Assignment10

A simple "tank" model for gas flow from a well controlled by pressure is

$$ \frac{V_p T_s}{P_s T}\frac{d}{dt}\left(\frac{P(t)}{z\left(P(t), T)\right)}\right) + J \left(P(t)^2

• P_{wf}^2\right)^n = 0 $$

where $P(t)$ is the tank pressure, $T$ is the tank temperature (constant), $V_p$ is the pore volume of the tank, $P_s$ and $T_s$ are standard temperature and pressure, $J$ is the well productivity index, $n$ is a fitting parameter that captures inertial effects near the well, $P_{wf}$ is the well pressure, and $z$ is the gas expansion factor.

Use DifferentialEquations.jl to solve this differential equation. Implement your solution inside the function gas_solver() in the assignment10.jl file. The argument list for gas_solver should be obvious from the equation above aside from Pₒ which is the initial tank pressure and tmax which is the maximum time you want the solver to run.

The function should return the full solution composite type (the thing that the solve function from DifferentialEquations.jl returns). A set of arguments to gas_solver that should return a decent solution is available in the runtests.jl file.

Just use the default solver, do not specify any additional parameters to solve. The $z$-factor function has already been coded up for your use.

Testing

To see if you answers are correct, run the following command at the Terminal command line from the repository's root directory

julia --project=. -e "using Pkg; Pkg.test()"

the tests will run and report if passing or failing.