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The Kozeny-Carman Equation with a Percolation Threshold

机译:具有渗流阈值的Kozeny-Carman方程

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A procedure has been developed for calculating permeability (k) from the Kozeny-Carman equation, a procedure that links ideas from percolation theory with the ideas of Koltermann and Gorelick (1995) and Esselburn et al. (2011). The approach focuses on the proportion of coarser pores that are occupied by finer sediments relative to a percolation threshold proportion (ω_c). If the proportion occupied is below ω_c, then the unoccupied coarser pores percolate. Otherwise they do not percolate. Following the ideas of Koltermann and Gorelick (1995), the effective grain-size term in the Kozeny-Carman equation is calculated using the geometric mean if the unoccupied coarse pores percolate, and using the harmonic mean if otherwise. Following ideas of Esselburn et al. (2011), this approach is implemented by evaluating the potential for grains in each size category to occupy pores among sediment of each larger-size category. Application of these ideas to physical sediment models for sands and gravels, which have known k, indicates that a threshold does indeed exist. Results also suggest that the Kozeny-Carman equation is robust and gives representative values for k, even though ω_c is not precisely known.
机译:已经开发了一种从Kozeny-Carman方程计算渗透率(k)的程序,该程序将渗流理论的思想与Koltermann和Gorelick(1995)以及Esselburn等人的思想联系起来。 (2011)。该方法的重点是相对于渗透阈值比例(ω_c),较细的沉积物所占据的较粗孔的比例。如果占据的比例低于ω_c,则未占据的较粗孔将渗透。否则它们不会渗滤。遵循Koltermann和Gorelick(1995)的思想,如果未占用的粗孔渗过,则使用几何平均值计算Kozeny-Carman方程中的有效晶粒尺寸项,否则使用谐波平均值进行计算。遵循Esselburn等人的想法。 (2011年),这种方法是通过评估每种尺寸类别的谷物在每个较大尺寸类别的沉积物中占据孔隙的可能性来实现的。将这些想法应用于已知为k的沙子和砾石的物理沉积物模型,表明确实存在阈值。结果也表明,即使ω_c未知,Kozeny-Carman方程也是鲁棒的,并且给出了k的代表值。

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  • 来源
    《Ground water》 |2013年第1期|92-99|共8页
  • 作者单位

    Department of Earth and Environmental Sciences, Wright State University, 3640 Colonel Glenn Hwy, Dayton, OH 45435;

    Department of Earth and Environmental Sciences, Wright State University, 3640 Colonel Glenn Hwy, Dayton, OH 45435,Department of Earth and Environmental Sciences, Wright State University, 3640 Colonel Glenn Hwy, Dayton, OH 45435;

    Department of Earth and Environmental Sciences, Wright State University, 3640 Colonel Glenn Hwy, Dayton, OH 45435;

    Department of Earth and Environmental Sciences, Wright State University, 3640 Colonel Glenn Hwy, Dayton, OH 45435;

    Department of Earth and Environmental Sciences, Wright State University, 3640 Colonel Glenn Hwy, Dayton, OH 45435;

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