Homework #3 Due Date: 02/26/2018 1. For the data given in the following table, 1

Question

Homework #3 Due Date: 02/26/2018 1. For the data given in the following table, 1) identify a suitable decline model, 2) determine model parameters, 3) calculate the project production rate till the end of the 10 year, 4) predict yearly oil productions and plot predicted decline curve and history data together. Time (year) Production Rate (1,000 stb/day) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 9.63 9.29 8.98 8.68 8.4 8.14 7.9 7.67 7.45 7.25 7.05 6.87 6.69 6.53 6.37 6.22 6.08 5.94 5.81 5.68 5.56 5.45 5.34 5.23 5.13 5.03 4.94 4.84 4.76 4.67 4.59 4.51 4.44 4.36 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.1 3.2 3.3 3.4

Explanation / Answer

The scatter plot showing the two variables looks like follows:

From the graph above, we find that exponential fitting is more suitable than linear.

Let y =Ae^bx

where y = dependent variable (production rate) and x = Time (independent variable)

Taking log we have log y = log A + bx

Thus log y and x has a linear relation. Let us find out that relation.

The relation showing log y and x is given below:

Linear equation connecting is

log Y = 2.231-0.236x

Or y = e2.231e-0.236x

a) y= 9.307 e-0.236 x is the suitable declining model for time and production rate.

b) Model parameters are 9.307 for coefficient of e^-0.236x where next parameter =-0.236

c) For the end of 10th year, we can substitute x =10

y =9.307e-2.36 =0.878984

=0.879

d) Yearly oil productions

Year Oil production rate 4 3.621414 5 2.860193 6 2.258981 7 1.784143 8 1.409116 9 1.11292 10 0.878984 11 0.694222 12 0.548296 13 0.433044 14 0.342018 15 0.270126

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