Patent ID: 8433516

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 the friction law function for the wave equation is represented as follows: C ⁡ ( x ) = δμ ⁡ ( x ) ⁡ [ Q ⁡ ( x ) + T ⁡ ( x ) ⁢ ∂ u ⁡ ( x , t ) ∂ x ] , wherein δ = ∂ u ⁡ ( x , t ) / ∂ t  ∂ u ⁡ ( x , t ) / ∂ t  t=time in seconds; x=distance of a point on the unrestrained rod measured from the polished rod in feet, and where u(x), Q(x) and T(x) are determined by mathematical modeling of a rod string in said wellbore.