Universal scaling of spontaneous imbibition for arbitrary petrophysical properties: Water-wet and mixed-wet states and Handy's conjecture

Schmid, Karen Sophie; Geiger, Sebastian

doi:10.1016/j.petrol.2012.11.015

Cited by 87 publications

(86 citation statements)

References 98 publications

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“…Injecting water into the gas-bearing rock leads to interactions between gas and water termed spontaneous imbibition. Although these effects are amenable to precise analysis (12) and have experimentally measurable consequences (13), we are able to neglect them because we discarded the first 3 mo of gas production, when these and other transient effects are most pronounced. In addition, as the pressure falls in a reservoir, gas adsorbed in the rock may escape, producing additional contributions to the gas flow.…”

Section: Resultsmentioning

confidence: 99%

“…Fig. 1 illustrates the well as [10][11][12][13][14][15][16][17][18][19][20] hydrofractures that are H ∼ 30 m high and 2L ∼ 200 m long, spaced at distances of around 2d ∼ 100 m. The fact that this is the right starting point for these wells was recognized by Al-Ahmadi et al (9), and the diffusion problem in this setting has been studied by both Silin and Kneafsy (10), and Nobakht et al (11).…”

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confidence: 99%

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Gas production in the Barnett Shale obeys a simple scaling theory

Patzek¹,

Columbu

Marder

2013

Proc. Natl. Acad. Sci. U.S.A.

328

258

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Natural gas from tight shale formations will provide the United States with a major source of energy over the next several decades. Estimates of gas production from these formations have mainly relied on formulas designed for wells with a different geometry. We consider the simplest model of gas production consistent with the basic physics and geometry of the extraction process. In principle, solutions of the model depend upon many parameters, but in practice and within a given gas field, all but two can be fixed at typical values, leading to a nonlinear diffusion problem we solve exactly with a scaling curve. The scaling curve production rate declines as 1 over the square root of time early on, and it later declines exponentially. This simple model provides a surprisingly accurate description of gas extraction from 8,294 wells in the United States' oldest shale play, the Barnett Shale. There is good agreement with the scaling theory for 2,057 horizontal wells in which production started to decline exponentially in less than 10 y. The remaining 6,237 horizontal wells in our analysis are too young for us to predict when exponential decline will set in, but the model can nevertheless be used to establish lower and upper bounds on well lifetime. Finally, we obtain upper and lower bounds on the gas that will be produced by the wells in our sample, individually and in total. The estimated ultimate recovery from our sample of 8,294 wells is between 10 and 20 trillion standard cubic feet.hydrofracturing | shale gas | scaling laws | energy resources | fracking T he fast progress of hydraulic fracturing technology (SI Text, Figs. S1 and S2) has led to the extraction of natural gas and oil from tens of thousands of wells drilled into mudrock (commonly called shale) formations. The wells are mainly in the United States, although there is significant potential on all continents (1). The "fracking" technology has generated considerable concern about environmental consequences (2, 3) and about whether hydrocarbon extraction from mudrocks will ultimately be profitable (4). The cumulative gas obtained from the hydrofractured horizontal wells and the profits to be made depend upon production rate. Because large-scale use of hydraulic fracturing in mudrocks is relatively new, data on the behavior of hydrofractured wells on the scale of 10 y or more are only now becoming available.There is more than a century of experience describing how petroleum and gas production declines over time for vertical wells. The vocabulary used to discuss this problem comes from a seminal paper by Arps (5), who discussed exponential, hyperbolic, harmonic, and geometric declines. Initially, these types of decline emerged as simple functions providing good fits to empirical data. Thirty-six years later, Fetkovich (6) showed how they arise from physical reasoning when liquid or gas flows radially inward from a large region to a vertical perforated tubing, where it is collected. For specialists in this area, the simplicity and familiarity of hyperbolic de...

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Gas production in the Barnett Shale obeys a simple scaling theory

Patzek¹,

Columbu

Marder

2013

Proc. Natl. Acad. Sci. U.S.A.

