Hui-Hai Liu

Unconventional Spontaneous Imbibition into Shale Matrix: Theory and a Methodology to Determine Relevant Parameters

Spontaneous imbibition of fracturing fluids into a shale formation has many practical applications for shale gas recovery. Because of the strong solid–liquid interaction in low-permeability media, Darcy law is not always adequate for describing liquid flow process in a shale formation. This unconventional (non-Darcian) flow behavior, however, has not been given enough attention in the shale gas community. The current study develops a systematic methodology to address this important issue. We first review related studies in the literature on relationship between liquid flux and hydraulic (or pressure) gradient in low-permeability media; the unconventional flow behavior is characterized by nonlinearity of the relationship. Then, we propose a phenomenological model for liquid flow in shale (in which liquid flux is a power function of pressure gradient) and develop an analytical solution to a one-dimensional spontaneous imbibition problem that obeys the model. The validity of our model is verified by satisfactory comparisons of theoretical and observed relationships between cumulative imbibition and time. The potential mechanisms of the unconventional flow are discussed. Furthermore, based on the developed analytical solution, we propose a laboratory test methodology to estimate parameters for the phenomenological model from spontaneous imbibition tests.

Constitutive Relations for Reactive Transport Modeling: Effects of Chemical Reactions on Multi-phase Flow Properties

The relationship between flow properties and chemical reactions is the key to modeling subsurface reactive transport. This study develops closed-form equations to describe the effects of mineral precipitation and dissolution on multi-phase flow properties (capillary pressure and relative permeabilities) of porous media. The model accounts for the fact that precipitation/dissolution only takes place in the water-filled part of pore space. The capillary tube concept was used to connect pore-scale changes to macroscopic hydraulic properties. Precipitation/dissolution induces changes in the pore radii of water-filled pores and consequently in the pore size distribution. The updated pore size distribution is converted back to a new capillary pressure–water saturation relation from which the new relative permeabilities are calculated. Pore network modeling is conducted on a Berea sandstone to validate the new continuum-scale relations. The pore network modeling results are satisfactorily predicted by the new closed-form equations.

Correction of source-rock permeability measurements owing to slip flow and Knudsen diffusion: a method and its evaluation

Source-rock permeability is a key parameter that controls the gas production rate from unconventional reservoirs. Measured source-rock permeability in the laboratory, however, is not an intrinsic property of a rock sample, but depends on pore pressure and temperature as a result of the relative importance of slip flow and diffusion in gas flow in low-permeability media. To estimate the intrinsic permeability which is required to determine effective permeability values for the reservoir conditions, this study presents a simple approach to correct the laboratory permeability measurements based on the theory of gas flow in a micro/nano-tube that includes effects of viscous flow, slip flow and Knudsen diffusion under different pore pressure and temperature conditions. The approach has been verified using published shale laboratory data. The “corrected” (or intrinsic) permeability is considerably smaller than the measured permeability. A larger measured permeability generally corresponds to a smaller relative difference between measured and corrected permeability values. A plot based on our approach is presented to describe the relationships between measured and corrected permeability for typical Gas Research Institute permeability test conditions. The developed approach also allows estimating the effective permeability in reservoir conditions from a laboratory permeability measurement.

Assessing Tensile Strength of Unconventional Tight Rocks Using Microwaving

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