Background

Oil exploration and extraction is a very expensive business. It is therefore very important to accurately estimate the life of oil wells that are found before drilling begins.

Objective

Estimate total oil production rate of all well up to 10 years using only the first 3 years (1 to 1,096 days) of production data. Provide a report that describes your algorithm briefly, compares the actual and estimated production rates by plotting the production rates, and calculates the l2-norm of the estimation errors.

Input

All 25 production wells are set to production at their maximum rate for 300 days at the beginning. Then the maximum well rate is reduced to 100 barrels of oil per day for 60 days. The production wells resume their maximum production rates after 360 days for a total of 10 years (3,653 days). The file “OilRate.xls” contains total oil production rate for all wells (barrels per day) vs. time (days).

Output

After your program analyzes the input data it should output the estimated oil production rate for the next ten years.

Details

The main data files are “pore_volume.maps” and “oil_saturation_year6.maps” which have cell initial pore-volume in barrels and oil-saturation in fractions at the 6th year (2,192 days). The amount of oil for each cell is calculated by multiplying pore volume with oil saturation. The I, J and K indices in the files are: I for x-direction, J for y-direction and K for z-direction. Note that the K-index and z-direction are positive increasing toward the earth center (i.e. positive downward which is opposite to our normal convention.)  Other supporting files are: “permeability.maps”, “water_saturation_year6.maps”, “gas_saturation_year6.maps” and “well_location.data”.

The data in the files are organized as x-z cross-sections, i.e. printed as I-K cross-section for each J index. A number with the letter “P” adjacent to it indicates the cell is a production interval for a well. Similarly, a number with the letter “I” adjacent to it indicates the cell is an injection interval for a well.

Find a well location in terms of I-J index that can give highest initial oil production rate. Provide a report that describes your algorithm briefly, and the reasons for selecting your in-fill well location.  Note that the problems of water and gas productions will not be considered for this project.