Question

# 2. (25 pts.) The reflow from fracture-based NG drilling (spent fracking water) contains substantial dissolved salt...

2. (25 pts.) The reflow from fracture-based NG drilling (spent fracking water) contains substantial dissolved salt content. One quick method of determining total dissolved salt concentration (nominally TDS is total dissolved solids – a well-known water quality metric, which in this case, equates to total dissolved salt) across a wide spectrum of is to measure the fluid conductivity. A sample from each of the n = 5 wells is taken, and repeated over the course of four days, yielding m = 4 aliquots. Suppose the cost of collecting a sample is c1 = \$500, the cost of measuring an aliquot is c2 = \$100, and the cost function C=c1n+c2nm applies. Estimate the optimum number of aliquots to measure for specific conductance, using the data in Table 2, below. Compute the mean, standard error of the mean, and the optimum m and n if c1=\$500, c2=\$100, and C=\$2000.

 Well Aliquot 1 3110 3180 3180 3190 2 3400 3400 3400 3400 3 3090 3100 3080 3040 4 3750 3750 3700 3750 5 3100 3100 3140 3100

Table 2.

 Well Aliquot sh whsh opt nh 1 3110 3180 3180 3190 3165 36.968 7.394 7 2 3400 3400 3400 3400 3400 0.000 0.000 0 3 3090 3100 3080 3040 3077.5 26.300 5.260 5 4 3750 3750 3700 3750 3737.5 25.000 5.000 5 5 3100 3100 3140 3100 3110 20.000 4.000 4 Total 21.654

Since, nh cannot be a fraction.

 Cost: 2000= 500n+100nm Therefore, n=n1=7 nm=n2=0 i.e. m=0

Theory: