Calculation Method For Permeability Research Articles

Study on Permeability Calculation Method Based on J Function and Fractal Theory.

Permeability is a required parameter for studying aquifer properties. However, for sandstone aquifers with low permeability, it is difficult to measure permeability directly through experiments. Based on fractal theory and the J function, a new method to calculate the permeability of a sandstone aquifer is derived. This work first solves the J function under each water saturation according to its definition. Combined with mercury pressure data, the J function and logarithmic curve equation of water saturation are then fitted by the drawing method, and the fractal dimension and tortuosity of the aquifer are further solved. Finally, the aquifer's permeability is calculated using the new permeability calculation method. To verify the accuracy of the proposed method, 15 rock samples from the Chang 7 Group, Ordos Basin, are taken as research objects. The permeability is calculated using the new method combined with mercury injection data and aquifer characteristic parameters, and the results are compared with the real permeability. The relative error of most samples is <20%, which shows the permeability calculated by this method is accurate and reliable. The effects of fractal dimension, tortuosity, and porosity on permeability are also analyzed.

Digital Core Permeability Computation by Image Processing Techniques

Calculation of REV (representative elementary volume) properties of geological porous media refers to the process of creating a 3D digital representation of a rock sample, typically obtained from imaging techniques such as X-ray microtomography. This technique allows for a detailed analysis of the internal structure and the properties of rocks, as well as precise calculation of various flow parameters. However, one major challenge with calculation of REV properties of geological porous media is the high computational cost required to generate accurate results, especially for large and complex samples. In this study, we constructed 3D digital cores of dune sand and fractured shale using CT scanning technology, and then used two image processing techniques, namely digital core image resampling and cutting, to reduce the computational cost of calculating digital core permeability. Next, a fast permeability calculation method is employed to reduce the complexity of permeability calculation. Finally, we summarized the applicability of different image processing methods to different rock samples, and provided prerequisites for high computational cost digital core permeability calculation.

Investigating the effects of effective stress on pore-dependent permeability measurements of crushed coal.

The accurate determination of permeability is one of the parameters essential for the study of fluid flow and transport state. However, a large number of fractured coal bodies are faced during the production of coal mines. The study of permeability of these special media composed of grains of a certain size, whose structure is different from that of raw coal, has been in the exploratory stage. In this paper, inspired by the calculation method of median particle size and the calculation principle of KC’s equation, we calculate the permeability parameters of broken coal particles. It is considered that its permeability is closely related to the compaction and re-crushing process of skeletal grains. The lateral limit compression test of the crushed coal body was designed, and the pore-dominated permeability calculation method was given to reveal the mechanism of the action of the effective stress. The dependence relationship between the effective stress and the pore-correlation permeability is obtained by data analysis, and the force and deformation process of the crushed coal grain media is described. In contrast to the conventional Darcy series of permeability discussions, our approach excludes the influence of fluid factors on the permeability of porous media. The permeability of porous media is considered to be determined only by its own pore structure.

Recognitions on the flow mechanism of shale during the plug pulse decay measurement

When using the plug pulse decay method to measure shale permeability, a comprehensive analysis of various factors influencing the measurement and analysis precision is conducive to improving the accuracy of the test result. A great number of nano-scale pores are developed in shale, so the lower the test pressure is, the more easily the non-Darcy flow tends to emerge. In order to ensure the gas is in the form of Darcy flow in the process of measurement, we put forward the lower pressure limit of Darcy flow in pores according to the definition of Knudsen number. Then, the gas desorption-flow coupling model for the gas flow process during the plug pulse decay measurement was established by considering the effects of gas on the adsorption in organic pores. After the partial differential equation set was solved and derived, the corresponding permeability calculation method was proposed. Finally, after the plug pulse decay measurement, the supporting nitrogen isothermal adsorption test and methane isothermal adsorption test were conducted on shale samples. And the following research results were obtained. First, during the plug pulse decay measurement, the flow of gas in rock samples is one-dimensional linear, so when establishing the flow equation, the gas pseudopressure can be replaced with the gas pressure to simplify the calculation. Second, the adsorption of nitrogen in shale is much less than that of methane in shale, so the influence of nitrogen desorption on the flow is negligible when the pressure difference (i.e. <5%) of upstream and downstream changes within 5% of the initial pore pressure. In conclusion, the available industrial standards don't take into consideration the influence of gas adsorption, but the shale permeability measurement can still satisfy the accuracy requirement.

