Problem $2.$ PTA

$(35\%)$

Objective: A simple practice to obtain reservoir properties using drawdown and build up data. A new well located in a large reservoir, was tested with the results shown in Table $1.$ After flowing for $96$ hrs $,$ the well was shut in for a pressure build up test. Reservoir and well data are as follows:

$q=519ST\frac{B}{D}{B}_o=1\mathrm{.}06R\frac{B}{?}$ STB ${}_o=0\mathrm{.}92cph=13ft.=0\mathrm{.}22,r_w=0\mathrm{.}27ft.c_t={13}^{**}{10}^{-6}{}^{-1}$ Connate water saturation $(S_{wi})$:$0\mathrm{.}32$

a$)$ Plot pressure versus time on a linear scale to get an overview of the drawdown and build up tests from $0$ to $168$ hrs$.$

b$)$ Perform log$-$log diagnostic plot for drawdown test and compute the well bore storage coefficient for the test.

c$)$ Analyze the drawdown and build$-$up tests by conventional semi$-$log methods and determine the formation permeability and skin factor from both tests and the average reservoir pressure from build$-$up test.

d$)$ Is the well damaged or stimulated? Why?

Make the appropriate plots with these data and show all of your work such as slopes, equations, units and calculations.

$\backslash$table$[[$Time $($hrs$),P_{wf}(a),$Time $($hrs$),P_{wf}(a),$Time $($hrs$),P_{wf}($psia$)],[0,P_i=3793,3,3593,97,3652],[0\mathrm{.}0334,3788,5,3563,97\mathrm{.}5,3684],[0\mathrm{.}0688,3783,10,3553,98,3707],[0\mathrm{.}1,3777,24,3547,98\mathrm{.}5,3724],[0\mathrm{.}1330,3773,48,3542,99,3737],[0\mathrm{.}1670,3768,72,3540,101,3768],[0\mathrm{.}25,3758,96,3537,106,3777],[0\mathrm{.}5,3723,96\mathrm{.}1,3553,114,3781],[0\mathrm{.}75,3698,96\mathrm{.}25,3572,120,3782],[1,3678,96\mathrm{.}5,3607,144,3786],[2,3623,96\mathrm{.}75,3632,168,3787]]$

Table $1$: Drawdown and build up tests data for Problem $2$

Note: Please use field units to calculate the reservoir parameters.

Note: A log$-$log graph of pressure change, $"P=P_i-P_{wf}"$ in a drawdown test vs$.$ production time $(t),$ is a diagnostic indicator of the well bore storage effect which is dominant during the early time region. Any point on the straight line passing through the data of this plot satisfies: Where $C_s$ is wellbore storage coefficient $(bb\frac{l}{}),$ t is production time $($ hr $)$ and q is well flow rate $($STB$/$day$),$ Pi is reservoir initial pressure $($psia$)$ and Pwf is flowing pressure $($psia$).$ For detailed information see the "chapter $1$ and $2$ of John Lee's Well Testing Book $(1982)".$