ارائه روابط بهبود یافته برای روندهای تراوایی-تخلخل سنک با استفاده از فیزیک سنگ رقومی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی معدن،دانشکده مهندسی،دانشگاه زنجان،ایران

2 گروه مهندسی معدن،دانشگاه زنجان،ایران

چکیده

هدف از انجام این مطالعه بررسی و بهبود روندهای فرکتالی تراوایی است. برای این کار دو نمونه 3بعدی رقومی از ماسه سنگ بنتهیمر و کربنات استیلادس با دو رفتار فرکتالی متفاوت از هم انتخاب شدند. نتایج اولیه نشان داد که رابطه کوزنی-کارمن برای ارزیابی روند تراوایی در این نمونه ها مناسب نیست. از این رو، از رابطه عمومی فرکتالی تراوایی استفاده شد و ثابتهای این رابطه با الگوریتم برازش منحنی بدست آمد. نتایج نشان داد که با وجود آن که این رابطه ممکن است برای تخمین تراوایی یک نمونه مناسب باشد، اما رابطه مناسبی به عنوان روند تراوایی به شمار نمیآید. این امر به علت آن است که ثابتهای این رابطه که همان ابعاد فرکتالی هستند، متغیر و تابعی از تغییرات تخلخلاند. برای بهبود این رابطه، ابتدا تابعیت ابعاد و ضرایب فرکتالی با تخلخل بررسی شد. سپس یک رابطه بهبود یافته با توابع جدید پیشنهاد گردید.
نتایج حاکی از آن است که نه تنها تابعیت ابعاد و ضرایب فرکتالی با تخلخل به درستی حفظ شده است، بلکه با توجه به رفتار فرکتالی متفاوت این دو نمونه، دو روند متفاوت از هم بدست میآید. مقایسه این روندها با روند کوزنی-کارمن بیان کننده دقت و کارایی بالاتر این رابطه است.

کلیدواژه‌ها


عنوان مقاله [English]

Improved relations for permeability-porosity trends using digital rock physics

نویسندگان [English]

  • seyed navid ghaffari 1
  • Sadegh Karimpouli 2
1 Mining Engineering group, Faculty of Engineering, University of Zanjan, Iran
2 Mining Engineering group, University of Zanjan, Zanjan, Iran.
چکیده [English]

. Since this equation does not properly cover geometrical properties of the porous medium of tock, fractal dimensions such as tortuosity and pore space dimensions are used for improving this equation. The aim of this study is to consider and improvement of fractal permeability trends. Therefore, two 3D digital sample namely Bentheimer sandstone and Estaillades carbonate with different pore space complexity and fractal behavior were selected.corresponding porosity and permeability were calculated. Results showed that Kozeny-Carman equation is not a good trend to consider all permeability data. Therefore, fractal equation of permeability was used and their constant values were obtained by a fitting algorithm. Results showed that although fractal equations can consider permeability in a specific sample, they are not applicable for permeability trend evaluation. This is because fractal constants are variable with porosity. To improve these equations, functionality of fractal constant with porosity were obtained and, then, a new equation derived from fractal equation was proposed. This equation was fitted to permeability data and its constant values for each original sample were also obtained. Results showed that this equation can predict permeability-porosity trends better than Kozeny-Carman trend. Also their differences obviously reflect complexity of porous medium of rock.

کلیدواژه‌ها [English]

  • Improved relations
  • Rock physical trend
  • Permeability-porosity
  • fractal
  • Digital rock
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