Existing transient triple-porosity models for fractured horizontal wells do not converge to linear dual-porosity models (DPM) in the absence of micro-fractures (MF). The reason is the assumption of sequential-depletion from matrix to MF, and from MF to hydraulic-fractures (HF). This can result in unreasonable estimates of MF and/or HF parameters. Hence, a quadrilinear flow model (QFM) is proposed which relaxes the sequential-depletion assumption.
To allow simultaneous matrix-MF and matrix-HF depletion, the matrix volume is conceptually divided into two sub-domains; one feeds HF and the other feeds MF. This breaks a single 2-D problem into two 1-D problems. Using Laplace transforms, the flow equations are solved under constant-rate and constant-pressure well constraints. Type-curves are generated by numerically inverting the resulting Laplace-space solutions to time-space using Gaver-Stefhest algorithm. QFM converges to the linear sequential triple-porosity model (STPM) in the absence of matrix-HF communication; and converges to the DPM in the absence of MF. Flow-regimes observed comprise linear, bilinear, and boundary dominated. The number of flow-regimes depends on the matrix-MF, matrix-HF andMF-HF communication coefficient values.
QFM matches production history of two fractured horizontal wells completed in Bakken and Cardium Formations. Reservoir parameters like HF half-length, HF and MF permeabilities and MF spacing are estimated from the history match. These reservoir parameters are estimated as ranges of values instead of single values to reflect the non-uniqueness of the type-curve match. A QFM comparative study reveals that STPM underestimates MF spacing while DPM overestimates HF half-length.