Significance of non-Darcy flow effect in fractured tight reservoirs

Saboorian‐Jooybari, Hadi; Pourafshary, Peyman

doi:10.1016/j.jngse.2015.03.003

“…Several researchers found a correlation to exist between local values of the Forchheimer coefficient and other properties of the porous medium; the different formulations of this relationship, either theoretically or empirically based, are summarized by Li and Engler (2001); according to them, a good representation of most of the previous work, either of theoretical or experimental nature, is provided by the formulation in which is porosity, is tortuosity, and c 1 , c 2 , and c 3 are three experimental constants for an assigned porous medium. Similar formulations are reported in Skjetne et al (2001) and Saboorian-Jooybari and Pourafshary (2015), albeit with = 1 . The former authors note that as [k] = [L 2 ] and [ ] = [L −1 ] , media that are scaled copies of each other have c 2 = 0.5 .…”

Section: Empirical ˇ− K Correlationssupporting

confidence: 63%

“…In what follows, we assume the latter value of a to be valid also for the case c = 1.5 as a = 187724450 m 2 . Additional, different experimental values of a can be found in Saboorian-Jooybari and Pourafshary (2015) for different correlations of and k.…”

Section: Empirical ˇ− K Correlationsmentioning

confidence: 99%

Effective Forchheimer Coefficient for Layered Porous Media

Lenci

¹

,

Zeighami

²

,

Federico

³

2022

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Inertial flow in porous media, governed by the Forchheimer equation, is affected by domain heterogeneity at the field scale. We propose a method to derive formulae of the effective Forchheimer coefficient with application to a perfectly stratified medium. Consider uniform flow under a constant pressure gradient $$\Delta P/L$$ Δ P / L in a layered permeability field with a given probability distribution. The local Forchheimer coefficient $$\beta$$ β is related to the local permeability k via the relation $$\beta =a/k^c$$ β = a / k c , where $$a>0$$ a > 0 being a constant and $$c\in [0,2]$$ c ∈ [ 0 , 2 ] . Under ergodicity, an effective value of $$\beta$$ β is derived for flow (i) perpendicular and (ii) parallel to layers. Expressions for effective Forchheimer coefficient, $$\beta _e$$ β e , generalize previous formulations for discrete permeability variations. Closed-form $$\beta _e$$ β e expressions are derived for flow perpendicular to layers and under two limit cases, $$F\ll 1$$ F ≪ 1 and $$F\gg 1$$ F ≫ 1 , for flow parallel to layering, with F a Forchheimer number depending on the pressure gradient. For F of order unity, $$\beta _e$$ β e is obtained numerically: when realistic values of $$\Delta P/L$$ Δ P / L and a are adopted, $$\beta _e$$ β e approaches the results valid for the high Forchheimer approximation. Further, $$\beta _{e}$$ β e increases with heterogeneity, with values always larger than those it would take if the $$\beta - k$$ β - k relationship was applied to the mean permeability; it increases (decreases) with increasing (decreasing) exponent c for flow perpendicular (parallel) to layers. $$\beta _{e}$$ β e is also moderately sensitive to the permeability distribution, and is larger for the gamma than for the lognormal distribution.

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“…For the flow behaviors of fluid in crushed coal are derived based on the Darcy‐Forchheimer law, which can be described as follows 23

- ((), \nabla P_{k} - italicρg) = \frac{μ_{k}}{{normalK}_{k}} \cdot normalv + ρ (‖‖, v) β_{k} normalv

where K and β can be calculated from a convinced relationship of porosity and grain size 24 …”

Section: Simulation Approachmentioning

confidence: 99%

Numerical approach of liquid carbon dioxide injection in crushed coal and its experimental validation

Yu

¹

,

Yang

²

,

Gu

³

et al. 2020

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Summary The safety issues are a major restriction on coal mining and growing efforts are being made in the search for solutions that will guarantee sustainable use of energy resources. Liquid carbon dioxide is attracting particular interest of coal fire‐fighting due to the promising efficiency of cooling and asphyxia. Our objective is to develop a valid model to simulate the dispersion and thermal behaviors of liquid carbon dioxide under crushed coal condition and assessment of liquid carbon dioxide injection for coal fire‐fighting. For this purpose, a numerical approach which requires an accurate state equation for calculating physical parameters of carbon dioxide, also accounts for appropriate description of energy transformation during the injection is presented. The validation of such a model against three experimental tests on temperature variation is proposed, and the model has proved capable of accurately predicting the heat and mass transfer process when liquid carbon dioxide is injected into crushed coal. Furthermore, the impact of nozzle diameter on the dispersion and thermal behaviors of liquid carbon dioxide is extensively investigated.

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“…To investigate the fluid flow mechanism in porous materials, Henry Darcy did massive experiments and developed his famous correlation to describe the dynamics of fluid flow in porous media, namely, for Darcy Law. However, the further research of percolation in tight reservoir, particularly in nanoporous reservoir, shows that hydraulic characteristics are more complicated and multicontrolled, which is beyond Darcy Low [3][4][5][6]. The deviation from the linearity of Darcy's equation was observed at high flow rate [7], and this is called non-Darcy flow [8].…”

Section: Introductionmentioning

confidence: 99%

“…The non-Darcy coefficient, as called by Saboorian-Jooybari and Pourafshary [4], in the equation that is used to describe the non-Darcy flow was hard to defined. Therefore, the behavior of fluid in tight reservoir still awaits to be revealed.…”

Section: Introductionmentioning

confidence: 99%

The Controls of Pore-Throat Structure on Fluid Performance in Tight Clastic Rock Reservoir: A Case from the Upper Triassic of Chang 7 Member, Ordos Basin, China

Zhang

¹

,

Bao

²

,

Yang

³

et al. 2018

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The characteristics of porosity and permeability in tight clastic rock reservoir have significant difference from those in conventional reservoir. The increased exploitation of tight gas and oil requests further understanding of fluid performance in the nanoscale pore-throat network of the tight reservoir. Typical tight sandstone and siltstone samples from Ordos Basin were investigated, and rate-controlled mercury injection capillary pressure (RMICP) and nuclear magnetic resonance (NMR) were employed in this paper, combined with helium porosity and air permeability data, to analyze the impact of pore-throat structure on the storage and seepage capacity of these tight oil reservoirs, revealing the control factors of economic petroleum production. The researches indicate that, in the tight clastic rock reservoir, largest throat is the key control on the permeability and potentially dominates the movable water saturation in the reservoir. The storage capacity of the reservoir consists of effective throat and pore space. Although it has a relatively steady and significant proportion that resulted from the throats, its variation is still dominated by the effective pores. A combination parameter ( ) that was established to be as an integrated characteristic of pore-throat structure shows effectively prediction of physical capability for hydrocarbon resource of the tight clastic rock reservoir.

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Significance of non-Darcy flow effect in fractured tight reservoirs

Cited by 29 publications

References 27 publications

Effective Forchheimer Coefficient for Layered Porous Media

Effective Forchheimer Coefficient for Layered Porous Media

Numerical approach of liquid carbon dioxide injection in crushed coal and its experimental validation

The Controls of Pore-Throat Structure on Fluid Performance in Tight Clastic Rock Reservoir: A Case from the Upper Triassic of Chang 7 Member, Ordos Basin, China

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