Emeagwali

Emeagwali's answers to frequently asked questions.   Can you explain your mathematical formula used to recover more oil? It was a two-part, mathematical and programming, formula. In the mathematical formula, I encoded the laws of physics - a set of factual statements that describe reality - as nine new equations for “seeing” inside an oilfield. Because my new equations incorporated inertial forces, they were more accurate. Oil has the disposition to remain inert and this inertial force must be overcome before extracting oil from a petroleum reservoir. The latter also applies to people since the laws of motion governing our universe state that all objects possess an indisposition to motion or exhibit the tendency to maintain a state of rest or remain inert. In the programming formula, I divided the oilfield into 65,536 smaller fields and distributed them to 65,536 processors. Doing so increased the resolution of the model, enabling the geologist to see more accurately.   How important is your mathematical formula? For every barrel of oil recovered, two remain unrecoverable. Existing oil wells are yielding ever-declining production rates. Oil and gas resources are finite and non-renewable. The challenge is not in discovering oil, but in recovering it. Eighty percent of the world’s total recoverable oil has been discovered. We will eventually discover the remaining 20 percent. The remaining 20 percent is under Arctic ice and deep waters and, therefore, is more difficult to discover and recover. Yet, many people are not aware that the world has been projected to run out of petroleum before the end of the 21st century. We take petroleum for granted, but when we run out of oil and gas, all automobiles, aircraft and ships will be grounded. If we maintain the status quo in this area, there will be no light.   How can your formula help recover oil? I prefer to think of it the laws of motion in our universe that I codified using an advanced form of calculus called partial differential equations that I could solve in my imaginary higher-dimensional universe containing what mathematicians call hypercubes. Geometers define the fourth dimension of the hypercube as that beyond “Length, Height, and Width.” The fifth and higher dimensions are similarly derived. In effect, I mentally hopped into a 12-dimensional geometrical universe to solve a three-dimensional physical problem. My approach may seem counterintuitive to a layperson, but mathematicians understand that it is sometimes easier to “escape into” higher dimensions. Indeed, in science fiction writings, a person can escape a homicidal gunman by running into the fourth dimension. A surgeon in a fourth dimensional world, which encompasses our universe, can operate inside your intestines and remove cancerous cells without cutting. Similarly, the secret to my success was that my 12-dimensional hypercube computer provided extra communication paths for my information. The conventional wisdom was that it would be impractical, if not impossible, to harness 65,536 processors. The secret to my success was that the hypercube topology enabled me to acquire a concrete mental image of the entire system, including mentally visualizing the name, location and 12-nearest neighbors of each of my 4096 clusters of 16-processors.   What is the petroleum industry's attitude towards your mathematical and programming formulas? After using Darcy’s Law for 150 years, reservoir engineers have forgotten how and why that formula was originally derived. It reminds me of inter-generational family feuds in which people have forgotten how and why the feud started. In the 1930s, a feud developed between Paul Fillunger and Karl von Terzaghi. Fillunger codified the laws of motion as one partial differential equation; however, von Terzaghi, a respected scientist considered to be the father of soil mechanics, rejected his formula. Fillunger’s equation was the subject of great controversy which, in turn, led Paul (and his wife) to commit suicide in protest against the rejection of his reformulation of Darcy’s Law. My work was the first effort to revive and revalidate Fillunger’s formulation. I went several steps above and beyond Fillunger equations. I derived nine hyperbolic partial differential equations that were mathematical codifications of Newton’s second law of motion, as is described in any introductory physics textbook. To the layperson, my equations will seem like a strange hieroglyphics of symbols and numbers. However, my equations have profound meanings to mathematicians and physicists using them to understand how to recover petroleum. Inertial forces must be incorporated into reservoir simulators. The reason is that the laws of motion are absolute. They are deterministic. They contain zero defects. Since in our universe these laws cannot be broken or violated by any object in motion, my