Revisiting the Mareekh Process: Part 1 - The Latent Heat Question

Mareekh Process is our patented ISRU hybrid power generation concept for Mars (Patent no. US 11421559 B1)

(Fig. 1: The Mareekh Process)

(Fig. 2: Simple flow diagram of the Mareekh Process)

In a nutshell, Mareekh Process utilizes recovered subsurface ice on Mars (permafrost or subsurface glaciers) as superheated water and releases it in the power generation apparatus (steam turbines) making use of the very low pressure and temperature of the Martian atmosphere as a perfect heat sink, achieving rapid decompression and high entropy, and releasing tremendous amount of energy.

Utilizing a ‘pinch’ of supercritical water, and avoidance of steam conversion in any of the energy input stages of the process, makes this concept incredibly powerful in the unique Martian context, releasing >10 megawatts of a net positive energy per kilogram conversion of ice into the atmospheric steam. 

Mareekh Process is a hybrid between a condensing steam turbine and a steam back pressure turbine, with no direct need of a surface condenser for the creation of a vacuum condition, and lets the Martian atmosphere do the job instead. The very cold temperature of the Martian atmosphere also ensures formation of cold saturated vapour, much of it can be condensed through supercooling by expansion while venting a small part of it to the exterior.

But there is a caveat. The end steam (supercooled vapour in the end turbine) cannot be condensed readily into water to be recirculated, without giving out latent heat, which on Mars, will require an impractically huge radiator surface area to give it off into the Martian cold atmospheric sink.

In our previous blog, we assumed sacrificing and venting 8-10% of the saturated end-steam mass through an exit valve will cause further expansion and cooling, causing rapid condensation, and reducing its dryness fraction to 0. This would have translated to nearly the entire enthalpy of the inlet steam converting into power output, minus the enthalpy sacrificed to the exterior.

After further scrutiny of the process going on in the end-turbine and the thermodynamics involved, I found two issues:

1. Venting out of a portion of end steam will cause its expansion and cooling, but also lower its saturation temperature at the same time (unless its saturated vapour component is captured and allowing only the supercooled vapour to escape). This will keep the end-steam in a saturated vapour form and not allow it to condense.

2. The condensation of the cold end-steam will still require surface nucleation and giving up the latent heat of vapourization as radiant heat, which needs to be released  into the environment. The end steam being already cold (7c), the surface area needed to radiate this heat at very low temperature needs to be extremely and impracticably large. 

The energy released by the Mareekh Process is higher than the input energy for recovering the subsurface ice in the form of superheated water; over 40 megawatt per kilogram conversion of subsurface ice into atmospheric steam. However, the amount of energy from the conversion of end-steam enthalpy into latent heat during the formation of condensate makes up a major fraction of the energy output of the Mareekh Process, leaving a lower fraction for conversion into mechanical work, which is smaller than the input energy.

According to our calculations, 1.5kg water can be recovered and converted into superheated steam at 195c at 2 bar pressure by spending 2700kJ of energy from the auxiliary (solar or nuclear). Over 4500kJ of energy (calculations later in the topic) can be recovered from its conversion into end steam, with a positive balance of 1700kJ. Out of this, nearly 1500kJ can be converted into mechanical work, and rest is released as latent heat.

(Fig. 3: Calculating energy input for the formation of 1.5kg steam at 195c under 2 bar pressure from 1.4kg recovered condensate and 0.1kg subsurface ice)

So, what is the advantage of using all the nuclear and solar auxiliary power to produce less work and more latent heat? 

Here is the method behind the madness.

Humans on Mars will require much more per capita energy to survive than on Earth. Not only being heavily technology dependent, merely creating a liveable habitable environment inside the habitats, such as the Craterhabs, will require a lot of energy; something we take for granted on Earth. Moreover, Mars has only little to offer in terms of energy resources. With less than one third of the solar flux as that on Earth, sunlight is still the most reliable source of energy on Mars, except during the famous planet-wide dust storms blocking the Sun for months on end. Mars has nothing else to offer as an energy source. With no wind, hydro, or geothermal resources, the future of a human civilization on Mars seems bleak, as Solar energy is not enough, not even close, in sustaining a heavily industrialized future Martian civilization. A combination of solar and small-scale nuclear such as SMRs can be the answer, but when the power resources are so stretched, an alternate unlimited source of energy must be found.

