Application of Mass Balance in Pumping Well Analysis (includes associated papers 11316 and 11317 and 11321 and 11343 )
Authors: Kabir C.S. , Hasan A.R. 
Published: December 2007

Summary
The principle of mass balance of gas phase in the annulus may be used to estimate flowing bottom hole pressure(BHP) of a pumping oil well. The method enables one to calculate the annular gas volume, including gas bubbles in the oil column. The knowledge of annular gas volume then can be used to find the pseudo length of both the oil and gas columns and hence the flowing BHP to allow calculation of a well's productivity index. This technique is particularly applicable in wells with a foaming annulusbecause, under such circumstances, the acoustic well-sounding (AWS) method yields questionable results because of the absence of a distinct gas/oil interface.
This paper demonstrates that improper application of the mass balance equation (MBE) may lead to seriouse rrors in estimating the annular gas rate and the flowing BHP. The inaccuracy stems from lack of knowledge of the true annular gas rate when the MBE is applied to the total gas in the system (tubing and annulus). Because only a fraction of the total gas is produced through the annulus, the actual annular gas rate is not known beforehand unless measured at the surface. The methods uggested in this work develops the MBE for the gas phase in the annulus only, there by avoiding the problem.
The flowing BHP can be estimated by conducting a short buildup test and extrapolating the buildup data to zero time. The proposed method avoids the erroneous application of the MBE for the saturated condition of the oil present down hole.

Introduction
The knowledge of flowing BHP, pwf, of an oil welloperating at either pseudo steady-state or steady-state condition is an essential element in predicting its deliver ability potential. The flow rate corresponding to the pwf is the first differential (i.e., the productivityindex) of the inflow performance curve, Ipr. The stable solution obtained by super imposing the tubing performance curve on the Ipr curve yields the maximum possible flow rate. This information is necessary for properpump design. Since about 76% of all oil wells in the U.S. are being operated by sucker-rod pumps, the importance of accurate estimation of flowing BHP cannot be over emphasized.
In-situ measurement of BHP in flowing oil wells can be accomplished by subsurface pressure recorders. However, the pumping oil wells present special problems. A conventional pressure recorder cannot be rundown the tubing string in a sucker-rod pumping oil well. The alternatives are a nitrogen tube or other permanent down hole equipment; however, the initial cost is high for such permanent pressure recording devices and the same wells must be tested each time.
AWS offers the potential for obtaining reliable flowing BHP data in certain cases. Unfortunately, estimating fluid density in the tubing/casing annulus is not easy when the oil is in a saturated condition-i.e., when the flowing BHP is below the bubble-point pressure(pwf is less than pb). In the case of AWS, inaccurate estimation of the fluid column density is a source of significant error, especially when the gas/oil ratio (GOR) is high. However, reasonable estimates of fluid column densitymay be made with the correlations either of Podio etal. or of Godbey-Dimon. The AWS completely breaks down when the oil has the tendency to foam. This is because the foam column absorbs the acoustic wave, and consequently the gas/oil interface, with foam inbetween, remains undetected. In some cases the foam may be dense enough to indicate an erroneously high liquid level. The AWS method can work reliably only when the oil present down hole remains in under saturated condition-i.e., pwf is greater than pb. In that situation the dead oil column density can be used, and confidence in the AWS data is enhanced considerably.
JPT
P. 1002^