Patent ID: 8036829

Claim:
An instrumentation system for assessing operation of a reciprocating pump system producing hydrocarbons from a non-vertical wellbore which extends from the surface into the earth, the system comprising, a data gathering system which provides signals representative of surface operating characteristics of the pumping system, and characteristics of said non-vertical wellbore, a processor which receives said operating characteristics with said characteristics of said non-vertical wellbore and generates a surface card representative of surface polished rod load, as a function of surface polished rod position, with said processor determining a friction law function based on said characteristics of said non-vertical wellbore, and with said processor periodically generating a downhole pump card as a function of said surface card and said friction law function for a wave equation which describes the linear vibrations in a long slender rod, wherein, said wave equation for a deviated well is of the form, ∂ 2 ⁢ u ⁡ ( x , t ) ∂ t = v 2 ⁢ ∂ 2 ⁢ u ⁡ ( x , t ) ∂ x 2 - c ⁢ ∂ u ⁡ ( x , t ) ∂ t - C ⁡ ( x ) + g ⁡ ( x ) in ⁢ ⁢ which C ⁡ ( x ) = δ ⁢ ⁢ μ ⁡ ( x ) ⁡ [ Q ⁡ ( x ) + T ⁡ ( x ) ⁢ ∂ u ⁡ ( x , t ) ∂ x ] δ = ∂ u ⁡ ( x , t ) / ∂ t  ∂ u ⁡ ( x , t ) / ∂ t  where C(x) represents rod on tubing drag force, and where v=velocity of sound in steel in feet/second; c=damping coefficient, 1/second; t=time in seconds; x=distance of a point on the unrestrained rod measured from the polished rod in feet; u(x,t)=displacement from the equilibrium position of the sucker rod in feet at the time t, and g(x)=weight of pump rod pump assembly in the x direction, and where μ(x), Q(x) and T(x) are determined by mathematical modeling of a rod string in said wellbore.