Mind over Matter

Here the human ingenuity comes to rescue us. 

Let’s go back to the basics. What is the definition of work in physics? It is the ability to bring about a  change through displacement at the expense of energy. But the energy cannot be created or destroyed. So how can something (in this case, the work) be created without using up something else? Since we are not using up energy, what are we changing in order to do work and achieve displacement? It is the entropy. We increase the disorder of the universe, or increase its entropy, when we bring any change. The greater and faster we do it, the bigger amount of change we can bring, or do work. 

In other words, bringing something from higher state of order to lower state or disorder, will bring change, which can be utilized.

On Mars, there are literally oceans' worth of water-ice locked away in the polar ice caps and subsurface permafrost or glaciers, spanning thousands of kilometers across, and can be several kilometers deep. This ice extends all the way from polar regions to close to the equator, including the recently discovered Medusa Fossae region of pure subsurface glaciers almost the size of India which is several kilometers thick. This ice was formed from percolation and freezing of surface water during global cooling on Mars when the atmosphere was still thick. With ice, the order of the water molecules as frozen lattice got preserved. As Mars lost almost all of its atmosphere, and cooled down further, a huge cold sink was formed above the surface, creating a massive entropy imbalance between subsurface ice and the cold near-vacuum environment of the Martian atmosphere. 

Mareekh Process is based around this innovative concept. It has two major components; an apparatus to bring up the subsurface ice by injecting heat into it, and converting it into superheated and supercritical water through two separate channels, without converting it into steam, and, releasing it into a steam turbine as superheated steam at Martian atmospheric conditions, enabling mechanical work through an explosive adiabatic expansion of this steam, all the way to the near-vacuum of the Martian atmosphere, extracting the last bit of its enthalpy into useful work. The seemingly extra energy (18,000kJ more than the input energy per kilogram conversion of ice into atmospheric steam) comes from the rapidly achieving maximum entropy due to the cold vacuum condition of the Martian atmosphere, something which was not present at the time of formation of this subsurface ice on Mars billions of years ago.

Extracting overall extra energy but less work output than the input energy doesn’t seem like a clever idea. And what to do with all this very large amount of low temperature latent heat present in the end steam, which is already difficult to condense in any achievable design.

So let’s go back to the basics of the energy requirement breakdown for a human settlement on Mars.

Craterhab - a large-scale surface habitat concept for Mars

(Fig. 4: AI generated image of a Craterhab lar-scale habitat system on Mars powered by the Mareekh Process)

(Fig. 5: AI depiction of the interior of a Craterhab with internal habitation structures)

Surface habitation on Mars comes with the need to maintain internal heated environments, against very low temperatures on the outside, which can be as low as -50to -70c on average, to below -150c at the poles. 

The main advantage of surface dwellings on Mars is the ability to achieve mini-terraformed habitats of enormous volume where humans can live in a luxury of not having to breathe into each other’s faces, unlike the proposed underground habitats with cramped volumes. Converting Martian craters into mini-terraformed structures into surface habitats, such as the Craterhab concept, will ease the engineering design and make construction simpler, and also protect against the solar and cosmic radiation. However, there is a price to pay for enjoying the surface living. And one of those is the power required to maintain a habitable internal temperature against extremely cold outside environments and also a powered radiation shield.

Imagine a 300m diameter Craterhab built over a Crater. The dome roof is directly exposed to the cold outside. During the day, this is partly compensated by the fact that the temperatures are more balmy - ranging from 0 to -20c, and also the Craterhabs being translucent, will capture a lot of sunlight by acting like a greenhouse. But during the night, as the planetary temperature plummets, the dome fabric is not ideal as an insulator, and unless novel materials such as aerogel do not become commercially available at a low price, maintaining the internal temperature of the domed habitat system will pose unique energy challenges. 

