# Calculating the Required Energy of Drilling into Europa

Drilling into Europa would be a huge engineering challenge. To demonstrate, I’ll calculate the required energy to pierce Europa’s ice surface.

To set the stage, Europa is Jupiter’s moon, which sits 390 million miles from Earth. It’s smaller than Earth’s moon, yet it’s believed to have twice the amount of water of all Earth’s oceans combined. Unfortunately, a thick sheet of ice covers these oceans.

Now, the calculations will be sci-fi only. But one day in the future, they may become a reality…

## Why look for life on Jupiter’s moon Europa?

To know we’re not alone.

Europa has a similar environment to Earth. Naturally then, a similar chemical soup for life may exist in Europa’s oceans. To illustrate, the following is a comparison between Earth and Europa:

Comparison metricsEarthEuropa
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

A trip to Europa won’t be a cakewalk though. It’s a hostile land, making Mars seem like a vacation spot.

Even with today’s tech, it’d be a suicide mission for humans. But robots this century, could possibly make the trip.

## Europa’s ice shell

According to NASA research, Europa’s ice shell is 25 kilometers thick on average. And it covers a 60 to 150 kilometer deep ocean. Just imagine an Antarctica-like planet, but 1000x more hostile!

In the calculations, we’ll use an ice thickness of 25 kilometers to penetrate.

### Size of the manmade hole in Europa’s ice sheet

There are two following schools of thought on the hole size:

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

Simple, right?! Let’s go over these choices.

Drill a large hole: create a large permanent access point. This allows for different types of ocean research, including a small submarine.

The downside is the cost and the difficulty. Tidal forces from Jupiter may cause constant shifting of ice. This may even render this option impossible. Plus, a large hole takes more time to drill, and thus more can go wrong.

Melt a small hole: a Cryobot penetrates water ice using heat. These robots on average weigh 25 kilograms and are 1 meter in length with a 0.06-meter radius. So, the hole would simply need to be large enough to support a Cryobot.

The ideal hole size: the small hole size is a no-brainer. Frankly, we may only need to drill down to 100 meters. Then, we transmit analyzed melted ice sample data back to Earth.

To make our calculation interesting, we’ll choose an in-between hole diameter of 1-meter.

### The ideal location for penetrating Europa’s ice sheet

The ideal penetration location would consider the following:

• Away from fault zones to not trigger large ice movements
• In thin ice areas to limit drilling
• Away from large cracks, which may ripple through the tunneling area
• Away from areas where Jupiter’s tidal forces are greatest

## Europa’s ice sheet penetration calculation

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

1. Drilling into the ice sheet
2. Melting through the ice sheet
3. Melting through the ice sheet with a lid covering the hole opening

### Method #1: Drilling into the ice sheet

Step #1: Calculate the mass of the ice column we need to remove. In our case, an ice column 1-meter in diameter and 25-kilometers long.

Where,
= ice column mass
= ice density is
= ice column height

Step #2: Calculate the potential energy to lift the entire mass of ice out from the hole. We’ll assume the ice column removal will be at a constant speed. This way, work isn’t turned into kinetic energy.

Where,
= potential energy
= ice column mass
= Europa’s gravitational force is 1.315 m/s²
= ice column height

We need a 164.4-megawatt electric generator, to produce electricity for 1 hour. Then assuming a generator efficiency of 50%, the figure doubles to 328.8MWh!

The electrical infrastructure to support this generator is then an entirely separate topic. For perspective though, check out my article on drilling into Mars with a mega drill. On Europa though, we wouldn’t need a mega drill. But, we’d still need a decently sized drill with millions of tons of shoring equipment.

### Method #2: Melting through the ice sheet

A nuclear-powered drilling bot would heat the ice as it travels downwards. This approach doesn’t require much heavy equipment and there are fewer moving parts. Thus, gained reliability.

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

At −75 °C and under near-vacuum conditions of 10−6 bar, ice sublimation should occur in theory. Europa has a surface pressure of 10−12 bar, and a surface temperature of -160°C.

The energy required to heat the ice column is

where,
= energy required to increase the temperature
= ice column mass
= specific heat of ice is 2,108 joules/kg°C
= change of temperature

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

We calculate the energy required to change the state of a substance 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.

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

Step #3: Calculate the total energy required.

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

Step #1: Place a lid on top of the hole, for pressurization to about 1 atmosphere. The same air pressure is found on Earth at sea level.

This method keeps the melted ice liquid. In return, energy isn’t required to boil the water away as calculated in Method #2.

Also, the water weight should create enough pressure to keep the tunnel from collapsing inwards. In return, a 25-kilometer tunnel wall isn’t required.

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.

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

Step #4: Calculate the total energy required.

