Calculating the Required Energy of Drilling into Europa

Drilling into Europa would be the biggest engineering challenge. To show the difficulty, we’ll calculate the required energy to pierce this ice surface.

I’ll also look at other methods of reaching Europa’s ocean as well. The more options the better.

Part of the challenge is that Europa is 390 million miles from Earth. It’s the moon of the huge planet Jupiter, yet it’s smaller than Earth’s moon.

It’s believed that Europa has twice the amount of water of all Earth’s oceans combined. Unfortunately, but not to anyone’s surprise, a thick sheet of ice covers the ocean.

I find this all amazing. It does make our mission much more complex though.

Why look for life on Jupiter’s moon Europa?

An ocean of water!

Humans love challenges. I think after we set foot on Mars, we’ll focus on Europa.

Our mission to Europa will be much more difficult than landing humans on Mars. To illustrate, here’s a comparison between Earth and Europa:

 EarthEuropa  
Average ocean depth2.3 miles62.1 miles
Volume of water0.31 billion cubic miles0.65 billion to 0.96 billion cubic miles
Diameter7,917.5 miles1,900 miles
Average distance from Sun93 million miles485 million miles
Surface gravity7.46 times that of Europa0.13 times that of Earth
Surface pressure1 bar10^(-12) bar

It’s obvious that Europa is a very hostile land. It makes Mars look like a vacation spot.

But, the search for life in Europa’s ocean will still drive this mission forward. Even if that means no humans will go.

With today’s tech, it’d be a suicide mission anyway. Even when it becomes safe, I bet it’ll become off-limits to humans.

We wouldn’t want to contaminate Europa with Earth’s bacteria. One day though, it may become a destination spot. Who knows?!

Regardless, I’m excited.

I hope we can find life in this harsh environment. If we do, it means a civilization much more advanced than us, could be living in a far corner of the universe.

The ice sheet covering Europa

Europa moon
Jupiter’s moon, Europa (Photo Credit: NASA)

According to NASA research, Europa’s ice shell is 25 kilometers thick on average. And the ice shell covers an ocean that’s 60 to 150 kilometers deep.

Just imagine a planet that’s all like Antarctica. Then make it ten times more hostile. That’s Europa!

I’m going to use this 25-kilometer ice thickness in my calculations. I know the ice thickness is not uniform everywhere. But let’s use this value as a possible worst-case scenario.

Most all our data for Europa are estimates anyway. No one has hard facts.

Going back to our mission now. The goal is to drill and melt through the ice to reach the ocean.

Sounds like the plot of a crazy sci-fi movie. But, people from one-hundred years ago would have viewed our gadgets from today in the same way.

Keep in mind though, what I’m proposing we couldn’t even do on Earth today if we wanted.

Size of the hole in the ice sheet on Europa

With the thickness of the ice out of the way, let’s go over the hole size we’ll make.

I’ve heard two schools of thought over the hole size:

  1. Make the hole large
  2. Make the hole small

Simple, right?! Let’s compare the two options together.

Drill a large hole: this gives us a large permanent access point. We’ll have a lot of options for different research we could do in Europa’s ocean.

Obviously, the downside is the cost and the difficulty of making a hole this size.

To top it off, tidal forces from Jupiter may cause constant shifting of ice. This may make our hole size option impossible.

Also, a large hole will take more time. This means more things can go wrong before we even complete the work.

Make a small hole: we’ll consider the Cryobot to help us with our hole size.

Cryobots are robots designed to penetrate water ice using heat. These robots on average weigh 25-kilograms and are 1 meter in length. They also have a radius of 0.06 meters.

So, the hole we need to make needs to be large enough to support a Cryobot.

The best hole size: the small hole size is a no brainer. And frankly, we may only need to go down less than 100 meters.

Then, we melt the water there and get a sample to send back to Earth.

But, what if we want to send a small submarine down the hole? We’d then need a large hole. Of course, if it’s too big of a hole, it’ll be impractical.

Also, if we want to keep the hole open we’ll need to insulate the tunnel wall. So, the hole can’t be too small.

So, to make our calculation interesting, we’ll choose a size in the middle. A medium-sized hole 1-meter in diameter.

