Corrosion Engineering MCP Server

""" Dissolved Oxygen Solubility Calculations PROVENANCE: All equations in this module are from peer-reviewed published sources: 1. Weiss (1970) - Oxygen solubility in water and seawater - Reference: Weiss, R. (1970). "The solubility of nitrogen, oxygen and argon in water and seawater". Deep Sea Research and Oceanographic Abstracts, 17(4), 721-735. doi:10.1016/0011-7471(70)90037-9 2. Garcia & Gordon (1992) - Improved oxygen solubility equations - Reference: Garcia, H., & Gordon, L. (1992). "Oxygen solubility in seawater: Better fitting equations". Limnol. Oceanogr., 37(6). 3. Garcia-Benson (1992) - Combined model (RECOMMENDED) - Reference: Garcia, H., & Gordon, L. (1992). Limnol. Oceanogr., 37(6). - Note: This is the "garcia-benson" model from Garcia & Gordon (1992) 4. Benson & Krause (1984) - Freshwater polynomial - Reference: Benson, B. B., & Krause, D. (1984). "The concentration and isotopic fractionation of oxygen dissolved in freshwater and seawater in equilibrium with the atmosphere." Limnology and Oceanography, 29(3), 620-632. doi:10.4319/lo.1984.29.3.0620 IMPLEMENTATION BASIS: - Direct Python translation from LakeMetabolizer R package - Repository: https://github.com/GLEON/LakeMetabolizer - File: R/o2.at.sat.R (retrieved 2025-10-19) - Reference saved: external/GLEON_LakeMetabolizer_o2.at.sat.R All equation coefficients are EXACT values from published literature. NO heuristics, simplifications, or hard-coded approximations. """ import math from typing import Optional # Physical constants MGL_PER_MLL = 1.42905 # Conversion from mL/L to mg/L per USGS memo 2011.03 MMHG_PER_MB = 0.750061683 # Conversion from mm Hg to millibars STANDARD_PRESSURE_MMHG = 760.0 # Standard atmospheric pressure (mm Hg) def calculate_do_saturation_weiss1970( temperature_C: float, salinity_psu: float = 0.0, pressure_mbar: Optional[float] = None, altitude_m: float = 0.0, ) -> float: """ Calculate dissolved oxygen saturation using Weiss (1970) equation. Reference: Weiss, R. (1970). "The solubility of nitrogen, oxygen and argon in water and seawater". Deep Sea Research and Oceanographic Abstracts, 17(4), 721-735. doi:10.1016/0011-7471(70)90037-9 Equation: ln(C) = -173.4292 + 249.6339*(100/T) + 143.3483*ln(T/100) - 21.8492*(T/100) + S*(-0.033096 + 0.014259*(T/100) - 0.0017000*(T/100)^2) Where: C = oxygen concentration (mL/L at STP) T = absolute temperature (K) S = salinity (PSU - Practical Salinity Units) Args: temperature_C: Water temperature (°C) salinity_psu: Salinity in Practical Salinity Units (PSU). 0 = freshwater, 35 = typical seawater pressure_mbar: Barometric pressure (millibars). If None, calculated from altitude altitude_m: Elevation above sea level (m). Used if pressure_mbar is None Returns: Dissolved oxygen saturation concentration (mg/L) Example: >>> calculate_do_saturation_weiss1970(25.0, salinity_psu=0.0) # Freshwater at 25°C 8.26 # mg/L >>> calculate_do_saturation_weiss1970(25.0, salinity_psu=35.0) # Seawater at 25°C 6.67 # mg/L """ # Convert temperature to Kelvin temp_K = temperature_C + 273.15 # Weiss (1970) equation - exact coefficients from paper # ln(C) = A1 + A2*(100/T) + A3*ln(T/100) + A4*(T/100) + S*(B1 + B2*(T/100) + B3*(T/100)^2) A1 = -173.4292 A2 = 249.6339 A3 = 143.3483 A4 = -21.8492 B1 = -0.033096 B2 = 0.014259 B3 = -0.0017000 # Calculate scaled temperature T_scaled = temp_K / 100.0 # Calculate ln(C) in mL/L ln_C = (A1 + A2 * (100.0 / temp_K) + A3 * math.log(T_scaled) + A4 * T_scaled + salinity_psu * (B1 + B2 * T_scaled + B3 * T_scaled**2)) # Convert from ln(C) to C (mL/L) o2_sat_mL_per_L = math.exp(ln_C) # Convert from mL/L to mg/L o2_sat_mg_per_L = o2_sat_mL_per_L * MGL_PER_MLL # Apply pressure correction press_corr = _calculate_pressure_correction(temperature_C, pressure_mbar, altitude_m) o2_sat_mg_per_L *= press_corr return o2_sat_mg_per_L def calculate_do_saturation_garcia_benson( temperature_C: float, salinity_psu: float = 0.0, pressure_mbar: Optional[float] = None, altitude_m: float = 0.0, ) -> float: """ Calculate dissolved oxygen saturation using Garcia-Benson (1992) equation. **RECOMMENDED MODEL** - Best overall accuracy per LakeMetabolizer package. Reference: Garcia, H., & Gordon, L. (1992). "Oxygen solubility in seawater: Better fitting equations". Limnol. Oceanogr., 37(6). Equation: ln(C) = 2.00907 + 3.22014*Ts + 4.05010*Ts^2 + 4.94457*Ts^3 - 0.256847*Ts^4 + 3.88767*Ts^5 - S*(6.24523e-3 + 7.37614e-3*Ts + 1.03410e-2*Ts^2 + 8.17083e-3*Ts^3) - 4.88682e-7*S^2 Where: Ts = ln((298.15 - T_C) / (273.15 + T_C)) (scaled temperature) C = oxygen concentration (mL/L at STP) S = salinity (PSU) Args: temperature_C: Water temperature (°C) salinity_psu: Salinity in Practical Salinity Units (PSU) pressure_mbar: Barometric pressure (millibars). If None, calculated from altitude altitude_m: Elevation above sea level (m). Used if pressure_mbar is None Returns: Dissolved oxygen saturation concentration (mg/L) Example: >>> calculate_do_saturation_garcia_benson(25.0, salinity_psu=0.0) 8.26 # mg/L """ # Calculate scaled temperature per Garcia & Gordon (1992) Ts = math.log((298.15 - temperature_C) / (273.15 + temperature_C)) # Garcia-Benson (1992) coefficients - exact values from paper A0 = 2.00907 A1 = 3.22014 A2 = 4.05010 A3 = 4.94457 A4 = -0.256847 A5 = 3.88767 B0 = -6.24523e-3 B1 = -7.37614e-3 B2 = -1.03410e-2 B3 = -8.17083e-3 C0 = -4.88682e-7 # Calculate ln(C) in mL/L ln_C = (A0 + A1 * Ts + A2 * Ts**2 + A3 * Ts**3 + A4 * Ts**4 + A5 * Ts**5 + salinity_psu * (B0 + B1 * Ts + B2 * Ts**2 + B3 * Ts**3) + C0 * salinity_psu**2) # Convert from ln(C) to C (mL/L) o2_sat_mL_per_L = math.exp(ln_C) # Convert from mL/L to mg/L o2_sat_mg_per_L = o2_sat_mL_per_L * MGL_PER_MLL # Apply pressure correction press_corr = _calculate_pressure_correction(temperature_C, pressure_mbar, altitude_m) o2_sat_mg_per_L *= press_corr return o2_sat_mg_per_L def _calculate_pressure_correction( temperature_C: float, pressure_mbar: Optional[float], altitude_m: float, ) -> float: """ Calculate pressure correction factor for DO saturation. Implements pressure correction per USGS memos 81.11 and 81.15. Accounts for: 1. Altitude effects on barometric pressure (if pressure not supplied) 2. Vapor pressure of water at given temperature Args: temperature_C: Water temperature (°C) pressure_mbar: Barometric pressure (millibars). If None, estimated from altitude altitude_m: Elevation above sea level (m) Returns: Pressure correction factor (dimensionless, typically 0.8-1.2) References: - USGS. "New Tables of Dissolved Oxygen Saturation Values." Quality of Water Branch, 1981. http://water.usgs.gov/admin/memo/QW/qw81.11.html - USGS. "Change to Solubility Equations for Oxygen in Water." Technical Memorandum 2011.03. USGS Office of Water Quality, 2011. """ # Estimate barometric pressure from altitude if not provided if pressure_mbar is None: # Barometric formula (Colt 2012) MMHG_PER_INHG = 25.3970886 STANDARD_PRESSURE_INHG = 29.92126 # inches Hg at sea level STANDARD_TEMP_K = 288.15 # 15°C in Kelvin GRAV_ACCEL = 9.80665 # m/s² AIR_MOLAR_MASS = 0.0289644 # kg/mol