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

By W. Fred Ramirez

In recent times, more advantageous oil restoration strategies have acquired a lot recognition within the oil undefined. superior oil restoration equipment should be divided into 3 significant different types: thermal strategies which come with steam flooding, steam stimulation, and in-situ combustion; chemical techniques which come with surfactant-polymer injection, polymer flooding, and caustic flooding; and miscible displacement methods which come with miscible hydrocarbon displacement, carbon dioxide injection of enormous quantities of particularly dear fluids into oil bearing reservoir formations. advertisement software of any improved oil restoration technique depends financial projections that convey an honest go back at the funding. as a result of excessive chemical expenditures, you will need to optimize greater oil restoration tactics to supply the best restoration on the lowest chemical injection price. the purpose of this ebook is to improve an optimum keep watch over idea for the selection of working concepts that maximize the commercial popularity of more advantageous oil restoration approaches. The selection of optimum regulate histories or working ideas is among the key parts within the winning utilization of latest better oil restoration innovations. the knowledge inside the publication will for this reason be either fascinating and worthy to all these operating in petroleum engineering, petroleum administration and chemical engineering.

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3 I tf t0 t Figure 2 . 2 . Fixed End Points. 3-9) 48 X Figure 2 . 3 . Free End Points. The Euier Equation of Equation 2 . 3-10) or ( 2 . 3 - 11) which has an analytical solution, x(t) = A sinh t + B cosh t The Transversality Conditions of Equation 2 . 3 - 5 state problem that the variation 6x is zero at the boundaries t = The specified end point conditions become the boundary Using these boundary conditions we Equation 2 . 3 - 1 2 . 3-12) that for this 0 and t = 1 . conditions for have for the ( 2 .

4) A total dissolved solids salinity should be less than 80,ooO ppm. The data bank field data does not give the a reservoir temperature, but considering the location of this :field it is assumed that the temperature is less than 175 degrees Fahrenheit. 6 cp at 60 degrees F. We assume that this meets the viscosity screening criterion. The capillary number is the ratio of viscous to interfacial forces. 4 which means that the reservoir passes the capillary criterion and is acceptable without any in-field drilling.

Also, the function F is continuous in x ( t ) , x ( t ) , and t and has continuous partial derivatives with respect to x and x. In other words both the functions x ( t ) and F are well behaved. 2-22) T h e increment therefore becomes AJ = It: [3! 2-24) Because of the smooth behavior of the functions x ( t ) and F , the higher order terms in 6x and (SX vanish as IlSx,GXI goes to zero. 1 As a specific example of a problem that satisfies the functional of Equation 2 . 6 = [to 2(xSx + Extrema of Func:tionals A functional J with domain X has a relative extremum at x * if there is an E ) 0 such that for all functions x in X which satisfy ( x - x * I < E , the increment of J has the same sign.

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