OpenWQ

Biogeochemistry Engines

From empirical kinetics to thermodynamic equilibrium geochemistry
— flexible frameworks for any water quality application

NATIVE_BGC_FLEX

Reaction Network Paradigm

Each transformation is defined by four elements:

Consumed species — reactant being transformed
Produced species — product being created
Kinetics expression — rate formula
Parameters — rate constants, K_m, etc.

Expression Parser: Uses exprtk — any mathematical expression is valid!

    ┌────────┐   nitrification   ┌────────┐
    │  NH₄⁺  │ ───────────────▶ │  NO₃⁻  │
    └────────┘                   └────────┘
           Rate = k × [NH₄] × f(O₂) × f(T)


    ┌────────┐   denitrification ┌────────┐
    │  NO₃⁻  │ ───────────────▶ │   N₂   │
    └────────┘                   └────────┘
           Rate = k × [NO₃] × f(DOC) × g(O₂)

Supported Rate Laws

First-Order Kinetics

Rate = k × C

Monod / Michaelis-Menten

Rate = k_max × C / (K_m + C)

Temperature Correction (Q10)

Rate = k₂₀ × θ^(T-20) × C

Available Functions

Math	exp, log, sqrt, abs, pow
Trig	sin, cos, tan
Compare	min, max, clamp
Logic	if(cond, true, false)

Available Variables

T — Temperature (°C)
[species] — Any defined species
Host model variables

JSON Configuration

// Define chemical species
"CHEMICAL_SPECIES": {
    "list": {
        "1": "NO3_N",
        "2": "NH4_N",
        "3": "DOC",
        "4": "DO"
    },
    "BGC_GENERAL_MOBILE_SPECIES": ["NO3_N", "NH4_N", "DOC", "DO"]
}

// Define transformation
"CYCLING_FRAMEWORKS": {
    "NITROGEN_CYCLE": {
        "1": {
            "_name": "nitrification",
            "consumed": "NH4_N",
            "produced": "NO3_N",
            "kinetics": ["k_nitrif * NH4_N * (DO/(Km_DO+DO)) * 1.047^(T-20)", "mg-N/L/day"],
            "parameter_values": { "k_nitrif": 0.1, "Km_DO": 0.5 }
        }
    }
}

No recompilation needed! Change reactions by editing JSON files.

02

Thermodynamic Extension

Why Thermodynamics?

Traditional Kinetic Approach

Uses inhibition terms (K_i) to suppress reactions:

F_inhibit = K_i / (K_i + [O₂])

⚠️ Empirical — requires calibration of K_i

Nature's Reality

Microbes use electron acceptors in order of energy yield:

O₂ → most energy
NO₃⁻
Mn(IV), Fe(III)
SO₄²⁻
CO₂ → least energy

✓ The "redox ladder" — thermodynamically controlled

                    Solution: Add a thermodynamic potential factor (FT) that automatically enforces the redox sequence
                

The F_T Factor

Jin & Bethke (2003, 2007)

F_T = 1 − exp( −(ΔG_avail − ΔG_min) / (χ × R × T) )

Symbol	Description	Value
ΔG_avail	Free energy from reaction	Varies by reaction
ΔG_min	Min. for ATP synthesis	~45 kJ/mol
χ	Stoichiometric number	1-4
R	Gas constant	0.008314 kJ/mol·K

F_T Behavior

ΔG >> ΔG_min → F_T ≈ 1.0
ΔG ≈ ΔG_min → F_T ≈ 0.5
ΔG < ΔG_min → F_T → 0

The Redox Ladder

F_T automatically enforces electron acceptor sequence based on energy yield

O₂ Aerobic respiration ΔG° = −125 kJ/mol F_T ≈ 1.0

NO₃⁻ Denitrification ΔG° = −119 kJ/mol F_T ≈ 1.0

Mn(IV) Manganese reduction ΔG° = −95 kJ/mol F_T ≈ 1.0

Fe(III) Iron reduction ΔG° = −50 kJ/mol F_T ≈ 0.64

SO₄²⁻ Sulfate reduction ΔG° = −25 kJ/mol F_T → 0*

CO₂ Methanogenesis ΔG° = −20 kJ/mol F_T → 0*

* Requires concentration-dependent ΔG adjustment to proceed

Implementation

Simply append the F_T term to your kinetic expression — no code changes!

// Standard kinetic expression:
"kinetics": ["k_denit * NO3_N * (DOC/(Km+DOC)) * (Ki/(Ki+DO))"]

// With thermodynamic constraint (add F_T term):
"kinetics": [
    "k_denit * NO3_N * (DOC/(Km+DOC)) * (Ki/(Ki+DO)) * (1 - exp(-((119-45)/(2*0.008314*(T+273)))))"
]

// F_T breakdown:
//   119 = ΔG° for denitrification [kJ/mol]
//   45  = ΔG_min (ATP synthesis) [kJ/mol]
//   2   = χ (stoichiometric number)
//   0.008314 = R [kJ/mol·K]
//   T+273 = temperature in Kelvin

                    Advantage: ΔG° values are known from literature — reduces calibration parameters!
                

