🧮♻️🍕 FROM FOOD WASTE TO FORMULAS

Where Trash Meets Math – A Smarter Way to Save the Planet!

🔍 What’s Cooking in the Lab? 👨‍🔬👩‍🔬

We're transforming everyday food waste into energy and value using a smart system driven by:

🍕 Dry Fermentation
🧪 Fractionation
🔥 Torrefaction

But here's the twist:
💡 It’s not just science.
🧠 It’s powered by pure math magic!

➊ 🔁 Dry Fermentation = Gas + Growth Models 💨📈

What happens?
Food waste breaks down in the absence of oxygen → produces biogas (mostly methane 🌿).

🔢 Key Equation:

B(t) = B_{\text{max}} \left(1 - e^{-kt} \right)

🧪 An exponential model to predict how fast biogas is produced over time.

📊 We use calculus and optimization to:

Maximize $B_{\text{max}}$ (total gas)
Choose the best $k$ (reaction speed)
Decide the optimal time $t$ for peak output!

➋ 🧫 Fractionation = Clean Cuts by Calculation ⚖️🔬

What happens?
The leftover slurry is split into 🔹 solids, 🔹 liquids, 🔹 gases.

🧮 Partition Math:

M_{\text{in}} = M_{\text{solid}} + M_{\text{liquid}} + M_{\text{gas}}

And for each nutrient or element:

P_i = \frac{C_{i,\text{phase}}}{C_{i,\text{total}}}

➡️ Used to track how much of each element goes where!

🔍 We apply linear algebra and flow matrices to optimize recovery.
🎯 Goal: Zero loss, full reuse!

➌ 🔥 Torrefaction = Heat + High-Energy Math ♨️⚡

What happens?
The solids are roasted at 250–300°C → converted into a clean-burning biofuel.

📐 Energy Modeling:

HHV = HHV_0 + aT + bM

Where:

$T$ = Temperature
$M$ = Time
$a, b$ = constants from regression

We also calculate:

EY = \frac{m_{\text{final}} \cdot HHV_{\text{final}}}{m_{\text{initial}} \cdot HHV_{\text{initial}}}

📈 Regression, thermodynamic modeling, and derivatives help us decide the perfect roast recipe for energy!

🔄 Math = The Mastermind Behind It All 🧠✨

We use:

✅ Differential Equations — to model time-based changes
✅ Multi-Objective Optimization — to balance gas, solids, and energy
✅ Statistical Modeling — for process prediction
✅ Matrix Algebra — for material tracking
✅ Python, MATLAB, R — to simulate the full system!