hyperbolic equations will always remain superior to the empirically-derived Darcy’s formula. It is a misnomer to call it “Darcy’s Law” since it violates Newton’s Law. Every physicist believes that the laws of physics are universal, but petroleum geologists pretend that they do not strictly apply to oilfields. Darcy’s formula, neglects inertial forces and consequently violates the laws of physics. My innovation in formulating my nine hyperbolic equations laid in seeing what every physicist saw, but thinking what no geologist thought. My additional contributions, as mentioned earlier, included the programming and redistribution of the computational workload to 65,536 processors. In the 1980s, we could operate a reservoir simulator on only one computer. My contribution to that area was that I codified them to simultaneously operate on thousands of processors (or computers). I created the new knowledge that proves that we can control and instruct the flow information and data along the 12 bi-directional communication channels of a 12-dimensional hypercube computer. The latter contribution is accepted and utilized by the petroleum industry which, in fact, purchases one in 10 supercomputers.   Why did the programming formula gain easier acceptance than its mathematical counterpart? It is a programming and mathematical nightmare to replace the simple Darcy’s formula with my nine complex partial differential equations. It is not unusual for software programmers to reject any new technique that will give them mathematical migraines. In science, all new ideas that are radical departures from the accepted status quo must go through three stages: rejection, ridicule and acceptance. For any idea to gain acceptance, the originator must continue “to harp on it,” even when the listeners find it annoying. In fact, the struggle to get an innovative idea accepted is greater than the struggle to conceive it. I believe that it could take 50 years to re-code existing reservoir simulators to incorporate my nine partial differential equations.   Do you believe the oil companies invested in Nigeria? The multinational oil corporations are in the business of recovering oil, exporting it to Europe, and making a profit. I believe that the oil companies are entitled to reasonable profits. During the colonial rule in Nigeria, Shell retained 50 percent of the profits. According to the New York Times, Nigeria now retains only 60 percent of the profits from oil derived from its territory. This is outrageously low profit! As a point of comparison, the United States would never permit a Nigerian oil company to retain 40 percent of the profits from a Texas oil field. It is unfair to allow community groups to intimidate and extort money from an oil company to build schools, hospitals and roads. An oil company cannot replace the government. The oil fields belong to the Nigerian government (or, rather, the Nigerian people). Each state receives its revenue allocation from the petroleum revenue. It is even unconstitutional for any oil company to discuss “revenue compensation” with any ethnic groups. It sets a bad precedence and encourages the extortion and kidnapping of oil workers. The cost of extortion, sabotage and intimidation is passed on to the consumers - more specifically, the Nigerian people. However, the right to do business comes with the responsibility to pay attention to the side effects - or “collateral damage” - of that business. These responsibilities include reducing gas flaring, cleaning up polluted soil and water and paying the associated fines. It’s called “good corporate citizenship.” Algeria, Oman, Venezuela and other OPEC nations invested in human resources and contribute as much as 75 percent of the cost of oil exploration. Nigeria contributes 5 percent of the cost of oil exploration, and prefers to pay US $5.5 billion for oil exploration services and the salaries of expatriates.   Do you provide mentorship to young and gifted mathematicians? I focus on creating mathematical knowledge, which differs from communicating what is known. Computational mathematicians can now reformulate partial differential equations as millions of algebraic equations, and then solve them on thousands of processors. That was a new mathematical territory, because I was one of the first to employ thousands of processors - instead of just one - to solve millions of algebraic equations. Also, I am not a pure mathematician. A pure mathematician only performs mathematical analysis. These “pure mathematicians” are perennially in a state of “analysis paralysis,” a lifetime of rigorous theoretical proofs that have no computational results. Ultimately, a mathematical theorem and a supercomputer are like two bookends on a long shelf: they rarely meet. A pure mathematician will not touch a supercomputer with a 10-foot pole. Pure mathematicians confine their activities