Location for penetrating Europa’s ice sheet

The goal is to find the easiest place to penetrate. Here are some considerations:

  • Away from fault zone type areas to not trigger large ice movements
  • In thin ice areas to limit the tunneling work
  • Away from large cracks that may ripple through our tunneling area
  • Avoid areas where Jupiter’s tidal forces are greatest

Calculations for penetrating Europa’s ice sheet

drilling into jupiters moon europa
Europa surface mockup (Photo Credit: Courtesy NASA/JPL-Caltech)

In our calculations, we’ll go over 3 methods to reach Europa’s ocean:

  • Drilling into the ice sheet
  • Melting through the ice sheet
  • Melting the ice sheet with a lid covering the hole opening

This way, we can better see if other methods beat directly drilling into Europa.

Method #1: Drilling into the ice sheet

Step #1: Calculate the mass of the ice column we need to remove

This is the amount of ice we need to remove to make our 1-meter diameter, 25-kilometer deep hole.

m = \rho \times h \times \pi \times r^{2}

Where,
m = mass of the ice column
\rho = density of ice is 916.7 kg/m^{3}
h = height of the ice column
r = radius of the hole

m =  916.7 \times 25,000 \times \pi \times 0.5^{2} = 17,999,362 kg

Step #2: Calculate the potential energy. In other words, the energy required to lift the entire mass of ice out from our hole.

Also, since we’ll remove the ice column at a constant speed, work isn’t turned into kinetic energy.

E = m \times g \times h

Where,
E = potential energy
m = mass of the ice column
g = gravitational force on Europa is 1.315 m/s²
h = height of the ice column

PE = 17,999,362 \times 1.315 \times 25,000 = 5.92 \times 10^{11}J = 164.4MWh

So we need a 164.4-megawatt electric generator to produce electricity for 1-hour.

If we assume our ice column remover machine is 50% efficient, we’d need 328.8MWh. Or, 0.038 megawatts for 1 year.

I already know the efficiency will be very low.

Regardless, that’s a lot of power. And a lot of equipment we’d need to haul over from Earth.

Method #2: Melting the ice sheet 

Here we’d use a nuclear-powered drilling bot. Powered by a small nuclear reactor, the bot would heat the ice as it moves down.

With this approach, we wouldn’t need a lot of heavy equipment. Also, there’d be fewer moving parts.

The more moving parts we have, the more things that can go wrong.

I discussed some of the problems of drilling into Mars with a mega drill. Obviously, we wouldn’t need a mega drill on Europa, but we’d still need a decently sized drill. Plus, millions of tons of shoring equipment.

Step #1: Calculate the energy to raise the temperature of the ice column from -160°C to -75°C

This sublimation temperature is all theory. At −75 °C and under near-vacuum conditions of 10−6 bar, ice sublimation should occur.

Keep in mind, the surface pressure on Europa is 10−12 bar. And the surface temperature of Europa is -160°C.

To that end, we calculate the energy required to heat the column of ice Q_{tr} = m \times c \times \vartriangle t

where,
Q_{tr} = energy required to increase the temperature
m = mass of the ice column
c = specific heat of ice is 2,108 joules/kg°C
\vartriangle t = change of temperature

Q_{tr} = 17,999,362 \times 2,108 \times [-75 - (-160)]

= 3.23 \times 10^{12} joules = 895.8MWh

Step #2: Calculate the energy for enthalpy of fusion of ice and enthalpy of vaporization

Here we calculate the energy required to change the state of a substance. All without increasing the temperature.

In our case, going from ice to vapor.

The enthalpy of fusion of ice is 333,550 joules/kg to go from ice to liquid

\Rightarrow Q_{fus} = m \times H_{fus} = 17,999,362 \times 333,550 = 6 \times 10^{12} \: or \: 1667 MWh

The enthalpy of vaporization of water is 2,257,000 joules/kg to go from liquid to steam

\Rightarrow Q_{vap} = m \times H_{vap} = 17,999,362 \times 2,257,000 = 4 \times 10^{13} \: or \: 11,111MWh

Step #3: calculate the total energy required

Q_{total} = Q_{tr} + Q_{fus} + Q_{vap} = 4.9 \times 10^{13} = 13,611MWh

Method #3: Melting the ice sheet with a lid covering the opening

Step #1: we place a lid on top of our hole. We want to pressurize the hole to about 1 atmosphere. The same air pressure we find on Earth at sea level.

