Section C: Exercises

Please attempt both exercises

Problem $1$

A reservoir has an average permeability value of $100mD.$ Its drainage area is $500$ acres acre is $43,560ft2$ and the well diameter is ${0\mathrm{.}7}^{\text{'}}.$ The fluid has a viscosity value of $0\mathrm{.}8cp$ and Bo equal to $1\mathrm{.}3r\frac{b}{s}tb.$ The reservoir is supported by a strong aquifer and it is producing at a constant rate, thus ensuring steady state conditions. There is some formation damage in the near wellbore area and as a result, the production flowrate has been

reduced by $20\%$ due to the presence of the damage $($i$.$e$.$ we know the production rates ratio rather their values$).$

Estimate the skin factor due to the formation damage

How much should be the skin factor to reduce the production loss into half?

Problem $2$

A cylindrical reservoir has a radius of $3,{000}^{\text{'}},$ a well radius of ${0\mathrm{.}35}^{\text{'}}$ and thickness of ${300}^{\text{'}}.$ The average rock permeability is $40mD$ and the initial pressure is $4,520$ psi. The wellbore is vertical with a length of $10,{000}^{\text{'}}$ and

an SSSV has been set at $1,000\text{'}$ causing a pressure drop of $100$ psi under flowing conditions. The reservoir fluid has a $B_0$ value of $1\mathrm{.}32r\frac{b}{s}tb,$ a viscosity value of $1\mathrm{.}5cp$ and a saturation pressure of $593.$ The liquid phase

density along the wellbore is assumed to be constant and equal to $6\mathrm{.}5ppg.$ The frictional pressure loss is ${0\mathrm{.}8}^{**}{10}^{-}{?}^5\frac{}{f}\frac{t}{st\frac{b}{d}}.$

A$.$ Compute the expected wellhead pressure when the well is shut in$.$

B$.$ Provide a chart of the pressure from the perforations level up to the wellhead choke when the well is shut in$.$

C$.$ Compute the expected wellhead pressure when the well is producing at a rate of $1,000$ stb$/$d$.$

D$.$ Can the well produce at a rate of $3,000st\frac{b}{d}?$