In order to keep a Craterhab warm, the interior should have a constant source of heating. What is the optimal interior night temperature? Since a craterhab is designed to mimic an Earth outdoor environment, a winter night at mid latitudes such as that around the Mediterranean region will provide the best mix of comfort and safety and maintenance of plant growth, maintained at roughly 5-6C. 

The heat loss from a Craterhab is calculated by the internal volume, internal ambient temperature, material properties of the fabric dome material, and the outside temperature. 

Let’s calculate the heat loss rate from the Craterhab dome

Parameters:

Diameter: 300m

Central height: 60m

Crater depth: 40m

Body of the dome: 2 x 5mm thick Silicone layers

Kevlar-resin-carbonfiber composite: 4 x 2mm thick sheets

Outside temperature: -50c

Outside pressure: 0.6kPa or 0.006bar

Internal temperature: 5c

Internal pressure : 0.6bar

Internal atmospheric composition: Nitrogen 78%, and oxygen 21%, and CO2 and inert gases 1%

Calculations:

• Hemi-ellipsoid area (300 m dia, 60 m tall): A ≈ 2.13 × 10⁵ m²

• Overall Heat Transfer Coefficient U (5 mm×2 silicone + 2 mm×4 Kevlar/CF stack + films): U≈1.8 W m⁻²K⁻¹

• ΔT=5−(−50) = 55

Q˙= U A ΔT ≈ 1.8 × 2.13 × 10⁵ × 55 ≈ 2.11 × 10⁷ W  =  21,100 kJ/s (kW).

So 21.1 Megawatts of power will be required (at night) simply to maintain 5c for sustain habitability of the Craterhab. 

Revision of the Input and Output Energy Dynamics of the Mareekh Process

Previously we have calculated the energy required to create 1.5 kg of superheated steam per second at 195c under 2 bar pressure as inlet steam in the steam turbine section of the Mareekh Process, and the energy output from its rapid expansion through the rotor blades until a part of it is vented out into the Martian atmosphere, and the remaining is recovered as condensate to be recycled into the process.

The energy input is subdivided into three main sections:

1. Water recovery from the sub-surface ice: 

   - This is equal to the amount of steam lost to the atmosphere, which is calculated for 0.1kg/s in our baseline calculations.

   - The energy is injected as superheated-supercritical CO₂ at 700c under 100bar pressure 300m into the Martian crust in the ice reservoir held at -70c under 30bar gravitational pressure, to create a water reservoir at 30c.

   - The energy consumption here is a combination of heat required to warm up the ice, latent heat of fusion to melt it into water and then further warming it up to prevent its freezing back into ice.

   - The total energy required to replenish 0.1kg water per second from subsurface ice at -70c to water at 30c is 60kJ/s.

   
   

2. Low Pressure Feeder System (LPFS)

   - Its main purpose is to create 1kg of saturated flash steam in our baseline calculation, which forms the bulk of the 1.5kg/s inlet steam.

   - LPFS takes water from the underground water recovery buffer tank, flash tank condensate, and the end-condensate from the back turbine.

   - Creates 3.5kg superheated water at 233c under 30bar pressure and releases it into a flash tank at 0.6bar causing formation of 1kg saturated flash steam and 2.5kg of condensate at 86.5c.

   - The energy required is calculated as 2,069kJ/s.

   - The 30bar pressure ensures water does not boil in the tubes, and avoids the thermal penalty of providing the heat of vapourization.

   
   

3. High Pressure Feeder System (HPFS)

   - Its main purpose is to create 0.5kg/s of supercritical water at 550c under 300bar pressure from the end-condensate of the back-turbine through an isochoric process, evading the pseudo-boiling.

   - The purpose of creating supercritical water is to allow not only its own flashboiling directly and completely into superheated steam, but also drawing the saturated flash steam from the flash tank via Venturi Effect, and mixing up with it to create a superheated steam mixture at 195c, which is injected into the steam turbine at 1.5kg/s at 2 bar.