This will keep the melted ice as a liquid. As a result, we don’t need to waste energy boiling the water away as we calculated in Method #2.

Also, the weight of the water should create enough pressure to keep our tunnel from breaking. As a result, we don’t need to engineer a 25-kilometer tunnel wall.

So, we kill two birds with one stone.

Step #2: using the phase diagram of water, we find the new phase change temperature at 1 atmosphere. We need to increase the ice temperature from -160°C to 0°C to liquefy the ice.

Q_{tr} = m \times c \times \vartriangle t

Q_{tr} = 17,999,362 \times 2,108 \times [0 - (-160)] = 6.07 \times 10^{12} joules = 1,686.1MWh

Step #3: calculate the energy for enthalpy of fusion of ice

\Rightarrow Q_{fus} = m \times H_{fus} = 17,999,362 \times 333,550 = 6 \times 10^{12} \: or \: 1667 MWh

Step #4: calculate the total energy required

Q_{total} = Q_{tr} + Q_{fus} = 1.2 \times 10^{13} = 3,361MWh

The best method for penetrating Europa’s ice

Method #3 is my pick. I know Method #1 requires the least energy.

But, given my experience with mega drills, I don’t see how it’d be possible. Too much can go wrong, especially since humans probably won’t be a part of the mission.

This is important given Europa is 390 million miles away. This means we need to haul fewer things from Earth.

That said, our power source will need to be nuclear reactors. It’s the most reliable energy source.

All this is assuming the tech is available to us. Plus, we’ll need to modify equipment for Europa specifically.

Until then, this is all sci-fi. But, my calculations do paint a picture over the massive scale of such a mission.

It’s important though, I go over all the assumptions I made in my calculations. This will show how complex a mission this really is.

Assumptions made in calculations

What I’ve outlined are only ideas that many have thrown around for several decades. My calculations certainly have flaws.

As I mentioned, the calculations for this problem are much more complex than what I’ve done. To do this problem properly, we’d need to use calculus.

But, since so much data is missing I didn’t even try. My goal was to only provide a rough value for the energy required. I believe I accomplished this.

That said, here are the 9 general assumptions I made in my calculations:

Assumption #1: constructing an insulating tunnel wall

This applies to Method #1 and Method #2.

As we drill into the ice sheet, we’ll need to install a thick metal tube. The tube should be steel containing a high amount of nickel. These alloys are less likely to break in low temperatures.

Also, the tube will span the full width and length of the tunnel.

Otherwise, as we drill down, the tunnel may freeze up behind us. Also, the tunnel will become deformed due to the high pressure it’s under.

Then throw in the tidal forces from Jupiter that could snap our steel tube like a toothpick.

This happens when the ice sheets flex and distort. All from Jupiter’s great gravitational forces.

To make matters more difficult, the pressure increases the lower down we go. Also, we’re assuming below the ice is liquid water.

Thus, at the top of the ice sheet, the ice is like granite. Then at the bottom, it’s gooier as we transition from ice to liquid.

So, at the bottom, we’d need to use a different type of material than steel for our tunnel’s wall.

Building our tunnel wall fast

When water molecules move slow ice forms. This is because of low energy.

As we apply heat water molecules move faster. Then once the ice hits the sublimation temperature the ice changes state.

After we melt the ice in Method #2, this becomes a big concern. The ice may reform higher up in our tunnel the farther the water molecules get from our heat source.

Keeping in mind our tunnel will be 25 kilometers in depth.

And, there are many other issues that we touched on, that’ll drive us to want to build our tunnel wall fast.

Lake Vostok as a guiding example from Earth

antarctica lake vostok drill
Lake Vostok drilling in Antarctica (Photo Credit: US National Science Foundation)

The Russians drilled 4 kilometers down into Lake Vostok in Antarctica. They had similar problems.

But, they didn’t try to install a steel outer wall or any other structure into their borehole. The pressure at Lake Vostok is 350 atm according to Antarctic Ecosystem.

This high pressure is because the gravity on Earth is greater than on Europa. This leads to a -3°C liquid water temperature under the ice.

Also, the Russians melt any ice that enters their tunnel with kerosene and now freon. Then they pump it out.

At Lake Vostok, the surface temperature reaches -89°C. But, the Russian crew drills in warmer months where the temperature reaches -50°C.