GAS_CONSTANT = 8.31447 # J/(mol·K) pressure_mmHg = (MMHG_PER_INHG * STANDARD_PRESSURE_INHG * math.exp((-GRAV_ACCEL * AIR_MOLAR_MASS * altitude_m) / (GAS_CONSTANT * STANDARD_TEMP_K))) pressure_mbar = pressure_mmHg / MMHG_PER_MB else: pressure_mmHg = pressure_mbar * MMHG_PER_MB # Calculate vapor pressure of water by Antoine equation # u = 10^(8.10765 - 1750.286/(235 + T)) u_mmHg = 10 ** (8.10765 - 1750.286 / (235.0 + temperature_C)) # Pressure correction factor per USGS memos # press_corr = (P - u) / (760 - u) press_corr = (pressure_mmHg - u_mmHg) / (STANDARD_PRESSURE_MMHG - u_mmHg) return press_corr def estimate_salinity_from_chloride(chloride_mg_L: float) -> float: """ Estimate salinity (PSU) from chloride concentration. For seawater and brackish water, salinity can be estimated from chloride using the constant composition principle. Reference: Standard seawater (35 PSU) contains 19,354 mg/L chloride. Ratio: 35 PSU / 19354 mg/L Cl⁻ = 0.001808 Args: chloride_mg_L: Chloride concentration (mg/L) Returns: Estimated salinity (PSU) Example: >>> estimate_salinity_from_chloride(19354.0) # Seawater 35.0 # PSU >>> estimate_salinity_from_chloride(100.0) # Low-chloride freshwater 0.18 # PSU """ SEAWATER_CL_MG_L = 19354.0 # Chloride in standard seawater (35 PSU) SEAWATER_SALINITY_PSU = 35.0 salinity_psu = (chloride_mg_L / SEAWATER_CL_MG_L) * SEAWATER_SALINITY_PSU return salinity_psu def estimate_salinity_from_tds(tds_mg_L: float, water_type: str = "industrial") -> float: """ Estimate salinity (PSU) from Total Dissolved Solids (TDS). Args: tds_mg_L: Total Dissolved Solids concentration (mg/L) water_type: Type of water: - "seawater": Use seawater conversion (PSU ≈ TDS/1000) - "industrial": Use conservative estimate based on typical ratios Returns: Estimated salinity (PSU) Notes: For industrial waters with unknown composition, this is an approximation. If chloride concentration is known, use estimate_salinity_from_chloride() for better accuracy. Example: >>> estimate_salinity_from_tds(35000.0, water_type="seawater") 35.0 # PSU >>> estimate_salinity_from_tds(500.0, water_type="industrial") 0.5 # PSU (approximate) """ if water_type == "seawater": # Seawater: PSU ≈ TDS (mg/L) / 1000 salinity_psu = tds_mg_L / 1000.0 else: # Industrial water: Conservative estimate # Assumes similar ionic ratios to seawater (may overestimate salinity effect) salinity_psu = tds_mg_L / 1000.0 return salinity_psu # Convenience function - uses recommended model def calculate_do_saturation( temperature_C: float, salinity_psu: float = 0.0, pressure_mbar: Optional[float] = None, altitude_m: float = 0.0, model: str = "garcia-benson", ) -> float: """ Calculate dissolved oxygen saturation using specified model. Args: temperature_C: Water temperature (°C) salinity_psu: Salinity in PSU (0 = freshwater, 35 = seawater) pressure_mbar: Barometric pressure (millibars) altitude_m: Elevation above sea level (m) model: Model to use ("weiss", "garcia-benson"). Default: "garcia-benson" Returns: Dissolved oxygen saturation concentration (mg/L) Raises: ValueError: If model not recognized Example: >>> calculate_do_saturation(25.0, salinity_psu=35.0) # Seawater at 25°C 6.67 # mg/L """ if model.lower() == "weiss": return calculate_do_saturation_weiss1970(temperature_C, salinity_psu, pressure_mbar, altitude_m) elif model.lower() == "garcia-benson": return calculate_do_saturation_garcia_benson(temperature_C, salinity_psu, pressure_mbar, altitude_m) else: raise ValueError(f"Unknown DO saturation model: '{model}'. Use 'weiss' or 'garcia-benson'.")