I would like to know how to answer part b and c, particularly c. I know how to calculate mean and standard deviation but didn't combine them to get proven reserves the right way according to my teacher in part c. Reserves = STOOIPx Recovery Factor

QUESTION 3 Done - Blue Notebook a) What is the basic formula used to calculate the Reserves of an oil reservoir using Monte- Carlo Simulation? Please explain the meaning of each term. (5 Marks) b) An oil field is composed of three independent reservoirs located at depths of respectively 1500 m, 2500 m and 3000 m. An uncertainty calculation has led to the probability density function (pdf) of the reserves of each reservoir. It is a Gaussian distribution N(m, ?) with the following parameters for each reservoir: Reservoir 1: mean m,= 100 MMBBLS and standard deviation of = 30 MMBBLS Reservoir 2: mean m2= 200 MMBBLS and standard deviation 62 = 50 MMBBLS Reservoir 3: mean m3= 250 MMBBLS and standard deviation 3 = 80 MMBBLS The reserves of reservoirs 2 and 3 have a correlation coefficient of 0.8, while the reserves of reservoir I are independent of the reserves of the two other reservoirs. What are the Proven, Probable and Possible Reserves of the field (use Hint 3 below)? (10 Marks) c) Suppose that the STOOIP and the Recovery Factor of an oil field are lognormally distributed independent random variables. The mean of the STOOIP is 300 MMBBLS and its standard deviation is 150 MMBBLS. The mean of the Recovery Factor RF is 50% and its standard deviation is 10%. What are the Proven Reserves of the field (use Hints 1, 2 and 3 below)? (10 Marks) Total 25 marks Hint 1: if the random variable X follows a lognormal distribution and has a mean M and a standard deviation E , then the random variable LogX follows a normal distribution with mean m = Log Jam and standard deviation a = Log (iz + 1) Hint 2: the exponential is an increasing function Hint 3: for a normal distribution of mean m and standard deviation a, the 10% quantile (or P90) is equal to: 910 = m - 1.280 and the 90% quantile (or P10) is : 990 = m + 1.280 Page | 4