Question 3 (10 points): Producing
gas from the shale formations requires drilling through the water table to
access the shale formations at greater depths.
The wells are typically âcasedâ with concrete and steel sleeves to
prevent natural gas or fracturing fluids from entering the water table. A single well may have multiple layers of
casing. Suppose that the failure rate
for a single layer of casing in a single well was 1 in 1,000. A typical Marcellus shale well might have
three casing layers. What is the
probability of methane contamination from three faulty casings in a Marcellus
shale well? Assume that the failure rate for casings are all independent.
Question 4 (10 points): Many Pennsylvania
households have had methane-tainted water even without natural gas drilling.
Suppose that 10% of households have high background levels of methane in their
drinking water prior to the onset of natural gas drilling. Suppose also that the probability of a casing
failure leading to an elevated level of methane in drinking water is 95%. Suppose that a household living near a
natural gas drilling site observes a high level of methane in their water. What is the likelihood that the high methane
level was caused by a failed well casing? Assume a single-cased well for this
Question 5 (10 points): In a
well-known incident in Susquehanna County, fifteen families had their well
water contaminated with methane. Assume
that there were 50 wells drilled in the area of the contamination, and each was
single-cased. Further assume that each
well could contaminate at most one drinking water source. Using the Poisson model, calculate the
likelihood of fifteen casing failures.