Abstract:
A pump apparatus has a downhole pump disposed in a wellbore and has motor at a surface of the wellbore, and the downhole pump is reciprocated in the wellbore by a rod string operatively moved by the motor. A card indicative of load and position of the downhole pump is generated using surface measurements and a wave equation model having a damping factor or two damping factors. Actual fluid load lines are determined from the downhole card for upstroke and downstroke of the downhole pump, and calculated fluid load lines from the load distribution of the downhole data. The actual fluid load lines are compared to the calculated fluid load lines so that at least one parameter of the pump apparatus can be modified based on the comparison. For example, the damping of the wave equation model can be adjusted so that another downhole card can be generated.
Abstract:
Diagnosing a pump apparatus having a downhole pump disposed in a deviated wellbore characterizes axial and transverse displacement of a rod string with two coupled non-linear differential equations of fourth order, which include axial and transverse equations of motion. To solve the equations, derivatives are replaced with finite difference analogs. Initial axial displacement of the rod string is calculated by assuming there is no transverse displacement and solving the axial equation. Initial axial force is calculated using the initial axial displacement and assuming there is no transverse displacement. Initial transverse displacement is calculated using the initial axial force and the initial axial displacement. Axial force and friction force are calculated using the initial displacements, and the axial displacement at the downhole pump is calculated by solving the axial equation with the axial force and the friction force. Load at the downhole pump is calculated so a downhole card can be generated.