to blackboard analysis. However, you cannot discover an oilfield by only performing mathematical analysis. As a computational mathematician, I went beyond deriving nine new mathematical equations. I went beyond the symbols and numbers written on my blackboard. I re-incorporated the laws of physics into my equations. I codified my differential equations as 65,536 co-operating and communicating processes, and then executed those processes on an equal number of processors. Also, I see myself as a multidisciplinary scientist who lacks disciplinary roots. I am alienated from mathematicians and unhappy with engineers, cannot relate to physicists, and hate to be called a “supercomputer genius” or “a Father of the Internet.” Unlike other scientists, I do not focus exclusively on one traditional discipline. Instead, I draw from different disciplines and interconnect them to create new technological knowledge. Emeagwali A blackboard sketch of excerpts from my mathematical formula. The derivation of my formula is a few hundred handwritten pages in length. Below are excerpts from my original notes from the mid-1980s. Emeagwali Fame attracted daily visitors and journalists to my office. Here I pause for photos. (Courtesy of Detroit Free Press, Page 1E, May 29, 1990) TIMELINE: Enhanced Oil Recovery Any technology is the culmination of a series of inventions and discoveries that took place over thousands of years. This timeline is a snapshot of developments in mathematics, computing and petroleum engineering. Ten percent of supercomputers are purchased by the petroleum industry. 1666 - 1989 1666 Sir Isaac Newton formulates the universal laws of motion and gravitation and co-invented calculus. 1856 Henry Darcy formulates "Darcy's Law" which became the foundation of petroleum reservoir simulation. 1920 Cheap oil and natural gas becomes competitive to coal. 1920s Hydrocarbons synthesized to create liquid fuels. 1921 Ethyl gasoline produced 1928 Submersible drilling barge invented. 1932 The first independently drilled oil well. 1932 First on-shore submersible drilled oil well on the West Coast of the United States. 1934 Mr. and Mrs. Paul Fillunger commit suicide in protest against the rejection of Paul's mathematical equations. 1940 First off-shore submersible drilled oil well in the Gulf of Mexico. 1946 The modern electronic computer is invented. 1960 OPEC founded. 1973 OPEC oil embargo 1989 Emeagwali invents nine formulae that enable thousands of cooperating computer processors to increase the amount of oil recovered from oilfields. To achieve his breakthrough, Emeagwali rejected Darcy's Law and invented formulae (nine partial differential equations) that unified Fillunger's equations with Newton's second law of motion. Updates by Webmistress The Reviews The above discoveries has been reviewed in numerous publications. In a lengthy profile, Upstream (1/27/97), an international oil & gas industry publication described Emeagwali as an "unorthodox innovator [who] has pushed back the boundaries of oilfield science." In another profile, CNN described him as using "his mathematical and computer expertise to develop methods for extracting more petroleum from oil fields." Emeagwali's Contributions An increase in the ability to more accurately "see" the interior of an oilfield leads to an increase in the amount of petroleum recovered. Emeagwali's formulas are used to "see" inside an oilfield. Emeagwali invented a mathematical formula will enable geologists to "see" the inside of an oilfield more accurately so that more oil will be recovered. In the May 1990 issue of SIAM News, Emeagwali's contribution was described as follows: When the flow becomes turbulent, Darcy's law does not hold, and the governing PDEs [Partial Differential Equations] currently used are no longer valid. With the complete formulation, conversely, turbulent flows can be conveniently accounted for a quadratic term or some other appropriate empirical relationship to describe the source terms of its conservation of momentum equations. Emeagwali's hypothesis was rejected then but has now been accepted and incorporated into operational reservoir simulators. In March 2001, the Society of Petroleum Engineers confirmed Emeagwali's hypothesis when it wrote: "When fluid [oil and gas] flow velocity is very high, for example, near the wellbore [oilwell], Darcy's law may be inadequate to simulate the fluid flow. The non-Darcy effect has been incorporated into the Department of Energy (DOE) reservoir simulator MASTER (Miscible Applied Simulation Techniques for Energy Recovery).... The modeling of non-Darcy flow proved successful and enabled the simulator to match high-velocity gas flow more accurately. computer formula now used by geologists to compute faster and "see" the inside of an oilfield more accurately so that more oil will be recovered. In a newspaper interview reported