Optimal Spline Based Gas-Lift Allocation Using Lagrange's Multiplier
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Date
2013-06
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Abstract
An accurate prediction of the production rate of
uids from a reservoir to the
surface is essential for e cient arti cial lift application in an oil eld. In an oil
production eld, a group of wells can be put under gas lift operation. For each
well, there will be an optimum point of gas injection and oil production rate where
the incremental oil production rate relative to an incremental gas injection rate
should be equal for all wells in the eld. The optimum point for a given group of
wells was found by Jamal (2001) using the application of Lagrange Multipliers.
An approach that depends on the functional relationship between oil production
and gas injection rates. Two types of functions, quadratic and rational functions
were used to t the gas injection against oil production data. This thesis used
spline based functions to t the gas injection verses oil production data. Gasin,
oil-out data t with spline based function produced better results than both
the rational function and quadratic function with regard to both data t and
resultant total optimum oil rate. The two methods used in this thesis were able
to increase the total oil production. However the total optimum oil production
rate for data tting with the spline based function is found to be higher than the
total optimum oil production rate for data tting with rational function. The
optimal value of the spline based function was found to be twice that of the
rational function.
Description
A Thesis submitted to the Department of Mathematics, Kwame Nkrumah
University of Science and Technology in partial ful llment of the requirements
for the degree of Master of Philosophy in Applied Mathematics