# 4NK Waste & Water - Complete Calculation Formulas Reference ## 1. Infrastructure Capacity Calculations ### 1.1 Daily Processing Capacity ``` Daily_processing_capacity (T/day) = Module_capacity (T) × Number_of_modules Daily_processing_capacity = 67T × 21 = 1,407T/day ``` ### 1.2 Water Content Calculation ``` Water_content (T) = Total_waste (T) × Water_percentage (%) Water_content = 67T × 75% = 50.25T water per module ``` ### 1.3 Total Containers ``` Total_containers = Number_of_modules × Containers_per_module Total_containers = 21 × 4 = 84 containers ``` ## 2. Processing Time Calculations ### 2.1 Mesophilic Digestion Duration ``` Mesophilic_duration (days) = Hygienization_duration + Additional_days Mesophilic_duration = 18 days + 3 days = 21 days ``` ### 2.2 Drying and Bioremediation Duration ``` Drying_bioremediation_duration (days) = Drying_duration + (Bioremediation_phases × Phase_duration) Drying_bioremediation_duration = 21 days + (3 phases × 21 days) = 84 days (variable) ``` ### 2.3 Thermophilic Digestion and Composting Duration ``` Thermophilic_composting_duration (days) = Thermophilic_duration + Composting_duration Thermophilic_composting_duration = 18 days + 3 days = 21 days ``` ### 2.4 Spirulina Cycle Duration ``` Spirulina_cycle_duration (hours) = 72 hours Spirulina_cycle_duration (days) = 72 / 24 = 3 days ``` ## 3. Methane Production Calculations ### 3.1 Dry Matter Calculation (VS - Volatile Solids) ``` Dry_matter (kg VS) = Waste_quantity (kg) × (1 - Water_percentage (%)) Dry_matter_percentage (%) = 100% - Water_percentage (%) ``` **Example**: - Waste quantity: 67,000 kg (67T) - Water percentage: 75% - Dry matter: 67,000 × (1 - 0.75) = 67,000 × 0.25 = 16,750 kg VS - Dry matter percentage: 100% - 75% = 25% ### 3.2 Methane Production from BMP ``` Methane_production (m³/day) = BMP (Nm³ CH₄/kg VS) × Dry_matter (kg VS/day) × Efficiency_factor ``` **Parameters**: - BMP: Biochemical Methane Potential (Nm³ CH₄/kg VS) - varies by waste type - Dry_matter: Calculated from waste quantity and water percentage - Efficiency_factor: Processing efficiency (typically 0.7-0.9) ### 3.3 Origin Units to Methane Conversion ``` Methane_per_1000m³ = Number_of_origin_units × Conversion_factor ``` **Parameter**: Number of origin units to produce 1000m³ of methane (varies by waste origin) ## 4. Gas Production Calculations ### 4.1 Biogas Composition ``` Biogas_total (m³/day) = Methane_production (m³/day) / Methane_percentage_in_biogas ``` **Biogas Composition**: - Methane (CH₄): 40% of biogas - CO₂: 60% of biogas ### 4.2 Methane from Biogas ``` Methane_production (m³/day) = Biogas_total (m³/day) × 0.40 ``` ### 4.3 CO₂ Production from Biogas ``` CO2_production (m³/day) = Biogas_total (m³/day) × 0.60 ``` **Alternative calculation**: ``` CO2_production (m³/day) = Methane_production (m³/day) × (0.60 / 0.40) CO2_production (m³/day) = Methane_production (m³/day) × 1.5 ``` ### 4.4 Total Gas Production ``` Total_gas_production (m³/day) = Methane_production (m³/day) + CO2_production (m³/day) Total_gas_production (m³/day) = Biogas_total (m³/day) ``` ## 5. Energy Calculations ### 5.1 Heat Energy from Biogas ``` Heat_energy (kJ/day) = Methane_production (m³/day) × Methane_energy_content (kJ/m³) × Combustion_efficiency ``` **Parameters**: - Methane_energy_content: 35,800 kJ/m³ (lower heating