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RULE 2 - PERMITS <br />• where: V = macroscopic velocity <br />K = hydraulic conductivity <br />I = hydraulic gradient <br />8 = porosity <br />The range of hydraulic conductivity for the overburden, Wadge Coal, and underburden <br />units is 0.0013 to 0.0999 ft/d, the average hydraulic gradient is 0.03, based on data from <br />the permit area. The effective porosity for the Basal Williams Fork aquifer, which <br />includes the three subject units, is assigned a value of 10 percent, considering density logs <br />of borings in the PSCM permit area, the low hydraulic conductivity values for the subject <br />stratigraphic interval, and data presented by Robson and Stewart (1990) and Willimas and <br />Clark (1994). Using these input values gives: <br />V =K•I /8 <br />= 0.0013 ro 0.0999 ft/d • 0.03 / 0.1 <br />= 0.000039 to 0.03 ft/d <br />= 0.014 to 11 ft/yr <br />Groundwater flow rates for the alluvium in the valleys of Little Grassy Creek or Grassy <br />Creek were estimated using a variation of the above equation, applied to the alluvial <br />aquifer below the confluence of the two creeks near the northern boundary of the permit <br />area. The applicable equation (Freeze and Cherry, 1979) is: <br />Q =K•I.A <br />where: Q = volumetric flow rate <br />K = hydraulic conductivity <br />I = hydraulic gradient <br />A = cross - sectional area of the aquifer for which the flow is calculated <br />The hydraulic conductivity of the alluvium is estimated to be 1 ft/d from compilation of <br />upper Grassy Creek Seneca II Mine aquifer testing (Peabody, 1980). The hydraulic <br />gradient, based on the land surface slope, is 0.015. The cross - sectional area, calculated <br />from the aquifer width of approximately 500 feet, thickness of approximately 20 feet, and <br />a triangular cross section, is 5000 square feet (ft). Substituting these values into the <br />equation gives: <br />Q =K•I•A <br />= (1 ft /d) - (0.015) - (5,000 ft <br />= 75 ft /d <br />= 0.4 gallon per minute <br />= 0.63 acre -foot per year <br />Mass balance considerations indicate that the flow through the area should equal the <br />recharge to the units upgradient of the location for which the flow was calculated, <br />provided there are no substantial additions or extraction of groundwater in the intervening <br />PSCM Permit App. 2.04 -51 Revision 03/05/10 <br />