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*Surface pressure (line pressure and restrictions) acting against the plunger travel. | *Surface pressure (line pressure and restrictions) acting against the plunger travel. | ||
Several publications have dealt with this approach. Beeson et al.<ref name=" | Several publications have dealt with this approach. Beeson et al.<ref name="r3" /> first presented equations for high-GLR wells in 1955, on the basis of an empirically derived analysis. Foss and Gaul<ref name="r4" /> derived a force-balance equation for use on oil wells in the Ventura Avenue field in 1965. Lea<ref name="r14"/> presented a dynamic analysis of plunger lift that added gas slippage and reservoir inflow, and mathematically described the entire cycle (not just plunger ascent) for tight-gas/very high-GLR wells. | ||
Foss and Gaul’s methodology<ref name="r4"/> was to calculate (p<sub>c</sub>)min, the casing pressure required to move the plunger and liquid slug just before it reaches the surface. Because (p<sub>c</sub>)min is at the end of the plunger cycle, the energy of the expanding gas from the casing to the tubing is at its minimum. Adjusting (p<sub>c</sub>)min for gas expansion from the casing to the tubing during the full plunger cycle yields (p<sub>c</sub>)<sub>max</sub> , the pressure required to start the plunger at the beginning of the plunger cycle. The pressure must build to (p<sub>c</sub>)<sub>max</sub> to operate successfully. | Foss and Gaul’s methodology<ref name="r4"/> was to calculate (p<sub>c</sub>)min, the casing pressure required to move the plunger and liquid slug just before it reaches the surface. Because (p<sub>c</sub>)min is at the end of the plunger cycle, the energy of the expanding gas from the casing to the tubing is at its minimum. Adjusting (p<sub>c</sub>)min for gas expansion from the casing to the tubing during the full plunger cycle yields (p<sub>c</sub>)<sub>max</sub> , the pressure required to start the plunger at the beginning of the plunger cycle. The pressure must build to (p<sub>c</sub>)<sub>max</sub> to operate successfully. | ||
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[[File:Vol4 page 0858 eq 002.png]] ........................(30) | [[File:Vol4 page 0858 eq 002.png]] ........................(30) | ||
Assume some values for S (bbl) and construct '''Table 3'''. | Assume some values for S (bbl) and construct '''Table 3'''. | ||
<gallery widths=300px heights=200px> | <gallery widths=300px heights=200px> |
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