Application of the renormalization group approach for permeability estimation in digital rocks

Rock permeabilities are typically calculated by applying some empirically derived relationships or expressions, which normally result in rough or erroneous values. Given advanced computing and smart techniques, rock samples acquired in boreholes or on outcrops can be imaged and broken down into small digital rocks. The renormalization group approach with isotropic block (RGAWIB) has been applied to calculate the permeability of digital rocks. The RGAWIB proposed by King can accurately derive the effective permeability if the pore structure is described correctly by the separated grid blocks. For King's method, the permeability of the grid block is assumed to be isotropic, which is not suitable for significant variance in neighboring permeabilities. In this study, we adopted discrete blocks with anisotropic permeability for the upscaling process of renormalization, which provided reasonable results for large perturbations of permeability in neighboring grid blocks. We assumed that the anisotropic block held different permeabilities in three orthogonal directions and calculated the effective permeabilities of idealized porous media and digital rocks by a renormalization group approach with anisotropic block (RGAWAB). Moreover, a permeability distribution method is presented in this paper. The original permeability distribution of an idealized porous media was calculated, along with the permeability distributions of the digital core data available in the literature in the x, y, and z directions using the method developed in this study. Then, we calculated the effective permeabilities of the digital rocks using RGAWAB in the x, y, and z directions, respectively. We compared the results with the absolute permeabilities calculated by the lattice Boltzmann method, which showed that the permeability calculation method was feasible for digital rocks.

A Coupled Thermodynamic Model for Transport Properties of Thin Films during Physical Aging.

A coupled diffusion model based on continuum thermodynamics is developed to quantitatively describe the transport properties of glassy thin films during physical aging. The coupled field equations are then embodied and applied to simulate the transport behaviors of O2 and CO2 within aging polymeric membranes to validate the model and demonstrate the coupling phenomenon, respectively. It is found that due to the introduction of the concentration gradient, the proposed direct calculating method on permeability can produce relatively better consistency with the experimental results for various film thicknesses. In addition, by assuming that the free volume induced by lattice contraction is renewed upon CO2 exposure, the experimental permeability of O2 within Matrimid® thin film after short-time exposure to CO2 is well reproduced in this work. Remarkably, with the help of the validated straightforward permeability calculation method and free volume recovery mechanism, the permeability behavior of CO2 is also well elucidated, with the results implying that the transport process of CO2 and the variation of free volume are strongly coupled.

Analysis of Factors Affecting Bottom Hole Pressure in Tight Gas Reservoir

In order to solve the problem of low accuracy of bottom hole pressure in tight gas reservoir, this paper presents a new way to analyze the bottom hole pressure. By combining literature research and starting from nonlinear motion equations, the model of bottom hole pressure was established through using various mathematical methods such as separation variable method, identity transformation method and differential discrete method. This paper presents a high-precision and high-efficiency method for solving bottom hole pressure in tight gas reservoirs, and a dynamic calculation method for permeability and conductivity is given. Through the sensitivity analysis of the influencing factors of dimensionless pressure and pressure derivative, it is concluded that the larger the power law index is, the larger the warpage of the dimensionless pressure and pressure derivative curve is. The larger the skin coefficient and the wellbore storage coefficient is, the earlier the fluid enters into the quasi-steady-state seepage. When the tight gas reservoir contains closed edges, the resolution points of the dimensionless pressure and pressure derivative curves are obvious with crossing. On the contrary, when the tight gas reservoir contains the constant pressure boundary, the resolution points of the dimensionless pressure and pressure derivative curves are not obvious without crossing.

