Oil rate prediction can be derived om Vogel's inow peribrmance relation as 9' P P 2 =10.2JL 0.8#WL (P) (P) qmax r r Where q and qmax are the predicted and maximum oil rate in bbl/d and ow and PI are well owing pressure and reservoir pressure in psi respectively. Given the following distributions for reservoir pressure, uncertain maximum oil rate and well owing pressure: Pr = Uniform distribution between 2400 to 2500 psi = Equilateral triangular distribution with the oil rate between 500 to 1000 bbl/d ow = Normal distribution with u= 1500 psi and o = 100 psi Correlation coefcients are 0.9 and 0.8 between the pressures and between pressure and maximum oil rate respectively. qmax Using the rst-order analysis method, compute the expected oil rate. Using the FOSM method, determine the variance of the o rate prediction. Ifyou can choose only one uncertainty check, which parameter should be checked to improve the certainty of the oil rate prediction? Also provide your reasons of the choice. Assume no correlation between pressures and between pressure and maximum ow rate determine the o rate prediction using MCS with 10, 100, and 5000 samples. Also construct the CDFs for the predicted o rate 'om diiferent sample sizes and compare the result. Using Latin Hypercube Sampling technique, calculate the mean and variance of the predicted oil rate with 10, 100, and 5000 samples and compare the result with the previous result in d)