Prized Science | Exploring the leagues under the sea; Seeking the right equation
Read about Rajnish Kumar's study on extracting methane from hydrates and Apoorva Khare’s efforts to connect branches of mathematics, like algebra and analysis
Rajnish Kumar, professor of chemical engineering at IIT Madras studies compounds called gas hydrates. A joint winner (along with Dipti Ranjan Sahoo of IIT Delhi) of this year’s Shanti Swarup Bhatnagar Prize for engineering sciences, Kumar explains how his team has developed processes for extraction of methane from natural gas hydrates below the sea bed, and for synthesising hydrates in the lab. Read edited excerpts.
To start with, please explain what exactly are gas hydrates?
Gas hydrates are ice-like crystalline compounds that naturally occur below the sea bed. India has huge resources of such natural gas hydrates, which could be a potential source of methane gas. Gas hydrates look very similar to ice, and can also form at 5-10°C, unlike ice which requires 0°C. The temperature and pressure under the sea bed are close to 5°C and 100 bars respectively, conditions that are suitable for hydrate growth. These hydrates were formed thousands of years ago and are stable because of the ideal conditions. Gas hydrates could also be synthesised in the laboratory at a large scale.
Why synthesise hydrates when there are natural resources?
Synthesis in laboratory settings is crucial to studying how methane can be extracted from marine gas hydrate reserves. In our laboratory, we synthesise these hydrates at the kilogram scale under conditions that exist below the sea bed, and study the associated thermodynamics and kinetics. These carefully designed experimental protocols allowed us to develop a process for methane recovery from such gas hydrate reservoirs. These studies were done in collaboration with GAIL; together, we have filed multiple patents for this process.
How is methane extracted from hydrates?
The gas hydrates are cage-like structures made up of water molecules, and each such cage holds a methane molecule inside it. If one has to recover the methane, millions of such water cages have to be broken. The process we have developed in our laboratory at IIT Madras allows us to break these cages with minimal energy. This process releases methane gas which could be produced in the same manner as any oil and gas operation.
Other than methane, what else are hydrates important for?
In a separate process where we studied the formation of carbon dioxide hydrates under the sea bed, we developed a process for carbon dioxide sequestration. The carbon dioxide that has been captured from any process either has to be utilised or sequestrated for its efficient removal from the atmosphere. In the process of sequestration, gaseous carbon dioxide is converted into solid carbon dioxide (carbon dioxide hydrates) under the sea bed. These transformations happen without any significant external intervention because deep inside the sea bed, in-situ conditions are conducive for carbon dioxide hydrate growth.
Another application where we have contributed significantly is in the form of water purification through hydrate formation. Effluent water from industries, which are contaminated with many impurities, could be purified by converting the pure water into solid hydrates, thus, leaving the contaminants in liquid water. In the next step, the solid hydrate is separated from the original liquid and dissociated to produce pure water.
Linking one branch of Math to another
Apoorva Khare of IISc Bangalore, who works in several subfields of mathematics, is one of the winners of this year’s Shanti Swarup Bhatnagar Prize for Mathematical Sciences, sharing it with Neeraj Kayal of Microsoft Research Institute. Khare explains his work in representation theory, combinatorics and matrix analysis and how he finds connections among these diverse fields. Read edited excerpts.
Why is it necessary to connect branches of mathematics? What does it mean to do that?
Connections in mathematics mean that the same object can be understood in multiple ways — or a concept in one field of mathematics can be understood using tools from another field. A famous example is from high school geometry: one can bisect any angle using just a ruler and compass, but one cannot trisect 60°, say, if one is restricted to just those two instruments. This is a fact in geometry, but to understand why the task is impossible, we need to use tools from another branch of mathematics, algebra — fields and roots of polynomials of degrees 2 and 3.
To put one aspect of my research in very simple terms, I worked with some special matrices using tools of calculus (or more broadly, “analysis”), and obtained objects called "Schur polynomials" that have traditionally been studied under "algebra". This connection between analysis and algebra was not explored before, and it has led to interesting new developments in both algebra and analysis.
Help us understand the branches you work in.
Matrices are arrays of numbers that encode information, including data of covariances and correlations. Such matrices are central to statistical analysis of data, which has real-world implications in all applied fields.
Combinatorics and discrete mathematics traditionally arose from counting objects with specified properties, but by now the field has grown to include the study of graphs and networks, symmetry groups, and even functions of many variables that remain the same when one permutes the variables.
And representation theory tries to take a symmetry group or some related structure, and attach to each symmetry a matrix such that the matrices interact among themselves exactly like the symmetries do. As matrices are more concrete objects than symmetries, one can study the symmetries through the matrices representing them.
What role does such research play in the real world?
The fields are broad areas in mathematics, with both theoretical and real-world applications.
A widespread use today of matrix analysis is in data science/statistics, where one makes observations of several different random variables together in order to try and understand their interrelationships, which make up the entries of covariance and correlation matrices. In analysing real-world data, an important goal is to "clean up" such covariance matrices while keeping intact a property called covariance, also known as positivity.
My research in matrix analysis broadly tries to understand what transformations of covariance matrices achieve this goal. Finding such classes of positivity-preserving transformations can have real-world applications in fields as diverse as the study of climate change, genetic markers of disease, and the behaviour of stock markets.
One aspect of analysis includes the study of distances between points, and how this can change or can be computed from minimum information. This is at the heart of GPS triangulation; for example, three satellites can pinpoint one's position on a hemisphere of the globe.
Combinatorics includes not just counting objects with certain properties in clever ways, but also has applications to cryptography and network security.
Representation theory is similarly theoretical, but is famously used in the Standard Model of Particle Physics, which is the currently accepted framework for understanding the subatomic particles that make up the world we live in.
The Shanti Swarup Bhatnagar Prizes for Science and Technology were awarded to 12 researchers in seven disciplines. The annual prizes, given by the Council of Scientific and Industrial Research, recognise scientists under the age of 45 for notable or outstanding research. Read interviews of all 12 awardees in the Prized Science series
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