value) - Combustion_efficiency: 0.90 (90%) ### 5.2 Heat Energy Conversion to kWh ``` Heat_energy (kW.h/day) = Heat_energy (kJ/day) / 3600 ``` ### 5.3 Electrical Power from Biogas Generator ``` Electrical_power_biogas (kW) = Methane_production (m³/day) × Methane_energy_content (kJ/m³) × Electrical_efficiency / (3600 × 24) ``` **Parameter**: Electrical_efficiency: 0.40 (40% for combined heat and power systems) ### 5.4 Electrical Power from Solar Panels ``` Electrical_power_solar (kW) = Solar_panel_surface (m²) × Solar_irradiance (kW/m²) × Panel_efficiency ``` **Parameters**: - Solar_irradiance: Varies by location and season (typically 0.1-1.0 kW/m²) - Panel_efficiency: Typically 0.15-0.22 ### 5.5 Total Electrical Power ``` Total_electrical_power (kW) = Electrical_power_biogas (kW) + Electrical_power_solar (kW) ``` ### 5.6 Module Electrical Consumption ``` Module_electrical_consumption (kW) = Sum of all equipment consumption: - 1 pump (méthanisation): 0.5 kW - 1 séchoir du gaz: 2.0 kW - 1 compresseur: 3.0 kW - 1 lampe UV-C × 12m: 0.3 kW - 5 racloires électriques × 3: 1.5 kW - 1 pompe (spiruline): 0.5 kW - 5 × 12m LED de culture: 0.6 kW - 3 pompes eau: 1.5 kW - Capteurs: 0.1 kW - 1 serveur: 0.2 kW - 1 borne Starlink: 0.1 kW - 1 tableau élec: 0.1 kW - 1 convertisseur panneaux solaires: 0.1 kW Total per module: ~10.5 kW ``` ``` Total_modules_consumption (kW) = Module_electrical_consumption (kW) × Number_of_modules Total_modules_consumption (kW) = 10.5 kW × Number_of_modules ``` ### 5.7 Net Electrical Power ``` Net_electrical_power (kW) = Total_electrical_power (kW) - Total_modules_consumption (kW) ``` ## 6. Bitcoin Mining Calculations ### 6.1 Number of Flex Miners ``` Number_of_flex_miners = Available_electrical_power (kW) / Power_per_miner (kW) Number_of_flex_miners = Available_electrical_power (kW) / 2 kW ``` ### 6.2 Bitcoin Production ``` Bitcoins_BTC_per_year = 79.2 × 0.0001525 / flex_miner ``` **Formula**: `BTC/year = 79.2 × 0.0001525 / number_of_flex_miners` **Parameters**: - 79.2: Constant factor - 0.0001525: BTC per flex miner factor - flex_miner: Number of 4NK flex miners (2kW each) ### 6.3 Bitcoin Value ``` Bitcoin_value (€) = Bitcoin_quantity (BTC) × Bitcoin_price (€/BTC) ``` **Parameter**: Bitcoin_price = 100,000 €/BTC ## 7. Material Output Calculations ### 7.1 Water Output ``` Water_output (t/day) = Water_input (t/day) - Water_consumed_in_processes (t/day) + Water_from_spirulina (t/day) ``` **Water Input**: ``` Water_input (t/day) = Waste_quantity (t/day) × Water_percentage (%) Water_input = 67T × 75% = 50.25T water per module per day ``` ### 7.2 Fertilizer Production ``` Fertilizer_output (t/day) = Composting_output (t/day) × Fertilizer_yield_factor ``` **Parameter**: Fertilizer_yield_factor: 1.0 (100% - all compost becomes standardized fertilizer) ## 8. Valorization Calculations ### 8.1 Waste Treatment Valorization ``` Waste_treatment_valorization (€/year) = Waste_quantity (t/year) × 100 €/t ``` **Parameter**: 100 €/t ### 8.2 Fertilizer Valorization ``` Fertilizer_valorization (€/year) = Fertilizer_quantity (t/year) × 215 €/t ``` **Parameter**: 215 €/t ### 8.3 Heat Valorization ``` Heat_valorization (€/year) = Heat_quantity (t/year) × 0.12 €/t ``` **Parameter**: 0.12 €/t ### 8.4 Carbon Equivalent - Burned Methane (CH₄) ``` CH4_carbon_valorization (€/year) = CH4_quantity (tCO₂e/year) × 172 €/tCO₂e ``` **Parameters**: - 630 €/tC ≈ 172 €/tCO₂e - Conversion: 1 tC = 3.67 tCO₂e - Formula: `172 = 630 / 3.67` ### 8.5 Carbon Equivalent - Sequestered CO₂ ``` CO2_carbon_valorization (€/year) = CO2_sequestered (tCO₂e/year) × 27 €/tCO₂e ``` **Parameters**: - 100 €/tC ≈ 27 €/tCO₂e - Conversion: 1 tC = 3.67 tCO₂e - Formula: `27 = 100 / 3.67` ### 8.6 Carbon Equivalent - Avoided Electricity Consumption ``` Energy_carbon_valorization (€/year) = Electricity_avoided (kW/year) × 0.12 €/kW ``` **Parameter**: 0.12 €/kW ### 8.7 Land Valorization (Brownfield) ``` Land_valorization (€) = Brownfield_area (m²) × Valorization_rate (€/m²) ``` **Parameter**: 4000 m² brownfield (valorization rate configurable) ## 9. Financial Calculations ### 9.1 Total Revenues ``` Total_Revenues (€/year) = Sum of all revenue items: - Raw_rental - Biological_waste_treatment_service - Bitcoin_management_service - Provision_of_standardized_fertilizers_service - Provision_of_waste_heat_service - Provision_of_carbon_credit_indices_service - Brownfield_redevelopment_service - Transport_service - Commercial_partnerships - Other_revenues ``` ### 9.2 Total Variable Costs ``` Total_Variable_Costs (€/year) = Sum of all variable cost items: - Rental_and_services - Commissions_intermediaries_import - Other_variable_costs - Transport ``` ### 9.3 Gross Margin ``` Gross_Margin (€/year) = Total_Revenues (€/year) - Total_Variable_Costs (€/year) ``` ### 9.4 Total Fixed Costs (OPEX) ``` Total_Fixed_Costs (€/year) = Sum of all fixed cost items: - Salaries_and_social_charges - Marketing_communication_expenses - R&D_product_development - Administrative_legal_fees - Other_general_expenses ``` ### 9.5 Operating Result (EBITDA) ``` EBITDA (€/year) = Gross_Margin (€/year) - Total_Fixed_Costs (€/year) ``` ### 9.6 Cash Flow ``` Cash_Flow (€/year) = EBITDA (€/year) - Non_cash_adjustments (€/year) - Working_capital_changes (€/year) ``` ### 9.7 Total Investments (CAPEX) ``` Total_Investments (€) = Sum of all investment items: - Equipment_machinery - Technology_development - Patents_IP ``` ### 9.8 Funding Need ``` Funding_Need (€) = Total_Investments (€) - Available_Cash (€) - Cash_Flow (€) ``` ### 9.9 Use of Raised Funds ``` Total_Use_of_Funds (€) = Sum of all fund utilization items: - Product_development_POC_MVP - Marketing_customer_acquisition - Team_strengthening_recruitment - Structure_administrative_fees ``` ## 10. Key Performance Indicators (KPIs) ### 10.1 Customer Acquisition Cost (CAC) ``` CAC (€) = Marketing_Costs (€) / Number_of_New_Customers ``` ### 10.2 Lifetime Value (LTV) ``` LTV (€) = Average_Revenue_per_Customer (€) × Average_Customer_Lifespan (years) ``` ### 10.3 Break-even Point ``` Break_even_days = Fixed_Costs (€) / (Daily_Revenue (€/day) - Daily_Variable_Costs (€/day)) ``` ### 10.4 Break-even Point (Alternative) ``` Break_even_days = Fixed_Costs (€) / Daily_Gross_Margin (€/day) ``` ## 11. Service Pricing Calculations ### 11.1 Service Pricing per Module per Year ``` Service_price_per_module_per_year (€) = Base_price (€) × Module_multiplier ``` ### 11.2 Service Pricing over 10 Years ``` Service_price_10_years (€) = Service_price_per_module_per_year (€) × Number_of_modules × 10 ``` ### 11.3 First Year Prototype Pricing ``` First_year_price (€) = Service_price_per_module_per_year (€) × Prototype_discount_factor ``` **Parameter**: Prototype_discount_factor: Typically 0.5-0.8 (50-80% of standard price) ## 12. Conversion Factors ### 12.1 Energy Conversions ``` 1 kW.h = 3600 kJ 1 kJ = 1/3600 kW.h ``` ### 12.2 Carbon Conversions ``` 1 tC (tonne of carbon) = 3.67 tCO₂e (tonnes of CO₂ equivalent) 1 tCO₂e = 1/3.67 tC ≈ 0.272 tC ``` ### 12.3 Time Conversions ``` 1 day = 24 hours 1 year = 365 days (or 366 for leap years) ``` ### 12.4 Mass Conversions ``` 1 tonne (t) = 1000 kg 1 kg = 0.001 t ``` ## 13. Processing Efficiency Factors ### 13.1 Anaerobic Digestion Efficiency ``` Methane_efficiency = Actual_methane_production / Theoretical_methane_production ``` **Typical range**: 0.70 - 0.90 (70-90%) ### 13.2 Electrical Conversion Efficiency ``` Electrical_efficiency = Electrical_power_output / Energy_input ``` **Typical range**: 0.35 - 0.45 (35-45% for CHP systems) ### 13.3 Solar Panel Efficiency ``` Solar_panel_efficiency = Electrical_power_output / (Solar_irradiance × Panel_area) ``` **Typical range**: 0.15 - 0.22 (15-22%) ## 14. Water Balance Calculations ### 14.1 Water Input from Waste ``` Water_input (t/day) = Waste_quantity (t/day) × Water_percentage (%) ``` ### 14.2 Water Consumption in Processes ``` Water_consumption (t/day) = Sum of water used in: - Mesophilic_digestion - Drying_process (evaporation) - Bioremediation - Thermophilic_digestion - Composting - Water wall cooling (evaporation) ``` ### 14.3 Water from Spirulina Cycle ``` Spirulina_cycle_duration = 21 days Spirulina_cycles_per_day = 1 / 21 = 0.0476 cycles/day Water_from_spirulina (t/day) = Spirulina_cycle_water_output (t/cycle) × Spirulina_cycles_per_day ``` **Spirulina Cycle Management**: - Spirulina culture: 21 days cycle - After 21 days: Water returns to thermophilic anaerobic digestion - Water output from spirulina: Depends on culture volume and evaporation ### 14.4 Water Evaporation ``` Water_evaporation (t/day) = Water_wall_surface (m²) × Evaporation_rate (m/day) × Water_density (t/m³) ``` **Parameters**: - Evaporation_rate: Depends on temperature, humidity, wind (typically 0.001-0.01 m/day) - Water_density: 1 t/m³ ### 14.5 Net Water Output ``` Net_water_output (t/day) = Water_input (t/day) - Water_consumption (t/day) - Water_evaporation (t/day) + Water_from_spirulina (t/day) ``` ## 15. Module and Container Calculations ### 15.1 Modules per Year ``` Modules_per_year = Total_modules / Project_duration (years) ``` ### 15.2 Containers per Module ``` Containers_per_module = 4 (fixed: mesophilic, drying/bioremediation, thermophilic/composting, water/spirulina) ``` ### 15.3 Total Container Capacity ``` Total_container_capacity = Number_of_modules × Containers_per_module × Container_capacity ``` ## Notes on Formula Display All formulas must be displayed with: - **Monospace font** (JetBrains Mono, Fira Code, or Courier New) - **Clear variable names** with units - **Parameter values** shown explicitly - **Calculation steps** when applicable - **Input values** used in the calculation - **Result** with appropriate units ## Formula Validation Rules - All input values must be positive (where applicable) - Division by zero must be prevented - Unit conversions must be consistent - Efficiency factors must be between 0 and 1 - Percentages must be between 0 and 100 - Time values must be positive - Mass/volume values must be positive