Accurate prediction of the average plunger rise velocity is important to optimally unload liquid from a plunger lifted well. A modified Foss and Gaul model presented in this paper predicts the minimum build casing pressure criteria to open the motor controlled valve for a selected plunger rise velocity. Results from the modified Foss and Gaul model are contrasted with results from the original Foss and Gaul model. The minimum build casing pressures predicted using both models are compared to measured casing pressures at the same rise velocities measured from field data acquired on 10 different plunger lifted wells.
During the shut-in time period the plunger falls through gas, liquid and then rests at bottom on the bumper spring. At the end of this time period when the surface valve opens sufficient pressure is required to build to enough magnitude to unload the accumulated liquid and conventional plunger from the bottom of the well to the surface. An industry rule-of-thumb load factor criterion is frequently used to determine at what casing pressure build, Pc, the well should be opened to unload the liquid to the surface. The best technique to predict the maximum casing build pressure, Pcmax, is to use a Foss and Gaul type model to predict the rise velocity within a range of 500–1000 feet per minute (fpm), more optimally at 750 fpm that will unload the plunger and liquid to the surface.
The modified Foss and Gaul model favorably predicts a required casing operating pressure to bring the plunger and liquid to the surface at a specified average rise velocity. Using the modified model will allow an operator to determine the maximum shut-in casing pressure a plunger lifted well should be allowed to build before opening the valve and safely bring the plunger to the surface.
The most common form of plunger lift is the conventional plunger lift method. This method includes an after-flow production time period with the plunger held at the surface. During the latter time of the production period, or when liquids are sensed to be accumulating in tubing of the well. The well is shut in for a period of time required for the plunger to fall through gas, through accumulated liquids, plus an additional time where the plunger will rest on the bottom hole bumper spring. The well is then opened to begin the unloading period and the plunger with liquids above, rises to the surface, delivers the liquid slug and then the production period begins again with the plunger held by differential pressure at the surface. Another form of plunger lift is continuous flow or a quick drop plunger cycle with minimum shut-in time. The type of plunger that opens to allow gas to pass through the plunger during the fall is not discussed in the paper. The emphasis of this paper is a model (compared to field data) to predict, during shut-in, when the casing operating pressure has reached a value of pressure that will bring the plunger and liquid slug up the well at a desired average velocity of rise. The desired velocity of rise, from industry experience, is 500–1000 fpm with be best value being 700–800 fpm average rise velocity. This paper presents a modified Foss and Gaul model to determine how casing operating build up pressure relates to average rise velocity of the plunger and liquid slug.