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Modification of the Kozeny-Carman Equation To Quantify Formation Damage by Fines in Clean, Unconsolidated Porous Media
- Eva D. Krauss (University of Colorado Denver) | David C. Mays (University of Colorado Denver)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- November 2014
- Document Type
- Journal Paper
- 466 - 472
- 2014.Society of Petroleum Engineers
- 6.3.1 Flow in Porous Media, 6.3 Fluid Dynamics, 6 Reservoir Description and Dynamics
- Kozeny-Carman, fines, permeability, formation damage
- 24 in the last 30 days
- 326 since 2007
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Estimating formation permeability as a function of porosity, grain size, and the quantity and structure of fines is important in reservoir engineering. One can use the Kozeny-Carman equation to estimate the permeability of clean, unconsolidated media as a function of porosity and grain size, but it does not account for the quantity and structure of deposited fines. This study shows how incorporating of the volume of fines and a dimensionless bulk factor into the Kozeny-Carman equation can be used to model how the quantity and structure of deposited fines control permeability. Several experimental studies from the literature are analyzed, representing a range of fines (type and diameter), porous media, fluids, and Darcy velocity. These studies indicate that, when other variables are held constant, experiments conducted at a higher Darcy velocity result in less plugging. For each experiment, a dimensionless bulk factor in the Kozeny-Carman equation was fitted, with use of the root-mean-square method, to best match the experimental data. Fitted values of the bulk factor were then correlated with the Péclet number to investigate how the structure of fines, quantified by the bulk factor, depends on the characteristics of the porous media, the depositing colloids, and the Darcy velocity. Larger bulk factors are observed at a lower Péclet number, when diffusive transport dominates, which could result from more-dendritic deposits. Smaller bulk factors are observed at higher Péclet numbers, when advective transport dominates, which could result from deposits that are more compact. By understanding how the bulk factor, and, therefore, the extent of permeability reduction, depends on the Péclet number, one can optimize pumping schemes. The primary application of this work is to optimize well-pumping rates to prevent or manage plugging that results from the deposition of fines in initially clean, unconsolidated porous media, including both geologic formations and gravelpacks used for sand control.
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