Preliminary Study of Dependence of the Modification Factor Controlling Generation of Periodic Wellbore Flow

Abstract

The authors previously revealed a universal condition controlling generation of periodic wellbore flow due to inflow of a lower-enthalpy fluid at a shallow feed zone, while producing from a deep feed zone. This paper reports a preliminary study of the dependence of a modification factor on dimensionless parameters involved in this universal condition, which remains unstudied. Revealing this dependence by deriving an empirical equation, we will be able to reduce computational loads dramatically to determine the modification factor. Based on the total derivative of the modification factor, two dimensionless parameters representing the productivity index of the deep reservoir and the shallow reservoir depth were selected for a further study. Investigating changes in the modification factor depending on these two dimensionless parameters, we have found nonlinear relationship with each dimensionless parameter, including steep and highly nonlinear changes depending on the dimensionless shallow reservoir depth. Vertical pressure gradient, which has been assumed to be constant, is also expected to play a key role in the dependence of the modification factor.