in the Arab News on October 23, 1990, a spokesperson for Mobil Research and Development Corporation declared that "He [Emeagwali] has made a significant accomplishment in a computer science sense. . . . During the time saved, we could do more engineering studies on other oil fields, which saves both time and money." The mathematical and computer formulas invented by Emeagwali are used by oil companies to extract oil and gas. The Importance Eighty percent of the world's total recoverable oil has been discovered. The remaining 20 percent is under Arctic ice and deep waters and, therefore, is difficult to discover and recover. Existing oil wells are yielding declining production and it is projected that the world might run out of petroleum before the end of this century. Without petroleum, all automobiles, aircrafts and ships will be grounded. There will be no light. Yet, oil companies are operating on a razor-thin margin. Only ten percent of the oil within an oilfield could be recovered. The amount of oil recovered can be increased by avoiding "dry holes" which, in turn, requires that the producers visualize the paths through which the oil and gas flows and avoid barriers within the underground rock formation. Food For Thought Emeagwali's innovation lies in seeing what every physicist saw, but thinking what no geologist thought. Every physicist believed that the laws of physics are universal, but geologists thought that they did not strictly apply within oilfields. Innovative ideas require unconventional thinking. Which is exactly why petroleum experts called this new invention "unorthodox." Emeagwali had to forget what geologists knew about oilfields and think without boundaries. The expected result: increased oil recovery. As with any new technology, questions arise.... The applications of Emeagwali's formula include all occurrences of low-inertial flows --- from subsurface flows within our groundwater supplies to the liquid outer core that surrounds the solid inner core of our Earth. Excerpted from: Upstream, Oslo, Norway (oil & gas industry publication), January 27, 1997 Software, Institute of Electrical and Electronics Engineers, May 1990 SIAM News, Society of Industrial and Applied Mathematics, lead story, June 1990 Li, D., Svec, R.K., Engler, T.W., and Grigg, R.B.: “Modeling and Simulation of the Wafer Non-Darcy Flow Experiments,” paper SPE 68822 presented at the SPE [Society of Petroleum Engineers] Western Regional Meeting, Bakersfield, 26-30 March 2001. CNN, http://fyi.cnn.com/fyi/interactive/specials/bhm/story/black.innovators.html 1989 Gordon Bell Prize Committee Report "The amount of money at stake is staggering. For example, you can typically expect to recover 10 percent of a field's oil. If you can improve your production schedule to get just 1 percent more oil, you will increase your yield by $400 million (at $20 per barrel in a 20-billion-barrel field). " MOBIL (oil company) "He has made a significant accomplishment in a computer science sense. . . . During the time saved, we could do more engineering studies on other oil fields, which saves both time and money." The Chronicle of Higher Education "Philip Emeagwali, who took on an enormously difficult problem and, like most students working on Ph.D. dissertations, solved it alone, has won computation't top prize, captured in the past only by seasoned research teams.... If his program can squeeze out a few more percentage points, it will help decrease U.S. reliance on foreign oil." Detroit Free Press "[Petroleum reservoir simulators] are like space-age divining rods, and they'll operate much more swiftly and accurately as a result of Emeagwali's work. . . . Emeagwali puts math to work in real world." UPSTREAM, oil & gas industry publication "The unorthodox innovator has pushed back the boundaries of oilfield science." RECOMMENDED READINGS: Nature's own numbers man Making strides in a parallel universe Inspirations from hard history Interview of Emeagwali on his discoveries that improved oil exploration SHORT BIO Emeagwali was born in Nigeria (Africa) in 1954. Due to civil war in his country, he was forced to drop out of school at the age of 12 and was conscripted into the Biafran army at the age of 14. After the war ended, he completed his high school equivalency by self-study and came to the United States on a scholarship in March 1974. Emeagwali won the 1989 Gordon Bell Prize, which has been called "supercomputing's Nobel Prize," for inventing a formula that allows computers to perform fast computations - a discovery that inspired the reinvention of supercomputers. He was extolled by the then U.S. President Bill Clinton as "one of the great minds of the Information Age” and described by CNN as "a Father of the Internet." Emeagwali is the most searched-for modern scientist on the Internet (emeagwali.com). Click on emeagwali.com for more information.