Approach to shape factor determination in estimating horizontal wells productivity for pressure transient model of Mutalik et al.

Abstract

AbstractHorizontal well productivity (Jh) equation at pseudo-steady state (PSS) of Mutalik et al. (in: Presented at SPE 63rd annual technical conference and exhibition, Houston, Texas, 1988) has long and widely been known to estimate well performance. One key parameter of that equation is the so-called shape factor (CA) that characterizes the effect of the pressure transient behavior at PSS depending on well and reservoir configuration. For limited well and reservoir configurations, CA tables had been generated decades ago, but at unknown accuracy they are still used widely via tedious correlation or interpolation from those reported CA tables to estimate Jh for different configurations even today. The innovation points in this study are as follows: (1) The pressure transient model of Mutalik et al. (in: Presented at SPE 63rd annual technical conference and exhibition, Houston, Texas, 1988) (PTM) is improved to generalized pressure transient model (GPTM) and verified by converting several dimensional parameters to dimensionless forms. (2) An efficient algorithm is developed, and accurate CA and Jh are obtained for any well and reservoir configuration. (3) The accuracy of the reported CA tables is quantified, and the consequences are determined when they are used to estimate Jh. (4) New CA tables and their correspondence dimensionless time based on drainage area at PSS ((TDA)PSS) tables are generated for a wider range of well and reservoir configurations. Although horizontal wells usually have been drilled with high dimensionless well length (LD) industrially (i.e., LD > 10), it is still a significant error in Jh by (< 7%) that has been determined when using the reported CA of PTM for rectangular reservoir aspect ratio (xe/ye) = (1) and (2) in the both assumed input data, while for (xe/ye = 5), significant error in Jh starts from (46.43%) to (1037%) for LD = (10) to (100), respectively, in the first assumed input data [variable, dimensionless wellbore radius (rWD)] and expected the same in the second assumed input data (constant rWD).