Abstract
The concept of an intermingled fractal unit (IFU) model was first proposed by Atzeni and Pia in 2008, and their model has since been successfully applied to predict thermal conductivity, electrical conductivity, and the mechanical properties of porous media materials. This paper, based on the Pia IFU model, fits the pore size distribution spectrum to quantitatively characterize the Triassic Karamay Formation conglomerate reservoirs in the Mahu region, in the Junggar Basin of Northwest China, and makes permeability predictions using the free fluidT2spectrum according to the nuclear magnetic resonance (NMR) experimental data. The results show that the accuracy of the IFU model is significantly higher than that of the classic Coates and SDR models for conglomerate reservoirs with complex pore structures, indicating that this is an effective method to calculate permeability based on NMR. In addition, preliminary discussions are entered into regarding the intermingled fractal expression of the Kozeny-Carman equation and the relative permeability, in order to widen the application of the IFU model in reservoir physics. The derived expressions appear complicated in form but are straightforward to calculate and apply using computer programming since their iteration parameters are definite. The findings set out in this paper provide a valuable reference for further research of the IFU model in reservoir physics.
Highlights
The pore structure of reservoir rocks has fractal characteristics [1]
When computing fractal dimensions using capillary data, for example, it has been noted that in a log-log coordinate system, the lg SHg to lg Pc plot sometimes exhibits multifractal characteristics for some kinds of rocks, instead of being linearly fitted, which significantly influences the accuracy of computation [5,6,7,8,9]
Sima et al [10] have pointed out that sand conglomerate rocks with high heterogeneity tend to exhibit more evident multifractal characteristics or even nonfractal characteristics, on log-log coordinates, illustrating that the probability of multifractal characteristics is greater in the conglomerate samples
Summary
The pore structure of reservoir rocks has fractal characteristics [1]. Because of this, a number of scholars have recently adopted fractal theory to establish the porosity or the permeability model of reservoir rocks and have achieved some productive results. Fractal dimensions of some large intervals of pore size, calculated by the graphical method, are greater than 3, and this phenomenon is interpreted as being attributable to nonfractal characteristics To address this problem , Li et al [11] and Lai et al [12] proposed to run a weighted average of the mercury saturation of each fractal segment to obtain a weighted fractal dimension. The fractal dimension is a highly significant parameter in fractal theory, it has limitations in characterizing a real rock pore space This is because porous media with different pore structures may have the same or similar fractal dimension [13]. Panel (b) was presented in our previous paper [14]
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