Many fractured horizontal wells are completed in tight oil/gas or shale gas reservoirs which have significant networks of interconnected secondary fractures (SF). However, the existing linear transient dual- and triple-porosity models do not properly account for SF. While the dual-porosity model assumes negligible SF, the linear sequential triple-porosity model assumes negligible fluid transfer between the rock matrix and hydraulic fractures. Hence, the application of these models for production data analysis of fractured horizontal wells could result in unreasonable reservoir/fracture parameter estimates and hydrocarbon forecast. For this reason, the quadrilinear flow model (QFM) was developed to account for matrix—hydraulic fracture communication. Although QFM properly accounts for the contribution of SF during reservoir depletion, reservoir parameter estimation from its type-curve matching procedure has a high degree of uncertainty. This paper proposes simplified QFM flow regime equations to reduce the uncertainty associated with reservoir parameter estimation.

This study carefully analyzes the general QFM solution by observing the flow regions from dimensionless rate and pressure type-curves. This solution is simplified by eliminating dimensionless parameters with negligible contribution to fluid depletion within the duration of each flow region. The resulting simplified equations are analytically inverted from Laplace space to time space. The simplification process 1) yields flow-region analysis equations for the specialized rate-normalized pressure and pressure derivative plots and 2) explains the possible physics behind the flow-regions.

The effect of secondary fracture networks on reservoir depletion can be investigated by applying QFM analysis equations on specialized rate-normalized pressure and pressure derivative production data plots. The choice of these plots is based on operational well constraints and observable flow regions. The analysis equations are applied to interpret production data of two multifractured horizontal wells completed in the Cardium and Bakken Formations. The results estimate effective half-length of hydraulic fractures, investigate the presence/absence of secondary fractures and propose a workflow for handling the uncertainty in reservoir parameter estimation when applying the specialized analysis equation plots.

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