On Europa, the surface temperature is -160°C. Yet, Europa’s ocean would be warmer than that of Lake Vostok according to the phase diagram of water.

We figure this because the bottom of the Europa ocean floor may have pressures as high as 130-260 MPa.

In short, we can learn a lot from Lake Vostok. But Europa is on another level.

Assumption #2: heat loss to the icy tunnel wall

There will be heat loss to the walls of our ice tunnel. So, as we heat the ice under the machine in Methods #2 and #3, the surrounding ice will conduct heat away.

In my calculations, I didn’t assume any heat loss through the tunnel wall. If I had, the energy required would be much greater than what I calculated.

The efficiency of our machines would drop.

Assumption #3: ice column is a uniform -160°C

The surface of Europa has a temperature of -160°C. I assumed the entire ice column has a uniform -160°C temperature.

But a thermal gradient does exist.

The farther you go down, the greater the temperature becomes. Otherwise, a liquid ocean wouldn’t exist below the ice as we’re assuming.

So, the temperature would decrease the closer we get to the ocean. Using the phase diagram of water, this temperature would be 0°C at the bottom of the ice sheet.

Assumption #4: Recondensing of sublimated ice

If the sublimated ice recondenses on the tunnel walls our machine can get stuck. This only applies to our melting methods.

But not to say our drill can’t get stuck either.

To combat this, we need to insulate around the tunnel wall as we drive deeper into the ice.

Assumption #5: Machine weight

I didn’t consider the machine weights in any of my methods. In other words, the drilling ability with gravitational acceleration wasn’t considered.

In reality, the heavier a machine is, the more force it’ll exert on the ice.

On the same token, if the force of gravity is small, a machine will exert less force on the ice. So, the machine will lose efficiency in melting or drilling into Europa.

This is because of reduced contact between the machine and the ice.

On Europa, the gravitational force is almost 1/9 that of on Earth. As a result, it’d be best to use a heavier machine.

Assumption #6: using the specific heat value of water at 1 atm

For water, the specific heat varies with change in pressure. But it’s very slight.

So, I used the specific heat value calculated at 1 atm in my calculations.

To illustrate this, imagine heating up water. The water molecules need to do work against the surrounding atmosphere to expand.

But what happens if the surrounding pressure is very low, like on Jupiter’s moon Europa? The expansion will take less work.

There’s nothing for the water molecules to push against. Because Europa has a very thin atmosphere.

So, the energy for expansion is negligible for pressures different than 1 atm. Especially when you compare to the high amount of energy you need to heat up water.

In short, we don’t lose much accuracy by using the specific heat value calculated on Earth at sea level.

Assumption #7: sublimation of ice happens at -75°C on Europa

The sublimation of water in places of very low pressures and temperatures is not known. Experimental data doesn’t even exist for this region on the phase diagram of water.

But, theoretical data mixed with computed data gives us some insight. It tells us the sublimation of ice is unlikely below -223°C in cosmic conditions. And impossible at -250°C.

I used -75°C in our calculation.

Assumption #8: boiling of ice

When we drill into Europa, we need to remove the column tailings. So, bring the broken ice pieces we’ve drilled to the surface.

By sublimating the ice, we’ll have a steam jet that removes the tailings without added energy. That’s my assumption.

But, as we learned in Assumption #1, the water vapor may turn back into ice.

I’m assuming because Europa has such a thin atmosphere, the ice wouldn’t reform very easily.

Assumption #9: pressurizing the tunnel

To pull off Method #3, we need to pressurize our tunnel to 1 atm. This is an engineering feat of its own.

I assumed it’s doable on Europa. Just like the many other assumptions I made.

The goal of drilling into Europa

This would be a mission for the ages. The greatest human achievement ever.

I will say though, finding a natural crevice and entering from there would be a much easier mission. It’s believed Europa does have cryovolcanoes.

But, our mission here was to explore the options of melting and drilling into Europa’s ice surface.

So, the day we pull this off will spark space exploration to a new level. Especially if we find life on Europa.

We’ll then have a great reason to explore farther corners of the universe. And, make humans multi-planetary species.

What are your thoughts on drilling into Europa? What other challenges do you foresee? 


Featured Image Photo Credit: NASA

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