Fluid load line calculation and concavity test for downhole pump card

A controller for a pump apparatus having a downhole pump disposed in a wellbore and having a motor at a surface of the wellbore, the downhole pump reciprocated in the wellbore by a rod string operatively moved by the motor, the controller comprising:

• one or more interfaces obtaining surface measurements indicative of surface load and surface position of the rod string at the surface;
• memory in communication with the one or more interfaces and storing a wave equation model having damping;
• and
• a processing unit in communication with the one or more interfaces and the memory and configured to:
• generate downhole pump data having values indicative of downhole load and downhole position of the downhole pump with the surface measurements and the wave equation model,
• determine, in a first determination, a first set of actual fluid load lines for actual fluid loads of each of an upstroke and a downstroke of the downhole pump from the values of the downhole pump data, the actual fluid load lines being additional to the values of the downhole pump data;
• determine, in a second determination different from the first determination, a second set of calculated fluid load lines for calculated fluid loads of each of the upstroke and the downstroke of the downhole pump from the values of the downhole pump data, the calculated fluid load lines being additional to the values of the downhole pump data and to the actual fluid load lines;
• compare the actual fluid load lines to the calculated fluid load lines to assess damping used to generate the downhole pump data, and
• modify at least one parameter of the pump apparatus based on the comparison.

A non-transitory program storage device having program instructions stored thereon for causing a programmable control device to perform a method of diagnosing a pump apparatus having a downhole pump disposed in a wellbore and having a motor at a surface of the wellbore, the downhole pump reciprocated in the wellbore by a rod string operatively moved by the motor, the method comprising:

• generating the downhole pump data having values indicative of downhole load and downhole position of the downhole pump by using surface measurements and a wave equation model having damping;
• determining, in a first determination, a first set of actual fluid load lines for actual fluid loads of each of an upstroke and a downstroke of the downhole pump from the values of the downhole pump data, the actual fluid load lines being additional to the values of the downhole pump data;
• determining, in a second determination different from the first determination, a second set of calculated fluid load lines for calculated fluid loads of each of the upstroke and the downstroke of the downhole pump from the values of the downhole pump data, the calculated fluid load lines being additional to the values of the downhole pump data and to the actual fluid load lines;
• assessing damping used to generate the downhole pump data by comparing the first set of actual fluid load lines to the second set of calculated fluid load lines;
• and
• modifying at least one parameter of the pump apparatus based on the comparison.