$4$:$58$

$.$Il $4$G $46$

Final $2024$ Problems

Problem $1(20$ marks$)$: A core is prepared for a series of flow experiments. It consists of two sections of rock joined in series:

Section $1($upstream$)$: Length $,$ Permeability

Section $2($downstream$)$: Length $,$ Permeability

The cross$-$sectional area of the core is $.$ Pressure taps are located:

At Point A$,5$ cm from the inlet $($midpoint of Section $1)$

At Point B$,10$ cm from the outlet $($midpoint of Section $2)$

Brine with a viscosity of $2$ cP is injected into the core at a steadystate flow rate of hour. The downstream pressure is maintained at atmospheric pressure $(0$ gauge pressure$).$

Tasks:

${?}_1$ Sketch: Draw a labeled diagram of the core setup, including:

Core dimensions $($length$,$ cross$-$sectional area$)$

Permeabilities of each section

Locations of the pressure taps $($Points A and B $)$

Flow direction and injection rate

${?}_2$ Derive: The pressure profile across the core, considering steady$-$state flow.

${?}_3$ Calculate: The gauge pressures $($in atm$)$ at Point A and Point B$.$

${?}_4$ Discuss: How the higher permeability of Section $2$ influences the pressure distribution and the total pressure drop across the core.

Problem $2(20$ manks$).$ An rueanzed on went s producing at a