Step‐drawdown tests and the Forchheimer equation

Mathias, Simon A.; Todman, Lindsay

doi:10.1029/2009wr008635

Cited by 47 publications

(37 citation statements)

References 34 publications

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“…In the field of reservoir engineering, fluid flow behavior near the well screen controls the efficiency of oil/gas production wells (e.g., Holditz and Morse 1976;Aulisa et al 2009), as well as the efficiency of injection/extraction wells in groundwater resources applications (e.g., Sen 1989;Mathias and Todman 2010;Wen et al 2011Wen et al , 2013Yeh and Chang 2013;Houben 2015;Mathias and Moutsopoulos 2016). Moreover, nonlinear flow at full-aquifer scale in a broad range of geological formations, such as gravel, karstic or fractured aquifers, is widely addressed in the literature (e.g., Moutsopoulos and Tsihrintzis 2005;Moutsopoulos 2007).…”

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confidence: 99%

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

et al. 2017

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The current study provides new experimental data on nonlinear flow behavior in various uniformly graded granular materials (20 samples) ranging from medium sands (d 50 > 0.39 mm) to gravel (d 50 = 6.3 mm). Generally, theoretical equations relate the Forchheimer parameters a and b to the porosity, as well as the characteristic pore length, which is assumed to be the median grain size (d 50 ) of the porous medium. However, numerical and experimental studies show that flow resistance in porous media is largely determined by the geometry of the pore structure. In this study, the effect of the grain size distribution was analyzed using subangular-subrounded sands and approximately equal compaction grades. We have used a reference dataset of 11 uniformly graded filter sands. Mixtures of filter sands were used to obtain a slightly more well-graded composite sand (increased C u values by a factor of 1.19 up to 2.32) with respect to its associated reference sand at equal median grain size (d 50 ) and porosity. For all composite sands, the observed flow resistance was higher than in the corresponding reference sand at equal d 50 , resulting in increased a coefficients by factors up to 1.68, as well as increased b coefficients by factors up to 1.44. A modified Ergun relationship with Ergun constants of 139.1 for A and 2.2 for B, as well as the use of d m − σ as characteristic pore length predicted the coefficients a and b accurately.

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confidence: 99%

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

et al. 2017

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“…The Geertsma (1974) correlation has been found to correspond to large quantities of empirical data (Mathias & Todman 2010). Multiplying the correlation by 10 represents an upper bound on likely non-Darcy effects in this porosity range.…”

Section: Numerical Solutionsmentioning

confidence: 99%

Heat transport and pressure buildup during carbon dioxide injection into depleted gas reservoirs

2014

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In this article, a two-layer vertical equilibrium model for the injection of carbon dioxide into a low-pressure porous reservoir containing methane and water is developed. The dependent variables solved for include pressure, temperature and CO 2 -CH 4 interface height. In contrast to previous two-layer vertical equilibrium models in this context, the compressibility of all material components is fully accounted for. Non-Darcy effects are also considered using the Forchheimer equation. The results show that, for a given injection scenario, as the initial pressure in the reservoir decreases, both the pressure buildup and temperature change increase. A comparison was conducted between a fully coupled non-isothermal numerical model and a simplified model where fluid properties are held constant with temperature. This simplified model was found to provide an excellent approximation when using the injection fluid temperature for calculating fluid properties, even when the injection fluid was as much as ±15 • C of the initial reservoir temperature. The implications are that isothermal models can be expected to provide useful estimates of pressure buildup in this context. Despite the low viscosity of CO 2 at the low pressures studied, non-Darcy effects were found to be of negligible concern throughout the sensitivity analysis undertaken. This is because the CO 2 density is also low in this context. Based on these findings, simplified analytic solutions are derived, which accurately calculate both the pressure buildup and temperature decline during the injection period.

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“…For example, the initial critical radius is zero for an initially hydrostatic aquifer, and it gradually increases with time until the system becomes quasi steady state near a constant-rate pumping well. The movement of critical radius may be more complex for the variable-rate pumping tests (Bear, 1972;Mishra et al, 2012), the slug tests (Quinn et al, 2013) or the step-drawdown tests (Louwyck et al, 2010;Mathias and Todman, 2010). Therefore, the two-region model with time-dependent critical radius is more reasonable for transient flow near a pumping well, and it is particularly true when the pumping rate changes greatly.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, Quinn et al (2013) showed that the hydraulic conductivity was underestimated by Darcy's law when the initial applied head differentials were greater than 0.2 m. They pointed out that Darcian flow conditions can be maintained in the sandstone when the initial applied head differentials were less than 0.2 m (Quinn et al, 2013). Mathias and Todman (2010) showed that the Jacob method, based on Darcy's law, cannot fit the step-drawdown tests of van Tonder et al (2001) when the pumping rate was greater than 10 m 3 h −1 . However, the Forchheimer law could fit the stepdrawdown tests data very well (Mathias and Todman, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…Mathias and Todman (2010) showed that the Jacob method, based on Darcy's law, cannot fit the step-drawdown tests of van Tonder et al (2001) when the pumping rate was greater than 10 m 3 h −1 . However, the Forchheimer law could fit the stepdrawdown tests data very well (Mathias and Todman, 2010). In this study, we will focus on the non-Darcian flow into a pumping well by the Forchheimer law.…”

Section: Introductionmentioning

confidence: 99%

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Forchheimer flow to a well-considering time-dependent critical radius

Wang

Zhan

Tang

2014

Hydrol. Earth Syst. Sci.

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Abstract. Previous studies on the non-Darcian flow into a pumping well assumed that critical radius (R CD ) was a constant or infinity, where R CD represents the location of the interface between the non-Darcian flow region and Darcian flow region. In this study, a two-region model considering time-dependent R CD was established, where the non-Darcian flow was described by the Forchheimer equation. A new iteration method was proposed to estimate R CD based on the finite-difference method. The results showed that R CD increased with time until reaching the quasi steady-state flow, and the asymptotic value of R CD only depended on the critical specific discharge beyond which flow became nonDarcian. A larger inertial force would reduce the change rate of R CD with time, and resulted in a smaller R CD at a specific time during the transient flow. The difference between the new solution and previous solutions were obvious in the early pumping stage. The new solution agreed very well with the solution of the previous two-region model with a constant R CD under quasi steady flow. It agreed with the solution of the fully Darcian flow model in the Darcian flow region.

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Step‐drawdown tests and the Forchheimer equation

Cited by 47 publications

References 34 publications

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

Heat transport and pressure buildup during carbon dioxide injection into depleted gas reservoirs

Forchheimer flow to a well-considering time-dependent critical radius

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