Determining Bottom-Hole Pumping Conditions in Hydraulically Pumped Wells
Authors: Buehner Lon D. , Nisbrugge Thomas W. 
Published: December 2007

Introduction
Determining the working bottom-hole pressure of a hydraulically pumped well without running a pressure bomb would be valuable in oilfield operations, saving time, money, and production. Also, constant surveillance of the pumping status of a well would enable field personnel to determine if a well is producing properly. The working bottom-hole pressure producing properly. The working bottom-hole pressure can be calculated by using the last-stroke pressure method, which involves a gradual decrease of the power-oil rate until the pump stops stroking. The power-oil rate until the pump stops stroking. The surface power-oil feed pressure observed at the time the pump stops stroking is the pressure required to balance the forces acting on the pump pistons. The hydraulics governing this system allow the working bottom-hole pressure to be determined from the last-stroke pressure.

Discussion
The hydraulics governing the open and closed power-oil systems theoretically provide for the last-stroke method of determining the working bottom-hole pressure. At the time the hydraulic pump stops stroking, the power-oil feed pressure is the pressure required to power-oil feed pressure is the pressure required to balance the forces on the pump pistons. Equating the forces at the engine with the pump-end pistons when they are balanced will result in the equations used to calculate the working bottom-hole pressure. Eq. 1 is the equation for the working bottom-hole pressure as it is applicable to an open power-oil system. Eq. 2 is the equation used to calculate the working bottom-hole pressure in a closed power-oil system. power-oil system.
p1 (Ap) + 1) (p2 + Dgf) − AD (p3 + Dgo).... (1)
p1 = AD (p4 − p3) + p2 + Dgf...............(2)
Eqs. 1 and 2 are similar to equations developed by Coberly and Barnes in their studies of determining bottom-hole operating conditions in hydraulically pumped wells. However, the last-stroke method pumped wells. However, the last-stroke method eliminates the need for determining the friction factor involved because, as the pump approaches the last stroke, the fluid velocities have decreased to a point where friction losses are negligible. The equations also may be applied in wells equipped with packers where fluid-level measurements cannot be obtained.

Field Application
The derived last-smoke method for determining bottom-hole conditions in hydraulic pumps was applied to a waterflood project producing no sand or gas, The average pump-setting depth was 4,950 ft.
In running the last-stroke tests, it was determined that the surface power-oil pressure is usually a large number, and thus is the most important value measured. Any error attributable to the inaccuracy of the gauge on the surface flowline is normally negligible because of its small value. When the last-stroke method was first applied, the pressure gauges in the wellheads were determined to be inaccurate, as much as 1,000 psi in error.
To eliminate this error, the wells were equipped with needle valves located between the three-way valve on the wellhead and the shut-off valve for the incoming power oil. The needle valve was adaptable to a power oil. The needle valve was adaptable to a precision pressure gauge. The use of the more accurate precision pressure gauge. The use of the more accurate pressure gauge greatly improved the accuracy of the pressure gauge greatly improved the accuracy of the laststoke method for determining the working bottom-hole pressure. pressure. The actual running of the last-stroke test is a relatively simple operation. One man is located at the wellhead watching the last-stroke pressure.
JPT
P. 810