Analysis of Well-Testing Data From a Restricted-Entry Well

Abstract

Abstract This work investigates the analysis of well test pressure data from a restricted-entry well using pressure pressure data from a restricted-entry well using pressure and pressure derivative type curves constructed from constant-rate solutions. For cases where wellbore storage effects are negligible, it is shown that type curves constructed from constant rate solutions can be used to analyze rate data from wells producing at a constant bottom-hole pressure and that these type curves can also be used to analyze data obtained from gas wells. For cases where data are influenced by wellbore storage and skin effects, it is shown that a new analysis procedure using complete-penetration type curves based on dimensionless pressure and a dimensionless assure/pressure derivative pressure and a dimensionless assure/pressure derivative group can usually be used to obtain a complete analysis of data. The analysis procedures presented yield estimates of horizontal permeability, the mechanical skin factor and the vertical permeability. Introduction Wells are often completed over a fraction of their productive zone in order to delay or prevent water and/or productive zone in order to delay or prevent water and/or gas coning. A well completed in this way is called a restricted-entry or partially-penetrating well. The restricted-entry well problem was considered in the petroleum engineering literature as early as 1949 (Muskat) petroleum engineering literature as early as 1949 (Muskat) and has since been considered in numerous publications; see for example Refs. 2–11. Pressure data obtained at a restricted-entry well may exhibit two semilog straight lines if wellbore storage effects are negligible. In such rare cases, a complete analysis can be obtained based on semilog methods see Ref. 5 for the single-layer case and Ref. 10 for the multi-layer case. The analysis procedures of Refs. 5 and 10 yield estimates of both horizontal and vertical permeability, an estimate of the mechanical skin factor due to damage or stimulation and an estimate of the pseudoskin factor due to restricted-entry. Various correlations for estimating the pseudoskin factor have been presented for the single-layer reservoir case. Refs. 8 and 11 have presented formulas for computing the pseudoskin factor which apply for both single and multilayer reservoirs. As the early time semilog straight line is usually obscured by wellbore storage effects, one must normally rely on the existence of the pseudoradial flow semilog straight line in order to analyze pressure data. Semilog analysis of pseudoradial flow data yields estimates of the horizontal permeability (thickness averaged horizontal permeability for the layered case) and the total skin factor permeability for the layered case) and the total skin factor which is a linear combination of the mechanical skin factor and the pseudoskin factor, see Refs. 5, 7, 8 and 10. Ref. 10 presented semilog type curves which could be used in presented semilog type curves which could be used in conjunction with semilog analysis of pseudoradial flow data to obtain a complete analysis of pressure data obtained at a restricted-entry well. The analysis procedure of Ref. 10 yields estimates of average horizontal permeability, average vertical permeability, the mechanical skin factor, the pseudoskin factor and the average flow capacity adjacent to the open interval. The analysis procedure requires that wellbore storage effects become negligible at least one log cycle prior to the time at which pseudoradial flow begins and is not applicable if the wellbore storage coefficient is large. Chu et al. have shown that for certain values of the correlating parameters, the wellbore storage and skin dimensionless pressure response for a restricted-entry well can be correlated with the analogous complete-penetration wellbore storage and skin solution provided that the penetration ratio is incorporated into the pressure and penetration ratio is incorporated into the pressure and time scales and the complete-penetration correlating parameter, CD exp(2s), is replaced by CD exp(2s)/b where parameter, CD exp(2s), is replaced by CD exp(2s)/b where b is the penetration ratio. Effectively, this correlation is valid if the reservoir/well parameters are such that the pressure response is dominated by the part of the reservoir which is adjacent to the open interval. On the other hand if vertical permeability and the wellbore storage constant are large, then Ref. 12 shows that the restricted-entry solution can be approximately correlated with the complete-penetration solution provided that the complete-penetration correlating parameter, CD exp(2s) is replaced by CD exp(2st), where st parameter, CD exp(2s) is replaced by CD exp(2st), where st denotes the total skin factor. As pointed out by Kuchuk and Kirwan, the two correlation techniques presented in Ref. 12 cannot be rigorously justified from the analytical solution. P. 463