328

258

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“…Chen et al (1990) and McWhorter and Sunada (1990) did some primary works for the corresponding analytical solutions. Actually the spontaneous imbibition model by Schmid et al (2011Schmid et al ( , 2013) is also derived from McWhorter and Sunada (1990)'s work. Analog to the fractional flow function, they introduced the concept of capillary fractional flow function defined as the ratio of wetting phase flow rate for various wetting phase saturation to that at inlet with the highest wetting phase saturation as shown in Eq.…”

Section: Introductionmentioning

confidence: 94%

“…However, these models still cannot consider some essential properties of porous media such as: variable wettability, the difference between countercurrent and cocurrent imbibition, etc. Apart from capillary tube based models, Schmid et al (2011Schmid et al ( , 2013 proposed an analytical solution of spontaneous imbibition based on the continuum dynamics using capillary pressure and relative permeability curves of the porous media. This model can be understood as the capillary analog to the classical Buckley-Leverett solution (Buckley and Leverett, 1942) model given the corresponding capillary pressure and relative permeability curves.…”

Section: Introductionmentioning

confidence: 99%

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A self-similar analytical solution of spontaneous and forced imbibition in porous media

Wang

Sheng

2018

Adv. Geo-Energy Res.

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Citation:Wang, X., Sheng, J.J. A self-similar analytical solution of spontaneous and forced imbibition in porous media. Both viscous and capillary forces control the two-phase flow in porous media. The Buckley Leverett solution for viscous flow in porous media has been proposed for over a half century. While the corresponding studies of capillary dominated solutions are mainly based on the capillary tube based models. The continuum solutions are just prevail in recently years. The analytical solution of the combination of both effects is rarely investigated. A self-similar analytical solution of spontaneous and forced imbibition in porous media is proposed in this work and the corresponding concise algorithms are presented. The proposed solution successfully solves this typical non-linear partial differential equation by introducing a transformation variable and the capillary fractional flow function analog to the fractional flow function of Buckley Leverett solution. Finally, the case study is performed, which demonstrates the feasibility and accuracy of this proposed solution to a general two-phase flow condition.

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Chemical osmosis in two-phase flow and salinity-dependent capillary pressures in rocks with microporosity

2014

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The situation of multiphase flow with varying salinity through rock formations with microporosity plays a key role in many applications. Experimental data for single-phase flow through rocks with microporosity show that chemical osmosis can lead to osmotic pressures in the range of several megapascal, but the effect of osmosis on multiphase flow so far has received little attention. Pore networks can be used to investigate these effects, but crucially depend on expressions for capillary entry pressures. Here we extend the classical theory for capillary entry pressures to the case where chemical potentials play a role. The inclusion of osmosis results into a ''capillary-osmotic'' pressure that also depends on salinity differences and temperature. Consequently, also the pore-scale events of piston-like displacement and snap-off depend on salinity contrasts and temperature and not only on pore geometry as has been assumed so far. Examples show that even small salinity differences can lead to significantly different entry pressures and changed pore invasion sequences compared to if osmosis is absent. We show that the ensemble behavior with osmosis often is identical to the case where the medium partly has become more water wet, which implies that osmosis might have a strong impact on laboratory-scale quantities, but also that their detection in experiments will be challenging. Hence, chemical gradients could be important drivers of multiphase flow in rocks with microporosity and should be included into flow models, which currently is not the case.

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Universal scaling of spontaneous imbibition for arbitrary petrophysical properties: Water-wet and mixed-wet states and Handy's conjecture

Cited by 87 publications

References 98 publications

Gas production in the Barnett Shale obeys a simple scaling theory

Gas production in the Barnett Shale obeys a simple scaling theory

A self-similar analytical solution of spontaneous and forced imbibition in porous media

Chemical osmosis in two-phase flow and salinity-dependent capillary pressures in rocks with microporosity

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