The backbone of this project is critical to get correct. There is an existing natural drainage valley that will be used to burry a Pumped Hydrogen Electrical Storage (PHES) pipes that will have dual purpose as a trout farm. The PHES system will be in conjunction with lithium battery storage. I had a little conversation with Grok and it gave me some useful information.
Got it—your ponds are set at **800 m³ each**, which is very close to the 809.4 m³ from the earlier oversized hybrid design. That gives us a solid starting point to refine the system, keeping the 60-ft (18.3-m) elevation delta, the 11.9 kWh/day Missoula home target, and the trout habitat goal. I’ll assume you still want solar to pump water and batteries to buffer, but we’ll optimize to reduce losses and complexity based on your last question. Let’s nail this down.
### Step 1: Hydro Energy Storage
Each pond holds 800 m³:
- Mass: \( m = 800 \cdot 1000 = 800,000 \, \text{kg} \).
- Energy: \( E = m \cdot g \cdot h \cdot \eta \)
\[ E = 800,000 \cdot 9.81 \cdot 18.3 \cdot 0.85 \approx 121,900,000 \, \text{J} = 121.9 \, \text{MJ} \]
\[ E = \frac{121.9 \times 10^6}{3,600,000} \approx 33.86 \, \text{kWh} \]
Total storage: **33.86 kWh**—nearly 3x the 11.9 kWh/day need, offering flexibility.
### Step 2: Daily Energy and Flow
To deliver 11.9 kWh/day (batteries or load):
- Ideal energy: 11.9 kWh = 42.84 MJ.
- Volume: \( V = \frac{E}{g \cdot h \cdot \eta \cdot \rho} = \frac{42.84 \times 10^6}{9.81 \cdot 18.3 \cdot 0.85 \cdot 1000} \approx 280.7 \, \text{m}^3 \).
- Over 24 hours: \( Q = \frac{280.7}{86,400} \approx 0.00325 \, \text{m}^3/\text{s} \) (3.25 L/s).
Using 280.7 m³ daily leaves ~519.3 m³ in each pond—stable for trout.
### Step 3: Solar Pumping Energy
Pump 280.7 m³/day against 18.3 m:
- Power: \( P = \frac{\rho \cdot g \cdot h \cdot Q}{\eta} = \frac{1000 \cdot 9.81 \cdot 18.3 \cdot 0.00325}{0.85} \approx 686 \, \text{W} \).
- Energy: \( E = 686 \cdot 86,400 \approx 59,250,000 \, \text{J} = 16.46 \, \text{kWh/day} \).
Solar input (80% efficiency):
\[ E_{\text{solar}} = \frac{16.46}{0.8} \approx 20.58 \, \text{kWh/day} \]
Missoula, 4.5 sun hours:
\[ P_{\text{solar}} = \frac{20.58}{4.5} \approx 4.57 \, \text{kW} \]
A **5 kW solar array** works (round up for reliability).
### Step 4: Battery Buffer
- Capacity: 15 kWh (covers 11.9 kWh + losses; 90% efficient, ~1.5 kWh lost).
- Hydro recharges 11.9 kWh/day at 0.5 kW (11.9 kWh ÷ 24 h = 0.496 kW).
### Step 5: Equipment
- **Turbine**: 0.5-1 kW, 3.25 L/s flow.
- **Pump**: 0.75-1 kW, 3.25 L/s.
- **Pipe**: For 0.00325 m³/s at 2 m/s:
\[ A = \frac{0.00325}{2} = 0.001625 \, \text{m}^2, \, D = 2 \sqrt{\frac{0.001625}{\pi}} \approx 0.0455 \, \text{m} \]
A **2-inch pipe** (5 cm) is fine.
### Step 6: Trout Habitat
- 800 m³/pond, cycling 280.7 m³/day, leaves ~519 m³ stable.
- Depth (e.g., 63 ft diameter, 4 ft deep = 403 m² × 2 m = 806 m³, close enough).
- ~20-40 trout/pond (10-20 m³/fish), viable with aeration if needed.
### Step 7: Losses and Complexity Check
- **Hydro**: 11.9 kWh output from 16.46 kWh input (~72% efficient).
- **Battery**: 11.9 kWh out, 13.2 kWh in (~90%).
- **Solar**: 20.58 kWh out, 25.7 kWh in (~80%).
- **Total**: 25.7 kWh solar → 11.9 kWh usable = ~46% end-to-end.
- Still lossy, but simpler than before (smaller solar, no oversized flow).
### Optimized Design
- **Ponds**: 800 m³ each (~63 ft diameter, 4 ft deep).
- **Elevation**: 60 ft (18.3 m).
- **Hydro**: 33.86 kWh, using 280.7 m³/day.
- **Solar**: 5 kW (~22 kWh/day).
- **Battery**: 15 kWh.
- **Pipe**: 2-inch.
- **Turbine/Pump**: 0.5-1 kW.
- **Trout**: ~20-40/pond.
### Final Thoughts
You’re not overcomplicating it too much now—800 m³ ponds are reasonable, and the solar (5 kW) and battery (15 kWh) are standard sizes. Losses are still high (~54%), but that’s the trade-off for hydro + trout + battery flexibility. To simplify further:
- Drop batteries, use hydro directly (16.46 kWh/day solar → 11.9 kWh, ~72% efficient).
- But with 800 m³ locked in, this hybrid keeps trout happy and power steady.
Additional functions of trench will include power cable and geothermal energy piping. I considered putting the geothermal into the pond but that could always be done later.
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