Patent ID: 7869978

Claim:
A method of controlling a centrifugal pump disposed at a depth of the pump Xp below a surface in a wellbore extending downward from the surface and having a fluid level Xc therein, with the centrifugal pump including an output thereof connected to an output tube extending upward from the pump through the wellbore to the surface, fluid within the wellbore defining a specific weight Dc of the fluid in the wellbore and a wellbore pressure Pc at the surface, and fluid within the tube defining a specific weight Dt of the fluid in the tube and an internal pressure Pt of the fluid within the tube at the surface, the method comprising: determining values of input torque T and input speed Up to the centrifugal pump; selecting a rated-operating input speed Ur of the centrifugal pump, and determining a rated-output pressure Hr of the centrifugal pump when producing output flow at the rated-operating input speed Ur and rated-output pressure Hr; determining a zero-flow input speed Uz of the centrifugal pump, without using output flow from the centrifugal pump, by monitoring input torque T to the centrifugal pump as input speed Up of the pump is reduced from the rated input speed Ur, and detecting the zero-flow input speed Uz as an input speed Up at which an incremental reduction in input speed Up is not accompanied by a corresponding incremental reduction in input torque T; calculating a zero-flow pump differential pressure Hpz at the zero-flow input speed Uz by multiplying the normal-operating output pressure Hr by the square of the quotient of the zero-flow input speed Uz divided by the normal-operating input speed Ur, according to a calculation substantially including the mathematical expression Hpz≈Hr (Uz/Ur)^2; determining values of the tube pressure Pt and wellbore pressure Pc; calculating the zero-flow discharge pressure Hdz of the pump in a manner substantially including the expression Hdz≈(Dt*Xp)+Pt; calculating an intake head pressure Hs of the centrifugal pump, in a manner including the expression Hs≈Hdz−Hpz; calculating the fluid level Xc in the wellbore in a manner substantially including the expression Xc≈(Hs−Pc)/Dc; and controlling the centrifugal pump using at least one of the group consisting of: the determined zero-flow input speed Uz; the calculated zero-flow pump differential pressure Hpz; the calculated zero-flow discharge pressure Hdz; the calculated intake head pressure Hs; and the calculated fluid level Xc in the wellbore.