This work presents new solutions to modeling the production performance of hydraulically fractured wells in unconventional reservoirs, where intensive hydraulic fracturing creates a stimulated reservoir volume (SRV) with an induced permeability field within.

We found previously that the permeability field induced in the SRV (single porosity) can be effectively represented by an exponential or linear dependence of permeability on the distance measured from the main hydraulic fracture plane. However, many researchers consider dual porosity as a necessary ingredient in modeling unconventional reservoirs.

In this work, we extend the induced permeability field model to the dual porosity idealization, considering transient fluid transfer from matrix to natural fractures and distance-dependent properties of the medium of secondary porosity (affected by the intensive stimulation).

We show that the combined effect of creating a main fracture and altering the properties of the medium of secondary porosity leads to a production behavior that can be characterized and understood provided that effects related to skin and varying flowing bottomhole pressure are correctly accounted for.

In addition to the standard diagnostic tools for decline-curve or rate-transient analysis, we use the ratio between the production time and material balance time, a dimensionless group that enables identifying the characteristic signatures of flow regimes. We provide practical criteria to identify various scenarios affecting the data during the pre-linear and prebilinear flow regimes in the reservoir (short times). Then we show that transient, late transient and boundary dominated flow periods can also be diagnosed using the dimensionless group, providing a useful addition to existing procedures involving conventional plots.

In connection to the new model, this work also discusses a novel approach to handle non-constant bottomhole pressure, the cause of significant distortion in production data at early times. In particular, we consider the effect of a bottomhole pressure exponentially approaching a stabilized value. We show that the deviation from the idealized constant bottomhole pressure case depends on the flow regime in the reservoir, fluid and reservoir properties, skin factor, and the mean lifetime (the time when 63% of the total change has happened) of the decaying part of the flowing pressure. The results reveal that half-, three-fourths-, and unit-slope straight lines (on log-log plot of production rate versus time) develop at short times during the increasing trend of production rate. These new flow regimes enable to gain useful information about the SRV from the early stage of the production history – if the quality of data allows such a detailed analysis.

We present a field example involving multi-fractured horizontal wells producing from a shale-gas reservoir, to illustrate, in a practical manner, how to apply the new approach when interpreting production history of wells in unconventional reservoirs.

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