Download Application of Optimal Control Theory to Enhanced Oil by W. Fred Ramirez PDF

By W. Fred Ramirez

In recent times, greater oil restoration ideas have bought a lot recognition within the oil undefined. superior oil restoration tools should be divided into 3 significant different types: thermal strategies which come with steam flooding, steam stimulation, and in-situ combustion; chemical procedures which come with surfactant-polymer injection, polymer flooding, and caustic flooding; and miscible displacement techniques which come with miscible hydrocarbon displacement, carbon dioxide injection of huge quantities of really dear fluids into oil bearing reservoir formations. advertisement program of any superior oil restoration method depends monetary projections that express a good go back at the funding. as a result of excessive chemical expenses, you will need to optimize improved oil restoration techniques to supply the best restoration on the lowest chemical injection rate. the purpose of this e-book is to increase an optimum keep watch over idea for the selection of working concepts that maximize the commercial acceptance of stronger oil restoration methods. The decision of optimum keep watch over histories or working ideas is among the key parts within the profitable utilization of recent greater oil restoration concepts. the data inside the publication will for this reason be either attention-grabbing and invaluable to all these operating in petroleum engineering, petroleum administration and chemical engineering.

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Let’s find the increment of the functional J(x) = x2(t)dt where x ( t ) is a continuous function of t . The increment is A J ( x , ~ x )= J(x+bx) - J(x) upon substitution ( 2 . 2 - 13) ( 2 . 5 The First Variaiion of a Functional T h e first variation of a functional, 6J, is the part of the increment of the functional, AJ, that is linear in the variation, S x . T h e increment of a functional can therefore be written as, AJ(x,dx) where SJ is linear in S x . 2-18) O then the functional J is differentiable o n x and SJ is the first variation of J evaluated for the function x ( t ) .

And White, J . A . , 1980. Capital Investment Decision Analysis f o r Management and Engineering, Prentice- Hall, Englewood Clifts, N . J . Casler, G . L . , Anderson, B. L . , and Aplin, R . D . , 1984. Capital Investment Analysis Using Discounted Cash Flows, T h i r d Edition, Grid Publishing, Columbus, Ohio. DeGolyer and MacNaugh t o n , 1982. Twentieth Century Petroleum Statistics, Dallas, Texas. Energy Economics Research L t d . , 1983. International Crude Oil and Product Prices, Middle East Petroleum and Economic Publications, Beirut, Lebanon, July.

This is illustrated in Figure 2 . 5 . 3-27) 52 Figure 2 . 5 . 4 Constrained E x t r e m a We now consider the development extremum of the functional J(x(t)) = of the necessary conditions for an F(x,x,t) dt where x is an n t h order vector which is a member of R n . 4-3) where X ( t ) are called the dynamic Lagrange multipliers. 4-4) By introducing the variations ax, ax, aX, and Stf t o the increment AJA, we get the first variation 54 T h e Fundamental Theorem of the calculus of variations states that a For unbounded necessary condition for an extremal is that ~ J A = 0.

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