03

PHREEQC

Equilibrium Geochemistry

A different paradigm: compute speciation based on thermodynamic equilibrium

Law of Mass Action

K = [C]^c[D]^d / [A]^a[B]^b

Automatic speciation — N → NO₃⁻, NH₄⁺, N₂...
Mineral reactions — precipitation/dissolution
pe-based redox — electron activity

What PHREEQC Computes

Ion speciation & complexation
Saturation indices (SI)
pH, pe, alkalinity
Gas-water equilibria
Mineral saturation states

Database: 100+ minerals, extensive thermodynamic data (USGS phreeqc.dat)

OpenWQ-PHREEQC Integration

┌──────────────────────────────────────────────────────────────────────────┐
│                          Each Timestep                                    │
├──────────────────────────────────────────────────────────────────────────┤
│                                                                           │
│  ┌─────────────────┐           ┌─────────────────┐                        │
│  │     OpenWQ      │  Convert  │    PhreeqcRM    │                        │
│  │  chemass [g]    │──────────▶│  conc [mol/kgw] │                        │
│  │  T, volume      │   Units   │  T, P, volume   │                        │
│  └─────────────────┘           └────────┬────────┘                        │
│                                         │                                 │
│                                         ▼                                 │
│                              ┌─────────────────────┐                      │
│                              │    RunCells()       │                      │
│                              │  • Equilibrate      │                      │
│                              │  • React            │                      │
│                              │  • Speciate         │                      │
│                              └────────┬────────────┘                      │
│                                       │                                   │
│  ┌─────────────────┐           ┌──────▼──────────┐                        │
│  │     OpenWQ      │◀──────────│    PhreeqcRM    │                        │
│  │ Δmass = new-old │  Convert  │  updated conc   │                        │
│  └─────────────────┘   Units   └─────────────────┘                        │
└──────────────────────────────────────────────────────────────────────────┘

PHREEQC Input (.pqi)

SOLUTION 1  Surface Water
    temp      20.0
    pH        7.5
    pe        12.0     # Redox (high=oxic)
    units     mg/L

    # Elements (NOT species!)
    N(5)      5.0      # Nitrate
    N(-3)     0.2      # Ammonium
    Ca        40.0
    C(4)      100 as HCO3

EQUILIBRIUM_PHASES 1
    O2(g)     -0.7  10.0
    Calcite   0.0   10.0

Key Blocks

SOLUTION	Initial chemistry
EQUILIBRIUM_PHASES	Minerals/gases
KINETICS	User kinetics (optional)
RATES	Rate expressions

                            Important: Use element names (Ca, N, S), not species (Ca²⁺, NO₃⁻). PHREEQC computes speciation!
                        

Comparison

Feature	BGC_FLEX (Kinetic)	BGC_FLEX + F_T	PHREEQC
Approach	User-defined kinetics	Kinetics + ΔG constraint	Thermodynamic equilibrium
Speciation	Manual	Manual	Automatic
Minerals	Not supported	Not supported	Full database
Redox	Manual K_i terms	Automatic via F_T	Automatic via pe
Parameters	Many (calibrate)	Fewer (ΔG° known)	Fewest (database)
Best for	Watersheds, SWAT-style	Sediment diagenesis	Groundwater, AMD

When to Use Each Approach

BGC_FLEX (Kinetic)

Nutrient cycling in watersheds
SWAT, HYPE, INCA methods
Calibrating against obs.
Computational efficiency
Simple, transparent

Thermodynamic + F_T

Sediment diagenesis
Multiple electron acceptors
Redox ladder enforcement
Research applications
Reduce calibration params

PHREEQC

Detailed speciation needed
Mineral reactions matter
Acid mine drainage
Carbonate chemistry
pH calculation critical

Available Templates

Individual Chemicals

Nitrogen, Phosphorus, Carbon
Dissolved oxygen
Phytoplankton/Algae
Plant uptake
Emerging contaminants
Groundwater age
Sediment diagenesis
Wetland/BMP
Tile drainage
pH/Alkalinity

Thermodynamic Templates

Aerobic respiration, nitrification
Denitrification, anammox
Fe/Mn/SO₄ reduction
Methanogenesis
Full sediment diagenesis

Model Frameworks

SWAT — N & P soil
QUAL2E/2K — Stream WQ
HYPE — Nordic nutrients
WASP8 — Eutrophication

PHREEQC Templates

Major ions, N/P speciation
DO, Phyto, Plant uptake
Emerging contaminants
Groundwater age tracers
Sediment diagenesis
Wetland processing
Tile drainage
pH/Alkalinity

Summary

🧪 BGC_FLEX

Flexible kinetic expressions for any reaction. JSON-based, no recompilation.

⚡ Thermodynamic

F_T factor enforces redox ladder. Fewer parameters, more mechanistic.

⚗️ PHREEQC

Full equilibrium geochemistry. Automatic speciation and mineral reactions.

                    Choose the right tool for the job — all three approaches use the same OpenWQ framework
                

Thank You

Questions?

OpenWQ

Contents

NATIVE_BGC_FLEX

Reaction Network Paradigm

Supported Rate Laws

Available Functions

Available Variables

JSON Configuration

Thermodynamic Extension

Why Thermodynamics?

Traditional Kinetic Approach

Nature's Reality

The FT Factor

FT Behavior

The Redox Ladder

Implementation

PHREEQC

Equilibrium Geochemistry

What PHREEQC Computes

OpenWQ-PHREEQC Integration

PHREEQC Input (.pqi)

Key Blocks

Comparison

When to Use Each Approach

BGC_FLEX (Kinetic)

Thermodynamic + FT

PHREEQC

Available Templates

Individual Chemicals

Thermodynamic Templates

Model Frameworks

PHREEQC Templates

Summary

🧪 BGC_FLEX

⚡ Thermodynamic

⚗️ PHREEQC

Thank You

The F_T Factor

F_T Behavior

Thermodynamic + F_T