A fractal model for threshold pressure gradient of tight oil reservoirs

Ye, Wenzhuo; Wang, Xiuyu; Cao, Chenguang; Yu, Wenshuai

doi:10.1016/j.petrol.2019.04.039

Cited by 39 publications

(24 citation statements)

References 10 publications

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“…Cai [3] pointed out that the scaling behavior between the TPG and the permeability of porous medium could be further expressed by the tortuosity fractal dimension D T , TPG ∼ k −D T /(1+D T ) . Ye et al [26] proposed a fractal model for the TPG in tight oil reservoirs. In this model, the residual water saturation was treated as connate water by forming a boundary layer fluid, which could hinder the gas flow.…”

Section: Tpg Correlationsmentioning

confidence: 99%

“…This boundary layer reduces the fluid flow space and applies a flow resistance to free fluid. The thickness of the water film is calculated by residual water saturation [26]:…”

Section: Derivation Of Threshold Pressure Gradient Based On Fractal Tmentioning

confidence: 99%

“…Ye et al [26] divided the core samples into three groups according to their permeabilities, which ranged from 0.001 mD to 0.5 mD, and measured the average threshold pressure gradient. These experimental data were used to verify this fractal model.…”

Section: Model Validation and Analysismentioning

confidence: 99%

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Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Wang

et al. 2020

Symmetry

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Low-permeability porous medium usually has asymmetric distributions of pore sizes and pore-throat tortuosity, thus has a non-linear flow behavior with an initial pressure gradient observed in experiments. A threshold pressure gradient (TPG) has been proposed as a crucial parameter to describe this non-linear flow behavior. However, the determination of this TPG is still unclear. This study provides multi-scale insights on the TPG in low-permeability porous media. First, a semi-empirical formula of TPG was proposed based on a macroscopic relationship with permeability, water saturation, and pore pressure, and verified by three sets of experimental data. Second, a fractal model of capillary tubes was developed to link this TPG formula with structural parameters of porous media (pore-size distribution fractal dimension and tortuosity fractal dimension), residual water saturation, and capillary pressure. The effect of pore structure complexity on the TPG is explicitly derived. It is found that the effects of water saturation and pore pressure on the TPG follow an exponential function and the TPG is a linear function of yield stress. These effects are also spatially asymmetric. Complex pore structures significantly affect the TPG only in the range of low porosity, but water saturation and yield stress have effects on a wider range of porosity. These results are meaningful to the understanding of non-linear flow mechanism in low-permeability reservoirs.

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Section: Tpg Correlationsmentioning

confidence: 99%

“…This boundary layer reduces the fluid flow space and applies a flow resistance to free fluid. The thickness of the water film is calculated by residual water saturation [26]:…”

Section: Derivation Of Threshold Pressure Gradient Based On Fractal Tmentioning

confidence: 99%

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Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Wang

et al. 2020

Symmetry

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“…Clearly, the curvature of the fluid channels can't be ignored in the real rocks. Both tortuosity fractal dimension and maximum pore diameter have an important role in the fluid flow in porous media (Yun et al, 2009;Ye et al, 2019;Huang et al, 2020). Thus, there will be a great error in the fluid exchange term if neglecting the effects of tortuosity fractal dimension and maximum pore diameter of matrix on the shape factor.…”

Section: Model Verificationmentioning

confidence: 99%

Fractal analysis of shape factor for matrix-fracture transfer function in fractured reservoirs

Mei

Zhang

Wang

et al. 2020

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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As the core function of dual-porosity model in fluids flow simulation of fractured reservoirs, matrix-fracture transfer function is affected by several key parameters, such as shape factor. However, modeling the shape factor based on Euclidean geometry theory is hard to characterize the complexity of pore structures. Microscopic pore structures could be well characterized by fractal geometry theory. In this study, the separation variable method and Bessel function are applied to solve the single-phase fractal pressure diffusion equation, and then the obtained analytical solution is used to deduce one-dimensional, two-dimensional and three-dimensional fractal shape factors. The proposed fractal shape factor can be used to explain the influence of microstructure of matrix on the fluid exchange rate between matrix and fracture, and is verified by numerical simulation. Results of sensitivity analysis indicate that shape factor decreases with tortuosity fractal dimension and characteristic length of matrix, increases with maximum pore diameter of matrix. Furthermore, the proposed fractal shape factor is effective in the condition that tortuosity fractal dimension of matrix is roughly between 1 and 1.25. This study shows that microscopic pore structures have an important effect on fluid transfer between matrix and fracture, which further improves the study on flow characteristics in fractured systems.

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“…Although reasonable progress has been made in this field, there is still a need for some improvement in many aspects. Many pieces of research have already proved the existence of TPG in tight and ultra-tight reservoirs (Wu et al 2019;Xiao et al 2016;Ye et al 2019;Zhou 2019). There is relatively less research has been carried out for TPG of a gas reservoir as compared to TPG of oil reservoir (Zeng et al 2018).…”

Section: Introductionmentioning

confidence: 99%

Tight gas production model considering TPG as a function of pore pressure, permeability and water saturation

Zafar

et al. 2020

Pet. Sci.

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Threshold pressure gradient has great importance in efficient tight gas field development as well as for research and laboratory experiments. This experimental study is carried out to investigate the threshold pressure gradient in detail. Experiments are carried out with and without back pressure so that the effect of pore pressure on threshold pressure gradient may be observed. The trend of increasing or decreasing the threshold pressure gradient is totally opposite in the cases of considering and not considering the pore pressure. The results demonstrate that the pore pressure of tight gas reservoirs has great influence on threshold pressure gradient. The effects of other parameters like permeability and water saturation, in the presence of pore pressure, on threshold pressure gradient are also examined which show that the threshold pressure gradient increases with either a decrease in permeability or an increase in water saturation. Two new correlations of threshold pressure gradient on the basis of pore pressure and permeability, and pore pressure and water saturation, are also introduced. Based on these equations, new models for tight gas production are proposed. The gas slip correction factor is also considered during derivation of this proposed tight gas production models. Inflow performance relationship curves based on these proposed models show that production rates and absolute open flow potential are always be overestimated while ignoring the threshold pressure gradients.

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A fractal model for threshold pressure gradient of tight oil reservoirs

Cited by 39 publications

References 10 publications

Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Fractal analysis of shape factor for matrix-fracture transfer function in fractured reservoirs

Tight gas production model considering TPG as a function of pore pressure, permeability and water saturation

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