### The selection for the best method to penetrate Europa’s ice

Method #3 is my pick, despite Method #1 requiring less energy.

Given my experience with mega drills, I don’t find Method #1 to be practical. Too much can go wrong, especially since humans won’t be present in the mission. With Europa 390 million miles from Earth, the less equipment we haul over, the better.

## Calculation assumptions

What I’ve calculated are only ideas, which have been thrown around for several decades. Also, my oversimplified calculations have many flaws, given the mission complexity and unknowns.

To better understand, below are the 10 general assumptions I made in the calculations.

### Assumption #1: constructing an insulating tunnel wall

Drilling into the ice sheet, we’ll need to install thick metallic tubing all the way down. The tubing will be made of steel, with a high amount of nickel. This alloy is less likely to break in low temperatures.

Without the tubing, the tunnel may freeze back up behind the machinery in Methods #1 and #2. Not to mention, the tunnel will deform from the surrounding high pressures. Jupiter’s gravitational forces will flex the ice sheets, causing the tunneling to snap.

Even more, at the top of the ice sheet, the ice is granite hard. The lower down you travel though, the ice becomes gooier in the transition from ice to liquid. So we’d need to transition to a different material than steel.

### Assumption #2: constructing the tunnel wall fast

Ice forms when water molecules move slowly because of low energy. Then with the application of heat, water molecules move faster.

In Method #2, after we melt the ice, this becomes a huge concern given the tunnel depth of 25 kilometers. The ice may quickly reform in the tunnel, the farther the water molecules get from the heat source.

#### Lake Vostok is a guiding example from Earth

The pressure at Lake Vostok is 350 atm (35 MPA) 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.

The Russians undeterred, drilled 4 kilometers into Lake Vostok without installing a steel outer wall. They melted ice entering the tunnel by pouring kerosene and freon down the borehole. Then, pumping it out.

This was carried out in the warmer months when the surface temperature was -50°C. Because in the wrong months, the temperature can drop down to -89°C.

On Europa though, the surface temperature is -160°C and the tunneling is 25 kilometers. But, Europa’s ocean would be warmer than Lake Vostok according to the phase diagram of water. Probably because Europa’s ocean floor may have pressures as high as 130-260 MPa. These are pressures much greater than what’s found at Lake Vostok.

### Assumption #3: heat loss to the icy tunnel wall

In Methods #2 and #3, the surrounding tunnel ice will conduct heat away. In return, the energy required to create the tunnel would increase, as machine efficiency drops. I didn’t include this heat loss in the calculations.

### Assumption #4: ice column is a uniform -160°C

The surface temperature of Europa is -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. Using the phase diagram of water, the temperature would be 0°C at the bottom of the ice sheet.

### Assumption #5: Recondensing of sublimated ice

An insulated barrier would wrap the inner tunnel wall in Method #2 as expounded on in Assumption #2. This would prevent recondensation and the machinery getting stuck.

### Assumption #6: Machine weight

I didn’t consider gravitational acceleration from the machines. Heavier machines exert a greater force on the ice, making the tunneling easier.

In the same vein, if the force of gravity is small, machines will exert less force on the ice. This is because of the reduced contact between the machine and the ice.

Europa has a gravitational force of roughly 1/9 of Earth. So it’s best to use heavy machines.

### Assumption #7: Specific heat value of water at 1 atm

The specific heat for water slightly varies with the change in pressure.

To illustrate this concept, imagine heating up water. The water molecules will work against the surrounding atmosphere and expand. But on Europa, the expansion requires less work due to the moon’s thin atmosphere or low pressure. There’s nothing for the water molecules to push against.

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

I used the specific heat value calculated at 1 atm in Method #3. But we wouldn’t lose much accuracy by using the specific heat value calculated on Earth at sea level.

### Assumption #8:sublimation of ice happens at -75°C on Europa

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

But, theoretical data mixed with computed data gives us insight. The sublimation of ice is unlikely below -223°C in cosmic conditions, and impossible at -250°C. I used -75°C in Method #2

### Assumption #9: boiling of ice

I assumed from the sublimated ice, a steam jet would remove the tailings without added energy. But, as we learned in Assumption #1, the water vapor may turn back into ice. Given Europa’s thin atmosphere, the other assumption is the ice wouldn’t reform easily.

For Method #1, a solution doesn’t exist to remove the column tailings. These are the broken off ice pieces in the tunnel.

### Assumption #10:pressurizing the tunnel

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

## The goal of drilling into Europa

Finding a natural crevice to enter, is a much easier mission. It’s even believed Europa has cryovolcanoes. But this wouldn’t be as interesting as melting and drilling into Europa’s ice surface.

Our mission here is to come up with sci-fi engineering on steroids. Because who knows, one day we may need to deploy this tech…

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

Featured Image Photo Credit: NASA

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