Revisiting the Dual-Porosity/Dual-Permeability Modeling of Unconventional Reservoirs: The Induced-Interporosity Flow Field

Abstract

Summary This work presents a new approach to account for variable matrix-block size in the well performance of unconventional shale reservoirs. In contrast to the standard models that consider either a fixed matrix-block size or a stochastic distribution of sizes with no particular dependence on the spatial location, in this model we consider the case when the characteristic length of the blocks depends on the distance from the main hydraulic-fracture plane. In particular, we assume that, as a result of the hydraulic-fracturing treatment, the density of microfractures (natural and induced) is high near the hydraulic-fracture face, but gradually decreases away from it. In other words, the matrix-block size is an increasing function of the distance from the fracture face. We show that the boost of the contact area between the matrix blocks and the microfractures can be the determinant feature of hydrocarbon production from shale reservoirs, even when the natural and induced microfractures do not have uniform density throughout the whole stimulated reservoir volume. In addition, the elongated linear flow (the consensus characteristic signature in the well performance of shale systems) may be the result of an induced interporosity flow when the matrix-/fracture-permeability ratio is small. The duration of this flow regime increases if the effective size of the matrix-block distribution increases. On the other hand, the linear flow can be the result of the total-system response when the matrix-/fracture-permeability ratio is high; in this case, the beginning of the linear flow is strongly affected by the small matrix blocks near the hydraulic-fracture faces. The resulting mathematical model in Laplace space has a fundamentally different structure compared with standard dual-porosity models because of the spatial dependence of the parameters characterizing the interporosity flow. In this work, we develop the Airy-spline scheme, a new technique to calculate the pressure solution in an efficient way. Closed-form approximate formulae in the time domain are also provided, revealing that during the induced linear-interporosity-flow period, the production behavior is controlled by the logarithmic mean of the minimum and maximum matrix-block size. A field example from the Barnett shale is presented to illustrate the use of the new model.

Pressure Response of a Horizontal Well in Tight Oil Reservoirs with Stimulated Reservoir Volume

“…During the process of the stimulated reservoir volume, a series of secondary fractures are formed, which greatly increases the contact area between the fracture wall and the reservoir, minimizes the seepage distance from pore to hydraulic fractures, and greatly improves well production [32]. There is a complex fracture network in the fractured area, and the dual porosity medium model is widely used to study the flow mechanism in the fractured area (Figure 3) [33,34]. Wang and Cheng used the slab model and fractal theory to build a mathematical model between the permeability and the effective stress of fracture system [31]:…”

A Markov-Chain-Based Method to Characterize Anomalous Diffusion Phenomenon in Unconventional Reservoir

“…• Although, in reality, the unconventional reservoir formations have the strong heterogeneity due to fractures in nearly all scales (Gale et al 2014), for the purpose of this work we only take into account the macroscopic fractures (larger than ~10 −3 ft).…”

“…Bello and Wattenbarger (2008) combined the slab matrix transient dual porosity model with RTA to study the usage of various shape factor formulations and the effect of matrix geometry on the transient linear response. Fuentes-Cruz and Valko (2015) applied the dual-porosity/dualpermeability model to study the proposed concept of variable matrix-block size and their resulting mathematical model is fundamentally different compared with the standard dual-porosity model due to the interporosity flow. Given the ultra-low permeability of the formation matrix and the extensively elongated transient regime, trilinear model (Lee and Brockenbrough 1983) has been introduced as a simplified but useful "asymptotic" model to study the flow in unconventional reservoirs.…”

A Hybrid Dual-Continuum Discrete Fracture Modeling Approach for Numerical Simulation of Production from Unconventional Plays

“…To better handle the heterogeneous properties within the SRV region, several models have been proposed to describe reservoir properties as a function of distance form the hydraulic fracture stages (Raghavan and Chen 2013;Fuentes-Cruz and Valko 2015). For each grid block in the SRV region, we record the distance between the center of the grid block to its nearest hydraulic fracture stage, thereby accounting for variation of properties with distance.…”