   - By evading the Widom Line by a decent margin through keeping the HPFS strictly as an isochoric process, the specific heat is kept very low, allowing the formation of supercritical water at 550c under 3bar pressure with minimal energy input.

   - Creation of 0.5kg/s of supercritical water via HPFS will require 582kJ/s of energy.

Total energy input for the creation of 1.5kg superheated steam at 195C under 2 bar pressure through Mareekh Process is:

60kJ + 2,069kJ + 582kJ = ~2,710kJ

The Energy output of the Mareekh Process

Like any steam turbine, the inlet steam (1.5kg/s at 195c under 2 bar pressure in our calculations) will rapidly expand adiabatically and move towards the low pressure end-turbine, spinning the turbine rotors in the process and generating power. On Earth, the pressure in the end-turbine housing is generally maintained at 0.1bar which is achievable through condensing all the steam using surface-condenser through rejection of a large proportion of the input energy into water flowing through the condenser tubes, and channeling it into the heat sink, which is generally a water body such as a river or sea. On Mars, extremely low back-pressure can be achieved simply by venting the end-steam to the exterior into the Martian surface where the pressure is 0.006 bar on average. However, to avoid the freezing of the condensate in the end-turbine, the pressure can be maintained at 0.01bar using a pressure control valve to modulate the amount of steam escaping from the end turbine. This will achieve a minimum 7c of temperature which is the saturation temperature of steam at 0.01bar.

(Fig. 6: Functional diagram of an Earth-based surface condenser. Source: https://www.elprocus.com/what-is-a-surface-condenser-construction-and-its-working-in-process/)

Imagine, if the back-pressure of 0.01bar is achieved by venting 0.1kg of steam to the exterior per second, and somehow cooling the remaining end steam completely into condensate at 6c, and recovering it, while maintaining the 1.5kg/s of inlet steam inflow and a back-pressure of 0.01bar. During the period of adiabatic expansion, a small part of the steam will condense into water, lowering the dryness fraction (Df) of the expanding and the end-steam. 

The Dryness Fraction (D_f) can be calculated as follows:

D_f = Entropy of inlet steam (S_i) - Entropy of condensate (S_c) / Entropy of end-steam (S_e) - Entropy of condensate (S_c)

D_f  = S_i - S_c / S_e - S_c

      = 7.487 - 0.025 / 8.975 - 0.025

= 7.462 / 8.95

= 0.83 or 83%

Power output = Inlet Steam Enthalpy (E_i) - End Steam Enthalpy (E_e)

                     = E_i - [Condensate Enthalpy (E_c) + D_f(E_e-E_c)]

= E_i - [E_c + D_f(E_e-E_c)]

                     = (2861x1.5) - [(25x0.255) + 0.83(2514x1.24 - 25x0.255)]

  = 4292 - [6.37 + 0.83(3117 - 6.37)]

= 4292 - 2588

= 1,704kW

With a generator efficiency of 90%, the power output will be around ~ 1,530kW.

This is the power output from a steam turbine in Mareekh Process through utilization of 1.5kg/s of superheated steam at 195c under 2 bar pressure, resulting in the formation of 1.4kgx0.83 = 1.16kJ saturated end steam, and 0.1kg of exit steam per second.

What to do with the rest of the 1.16kg of cold saturated steam at 7c under 0.01bar pressure in the end-turbine housing? The amount of latent heat (L_h) contained in this steam is the difference between the enthalpy of the 1.16kg end steam (E_e) and the enthalpy of the condensate if this entire 1.16kg could be somehow condensed (E_c2):

L_h = E_e - E_c2

= (2514 x 1.16) - (25 x 1.16)

= 2916 - 29

= 2,887kJ

2,887kJ of latent heat needs to be rejected to convert 1.16kg of saturated end-steam completely into the condensate i.e. water.

Total energy output = Power output + Latent heat

= 1704 + 2887

= 4,591kJ/s

(Fig. 7: Calculating energy output of the Mareekh Process)

On Earth, as previously mentioned, this condensation in a steam turbine is achieved through the use of surface condensers and this latent heat is released into a water body such as a river or the sea.

