Extreme hydroelectricity on the Danube

When it comes to discharge, one the largest rivers (if not the largest river) in Europe is the Danube. This river, too, passes through a convenient gorge at the Iron Gate, in which the border between Serbia and Romania lies. This fact has not been lost on these two countries, and they have indeed build not just one, but two hydroelectric power installations: Iron Gate I and II. These two stations have a peak capacity of somewhat above 2 GW, and an average capacity of much less than that.

Hey, sure, two power stations is nice, but guys, show some ambition! Here is how:

Again, the GTOPO30 data set is our friend. The critical region on the Danube's watershed is the Moravian Gate, which lies here in the saddle between the Sudetes range and the Carpathian mountains, at 310 meters above sea level. Going any higher than that would cause the lake to spill over into southern Poland, and from there into the Baltic sea. Putting the lake surface at an conservative 300 meters above sea level, we obtain the following, huge, Lake Danube:

Yes, Hungary has transformed into a lake, but as said before: this is purely a technical exercise.

Now, as before, we need our two key parameters: the average discharge at the dam, and the maximum drop height. The average discharge at the Iron Gate is large, at 5600 cubic meters per second, as can be seen on page 540 of this article. The Danube flows at some 50 meters above sea level there, allowing for a full 250 meter drop. Calculating the average power output yields:

P = ρhrgk = 1000 * 250 * 5600 * 9.81 * 0.5 = 6.87 GW.

On a yearly basis, this would yield 59.6 TWh, or 2.15e+17 Joule. This is a lot more than our previous attempts: this installation could cover 2.15% of Europe's electrical power.

Extreme hydroelectricity on the Rhine

I closed my last post with the question "can we do better?". Well, at least we can try, by using one of the other major rivers in Europe: the Rhine. The Rhine passes through a convenient gorge between Bingen and Bonn.

Almost any place in that gorge is suitable for a dam, so I planned one about in the middle near Kamp-Bornhofen. Now, we need to ask the same question as before; how high can be make the reservoir? Using the same procedure on the GTOPO30 data set shows that the critical point on the Rhine's watershed lies in the saddle between the Taunus range and the Vogelsberg, or right about here. GTOPO30 suggests that a waterlevel of 210 meters above sea level would leave some 5-10 meters of headroom.

Now, filling up the lake to 210 meters above sea level floods the entire middle Rhine valley, and even partly extends into the Elzas in France:

So how much power do we get from this? One can find here that just below Mainz (or just above the Rhine gorge), the average discharge is 1620 cubic meters per second. Wikipedia tells us that the Rhine flows at 69 meters above sea level in Kamp-Bornhofen, which gives us a 210 - 69 = 141 meter drop. Using the same calculation as before, this yields:

P = ρhrgk = 1000 * 141 * 1620 * 9.81 * 0.5 = 1.12 GW

This is already better than our previous installation. Over the course of a full year, this would give us 9.82 TWh of electrical energy, or about 3.54e+16 Joules. This would cover 0.35% of Europe's needs.

But we can do better. Check in later!