Paper: A Method to Find the Viscous Damping Coefficient And A Faster Diagnostic Model

Several methods of calculating downhole dynamometer cards from surface dynamometer cards have been presented in the literature. Each of the methods requires knowing the viscous damping coefficient. This paper presents a non-iterative method for finding this term. A new method for calculating-a downhole dynamometer card is also presented. This method is faster and more accurate than the fourier analysis and the finite difference method using the second order damped wave equation. In Gibb's patent, two methods of determining the damping coefficient are presented. One is empirically based and the other is an equation that requires knowledge of the pump horsepower. But to calculate the pump horsepower the damping coefficient must be known. Therefore, an iterative procedure is required. This paper presents a non-iterative method for calculating the viscous damping coefficient. An improvement of the method presented by Everitt is suggested and comments on variable damping are made. A coupled set of first order linear differential equations is solved using finite differences to obtain a pump card. A cyclic boundary condition called the wrap around is used to eliminate problems associated with the end points. The wrap around condition eliminates iterating and allows for direct solution.