On Mars, there are no water bodies, and the atmosphere is too thin to release this as direct convection. Alternatively, it can be radiated out but it will require a very large radiating surface area which is practically impossible.

Can this huge amount of latent heat be somehow used for power generation? The short answer is NO! The second law of thermodynamics does not allow this.

But this latent heat can be used for SAVING power; a lot of it, through a cleverly designed strategy of heating up the Craterhab internal environment against the extreme cold of the outside world

The answer lies in the use of a Centrifugal Mechanical Vapour Recompressors (MVR).

(Fig. 8: Centrifugal MVR. These can range in size from small to very large, depending upon the intended rate of vapour or steam flow. In the Mareekh Process, its  intake can be tens of square meters in cross section due to the high volume of the very low pressure end steam. www.northamerica.tlt-turbo.com/wp-content/uploads/2023/11/CF006472-Kopie.jpg)

Compressing steam takes a lot of power. But in the Mareekh Process, the end steam is cold and saturated. Any increase in the pressure will increase its boiling point, leading to its rapid condensation and releasing latent heat. But there is a problem. If the latent heat is not removed soon enough, it will also warm up the condensate to above its boiling point for that pressure causing it to turn back into saturated steam.

The solution is the centrifugal MVR which will compress the saturated steam into condensate and pump it away to spread out over a large surface area where the latent heat will be released. 

According to the Second Law of Thermodynamics, the latent heat released during condensation must be transferred to a reservoir at a lower temperature than the condensate itself, since heat cannot spontaneously flow from a colder to a hotter body without external work.

If this condensate’s temperature is raised to, say 20c using the MVR, the latent heat released despite being at a lower temperature, can help heat up the Craterhab’s internal environment. 

The condensate after releasing the latent heat of vapourization will then return to the Mareekh Process to be recycled through the LPFS and HPFS..

As calculated earlier, a 300m diameter Craterhab with height and depth of 60m and 40m, will require 21,100kJ/s energy to maintain an internal temperature of around 6c. 

If the Mareekh Process is running on 12kg/s inlet steam (0.8kg/s recovery water cycle), the amount of power output and latent heat will be 8 times, cranking up the power to 1530x8 = 12,240kW or 12MW, and latent heat L_h release at 23,080kJ/s. This latent heat is roughly equal to the power required for maintaining an ambient and liveable 6c inside the massive Craterhab. The personalized habitat and building temperature inside the Craterhab can be customized to match indoor environments as on Earth.

In order to harness this latent heat to warm up the Craterhab internal environment, the MVR must collect the saturated vapour at 7c under 0.01bar, and condense it under high enough pressure where the boiling point is higher than 20c, i.e. 2.33kPa or 0.0233bar or above. This requires tens of kilowatts of power. Not only that, the condensate must be channeled through tubes with large overall surface area to rapidly release this heat in an environment held at temperature below 20c i.e. interior of the Craterhab, so as to prevent further heating and flash boiling of the condensate due to the latent heat released during the condensation process.

In my new proposed iteration to the Mareekh Process, the saturated end-steam at 7c under 0.01bar pressure is removed from the end turbine into a centrifugal MVR. A large inlet area will be required, something in order of tens of square meters, but this is achievable. Inside the recompressor, the saturated steam is compressed into condensate while being pumped into the Craterhab in a radiator complex composed of a mesh of convoluted copper tubes. This radiator complex can be placed inside the central anchor shaft tower of the Craterhab in the centre of the Crater floor. The MVR can be strategically placed directly under the shaft. The top of the shaft is open and is fitted with a series of fans, 4-5 or more, forcing air downwards to channel through the convoluted tubes complex and taking the released latent heat with it. The latent heat released from water inside the copper tubes will warm up the incoming air from the top (temp <6c) to temperatures between 6-20c (around 10-15c), which will be vented out through the ventilation windows directly into the main body of the Craterhab, warming up the entire Craterhab interior anywhere from 6-10c. The condensate flowing through the convoluted tubes will cool down to below 20c, likely around 10-15c as well, and will be channelled back into the Mareekh Process to be recycled through the HPFS and LPFS. 

