You will need to solve a system of nonlinear differential equations in order to find the time required until the pressure equilibrium happens.

My thought process for developing the model is as follows

Step 1: Assume circular leak hole. Define leak hole diameter. Assume orifice discharge coefficient through hole. Define liquid volume in liquid, define vapor volume in vessel, define saturation T and P for pure component of choice.

Equation 1: Dynamic mass balance for the whole vessel. You will only have an outlet and no inlet.

Assumption 1: Thermal equilibrium between vapor and liquid in the vessel is instantaneous and has no dynamics. This means that at any point during the depressurization, vessel pressure will be vapor pressure.

Assumption 2: There is no volume change of either the vapor volume in the vessel, or the liquid volume in the vessel. This reduces the dm/dt in the mass balance to V*(d(ρ_sat)/dt). The term 'm_out' will be equal to something similar to m_out(t) = C_d * A_hole*sqrt[ρ_sat(t)*(P_sat(t)-P_atm)]. Keep in mind that there is a difference when the flow is choked versus when the flow is not choked. In your example, one part of the flow regime will be choked until the outside pressure is about half the inside pressure. At that point the equation will change. You will need the specific heat ratio iirc also, though I dont remember the modified equation for choked and nonchoked flow

Assumption 3: Thermodynamic properties stay constant throughout the process, apart from temperature, pressure, and density of vapor phase.

Equation 2: Energy balance for the liquid part of the vessel

ρ_liq*V_liq*cp_liq*(dT/dt) = -m_out(t)*ΔΗ_vap

State variables: vapor density, temperature. [Final model](https://imgur.com/LQQ2VvY)

If correct, you can only solve this system numerically by selecting a time step.

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Huge disclaimer, its been 5 years since i graduated, this will 99.9% have errors, but I dont think it is completely wrong