
Emeagwali's answers to frequently asked questions.
Can you explain your mathematical formula used to recover more oil?
It was a twopart, 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 everdeclining production rates. Oil and gas resources are finite and nonrenewable. 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 higherdimensional 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 12dimensional geometrical universe to solve a threedimensional 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 12dimensional 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 12nearest neighbors of each of my 4096 clusters of 16processors.
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 intergenerational 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 empiricallyderived 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 bidirectional communication channels of a
12dimensional 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 recode 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 10foot 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 reincorporated the laws of physics into my equations. I codified my differential equations as 65,536 cooperating 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 mid1980s.
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
coinvented 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 onshore 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 offshore 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 nonDarcy effect has been incorporated into the Department of Energy (DOE) reservoir simulator MASTER (Miscible Applied Simulation Techniques for Energy Recovery).... The modeling of nonDarcy flow proved successful and enabled the simulator to match highvelocity 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 razorthin 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 lowinertial 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 NonDarcy Flow Experiments,” paper SPE
68822 presented at the SPE [Society of Petroleum Engineers] Western
Regional Meeting, Bakersfield, 2630 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 20billionbarrel 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 spaceage 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 selfstudy
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
searchedfor modern scientist on the Internet (emeagwali.com).
Click on emeagwali.com for more information.