In order to minimize the total length of the convoluted tubes and increase its surface area to expedite transfer of latent heat from the flowing condensate to the surrounding air channelling through the radiator complex, the copper tubes will have longitudinal grooves. This will increase the efficiency of the radiator system in giving up latent heat as quickly as possible.

This latent heat will eventually be radiated out to the exterior cold sink of the Martian atmosphere from the dome surface, but not before warming up the Craterhab interior.

Though the latent heat released cannot contribute to further power generation or be used in carrying out mechanical work or run any machinery or equipment, a penny saved is a penny earned. The utilization of the latent heat obviates the need for using direct mechanical power generated by the Mareekh Process into heating the interior, and will help utilize this power for other industrial purposes.

(Fig. 9: Schematic diagram of the internal heating of a Craterhab with latent heat from the Mareekh Process using MVR)

(Fig. 10: Radiator shaft has been depicted in the earliest Craterhab drawings)

Now let’s analyze the need for the Mareekh Process and its advantages over the Auxiliary power sources on Mars

The only indigenous source of power on Mars is the Sunlight. The solar flux on Mars is 590W/m². This is roughly 43% of solar flux on Earth which is 1,361W/m²  on a clear day. The solar flux declines from equator to poles on both worlds. While Mars has the advantage of the absence (or near absence of) overcast and the sunlight is fully available in most part of the daytime, which is roughly the same duration as on Earth but this solar power may get completely cut out during global dust storms which can last for several months at a time.

Mars has no other sources of energy. With a complete lack of liquid water on the surface, there is no prospect of hydel or tidal power. The Martian atmosphere is only less than 1% dense as on Earth, and even during the global dust storms, not enough wind power can be harnessed as a backup without some extraordinary engineering. And there are no known geothermal reserves. It is not known if there are any radioactive minerals available on the Martian surface, and harnessing fusion energy is still a far cry.

This leaves us with Solar and limited nuclear energy such as Small Modular Reactors (SMR). Radio-isotope Thermonuclear Generators (RTGs) only generate a few kilowatts of power only, so they are not practical.

Now let’s compare the overall efficiency of Mareekh Process with that of solar panels and SMRs.

For utilization of 1.5kg steam at 195c under 2 bar pressure, and replenishing 0.1kg steam per second, the energy consumed as per the calculations of recovery, LPFS and HPFS stands out at 2710kJ. The energy output from the rapid expansion, turbine work and condensation with latent heat release = 1704 + 2887 = 4,591kJ/s

There is a net positive energy balance of 4591 - 2710 = 1,881kJ 

(Fig. 11: Pie chart of the comparison of input and output energies in the Mareekh Process)

This is the amount of energy obtained from net 0.1kg loss of ice as atmospheric steam per second. Out of this, nearly 90% of the power output of 1705kJ. i.e. 1535kJ/s is the mechanical work output which is 56.6% of the energy input.

Let’s compare this with the mechanical efficiencies of SMR and solar power.

Solar power mechanical efficiency: 15-25%

SMR mechanical efficiency: 30-35%

Mareekh Process: 56%

While the Mareekh Process is not a self sustained perpetual process as the mechanical power output is still less than the input energy (the rest being the latent heat being used indirectly to reduce power consumption), the conversion efficiency is better than the auxiliary, and net energy output is still higher than the input energy.

The mechanical power output (1535kW per 1.5kg inlet steam, 0.1kg recycled ice/water) can be used for all other industrial, domestic and agricultural processes requiring power, except habitat heating, but during times of low activity such as night time, a significant fraction of this power output can be fed back into the Mareekh Process for steam production and running of the steam turbine, reducing the load on the auxiliary system.

Conclusion

The subsurface ice on Mars, and its thin cold atmosphere create a perfect interface for harnessing the entropy imbalance created between the two several billion years ago, providing an inexhaustible reserve of energy. Mars is a different world, where humans will have to think differently. Mars holds many unique treasures in substance or in the absence of it, waiting to be harnessed through sheer human spirit of innovation and ingenuity.