 32 (2007) 1210–1221.
- R. O. Fournier, J. J. Rowe, "The solubility of amorphous silica in water at high temperatures and high pressures," American Mineralogist 62 (1977) 1052–1056.
- D. M. Snyder, K. F. Beckers, K. R. Young, "Update on geothermal direct-use and power-plant thermal decline," GRC Transactions 41 (2017).
- F. Heberle, D. Brüggemann, "Thermo-economic evaluation of organic Rankine cycles for geothermal power generation using zeotropic mixtures," Energies (2015) — glide-matching raises second-law efficiency for low-enthalpy resources.
- C. Augustine et al., "A comparison of geothermal binary cycle working fluids" (NREL), GRC Transactions — isobutane optimal for 140–170 °C subcritical binary resources.
- W. Su et al., "A limiting efficiency of subcritical Organic Rankine cycle under the constraint of working fluids," Energy (2018) — subcritical ORC thermal efficiency ~10%, below 50% of Carnot perfectness.
- R. Turton, R. C. Bailie, W. B. Whiting, J. A. Shaeiwitz, Analysis, Synthesis and Design of Chemical Processes, Prentice Hall — module-costing method and equipment cost correlations (USD 2001 basis, updated via CEPCI).
- F. Yang et al., "Thermo-economic optimization of organic Rankine cycle systems for geothermal power generation," Front. Energy Res. 8 (2020) 6 — finds recuperation economically unattractive (extra exchanger cost outweighs the gain) and transcritical cycles favoured, validating the Tier 2/3 findings.
- Lazard, Levelized Cost of Energy+, and IRENA, Renewable Power Generation Costs — geothermal LCOE benchmark (~$60–150/MWh for medium-temperature binary).
- W. Short, D. J. Packey, T. Holt, A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies, NREL/TP-462-5173 (1995) — LCOE, capital-recovery factor, and discounted-cash-flow conventions.
MIT — see LICENSE.