A new permeability calculation method using nuclear magnetic resonance logging based on pore sizes: A case study of bioclastic limestone reservoirs in the A oilfield of the Mid-East

Abstract It is difficult to accurately obtain the permeability of complex lithologic reservoirs using conventional methods because they have diverse pore structures and complex seepage mechanisms. Based on in-depth analysis of the limitation of classical nuclear magnetic resonance (NMR) permeability calculation models, and the understanding that the pore structure and porosity are the main controlling factors of permeability, this study provides a new permeability calculation method involving classifying pore sizes by using NMR T2 spectrum first and then calculating permeability of different sizes of pores. Based on this idea, taking the bioclastic limestone reservoir in the A oilfield of Mid-East as an example, the classification criterion of four kinds of pore sizes: coarse, medium, fine and micro throat, was established and transformed into NMR T2 standard based on shapes and turning points of mercury intrusion capillary pressure curves. Then the proportions of the four kinds of pore sizes were obtained precisely based on the NMR logging data. A new NMR permeability calculation model of multicomponent pores combinations was established based on the contributions of pores in different sizes. The new method has been used in different blocks. The results show that the new method is more accurate than the traditional ones.

Optimized pressure pulse-decay method for laboratory estimation of gas permeability of sorptive reservoirs: Part 1 – Background and numerical analysis

Analysis of transient fluid flow in porous media has several applications in geophysics/geotechnics and engineering. An in-depth evaluation of fluid flow behavior is critical in order to improve the understanding, and development of, laboratory measurement techniques in geo-mechanics, particularly permeability estimation. Given that considerable errors may be yielded in the derived permeabilities of sorptive rocks when using the conventional pressure-pulse decay method (PDM), this paper proposes a new experimental design, an optimized PDM, by creating dual pressure pulses to avoid the pressure disturbance due to compressive storage, ad-/de-sorption and thermal effect during the course of measurement. In this paper, the first of a two-part series, a mathematical model established for the conventional PDM was modified to closely represent the new experimental design, thereby extending the transient technique for permeability measurement of unconventional reservoir rocks, particularly ones with large sorption potential. Considering the complexity of analytical solutions of mathematical models, a comprehensive numerical investigation was established and a detailed comparison was carried out between the conventional and optimized PDMs. The results showed how the profiles of the decay curves change in space and time domain, and how pressure responses are influenced by various parameters in the experimental design for PDM. Combining the new design with numerical simulation results in an optimized technique for fast and accurate permeability measurement of sorptive rocks. In particular, Brace et al.’s solution, the most acknowledged and commonly-used permeability calculation method, was extended for permeability estimation of sorptive rocks. In Part 2, the experimental work under best-replicated in situ stress/strain conditions using the optimized method along with the numerical pressure response results obtained from computer simulation is presented. The results verified the practicality of the optimized PDM and the validity of Brace et al.’s solution for permeability measurement of sorptive rocks.

The Productivity Calculation Method of a Carbonate Reservoir

The storage spaces of carbonate reservoir are complicated, and vugs and fractures coexist, which results in the development of a reservoir always being a worldwide problem, and single-well productivity is very difficult to determine. Because of it is difficult to distinguish and describe vugs and fractures quantificationally, traditional methods such as the dual-continuum model and discrete fracture network model have great difficulties in actual application. A single-well productivity calculation method of fractured-vuggy carbonate reservoir was developed based on the theory of equivalent continuum media. Combined with the capillary model and the law of equivalent seepage resistance, an equivalent permeability calculation method of this reservoir was also presented. An application analysis was carried out combined with a practical reservoir, major factors that influence the productivity of fractured-vuggy carbonate reservoir and the changing rules of productivity were analyzed. The conclusion showed that single-well productivity was low when matrix permeability was low and matrix region was large, in extreme cases, the well had no production; vugs and fractures could improve the flow capacity of low-permeability reservoir, and enhanced productivity in a certain range.