ECO2N/T2WELL to initialize a depleted reservoir (low pore pressure)

The best approach is using an initial condition that can represent the real situation. For example, if the reservoir was depleted by 3 MPa, you can have the elements at well screen has a pressure  3 MPa lower than  original pressure and set these elements to a large volume (v=1.0e50) and run the model to quasi-steady state. 

Dear Facheng,

I had a look to Pan et al paper you mention, and specifically to Case 3.

In Case 3 they simulate the injection of CO2 in a gas field pool at 3000 m depth. They wanted to verify what happen when injecting in an already depleted gas pool, so they set the initial P much below the hydrostatic P of around 300 bar (at 3,000 m). They assigned an initial P of 34 bar, which is lower than the CO2 critical P. As reservoir T is 90°C, the CO2 is initially in gas-like supercritical conditions in the reservoir.

I think they wrote "The initial pore pressure in the reservoir is arbitrarily set at approximately 3.4 MPa." because they did not want to replicate a real field problem, but simply verify the processes connected to the injection in a depleted gas pool. In real field conditions, the reservoir P would be the result of past natural gas extraction. So initial conditions may be assigned just looking at measured reservoir P or might be the result of simulated natural gas extraction. Initial conditions were also chosen to avoid the phase transition from single-gas CO2 to two-phase gas-liquid CO2 that cannot be handled by ECO2N.

To note that ECO2N can only model the H2O-NaCl-CO2 ternary system. Thus, the natural gas reservoir is already filled by CO2 at initial conditions and no displacement of CH4 by CO2 can be simulated.

For Case 3 you need to assign the initial condition to the wellbore. Assuming steady-state initial conditions in equilibrium with the reservoir P&T, you should run a steady state to have the column of gaseous CO2 in the wellbore at T equal to formation T  vs depth (90°C at 3,000 m, 35°C at surface - as per Case 1? - with a linear profile vs depth), and P according to gas-static equilibrium.

To note that they simulated the injection of CO2 at 100 kg/s (rather high rate) and at 60°C, which is also a rather high injection T. I guess this high T, as well as 35°C for ambient T at ground level, was chosen to avoid the crossing of CO2 saturation line in wellbore elements, as phase transition cannot be handled by ECO2N. The high injection rate helps in maintaining a high pressure along the wellbore which also avoid the crossing of saturation line.

If you want to adapt Case 3 parameters to your specific needs, may be with different depth, reservoir P, different geothermal gradient, you need to check if CO2 phase transitions are likely to occur, as they would not allow to complete the simulation with T2Well-ECO2N. For multiphase wellbore flow conditions you need T2Well-ECO2M capabilities. They should be available in the new TOUGH4 release.

I used T2Well-ECO2M some years ago. The experience we gained is that multiphase flow is likely to occur any time the CO2 is injected in a reservoir with P well lower than hydrostatic. The WHT, or better the WH enthalpy, of injected CO2 plays a very important role in determining the thermodynamic conditions along the wellbore. See the figure below from Strpić et al. (2021). Left= numerical heat exchange, right= semi-analytical heat exchange.

Imagine CO2 arrives at the well site in a supercritical compressed state through a long buried pipeline. The CO2 T would be close to average annual ambient T, between 5 - 30°C depending on the well geographical location. Thus, what will be constant at WH will probably be the CO2 enthalpy at pipeline P&T. For a depleted gas reservoir, the required WHP may be low, depending on reservoir P and depth, and could be lower than pipeline P. When starting to inject it is likely that CO2 will expands because its P is higher than WHP. The expansion will cause cooling (with T going down, even below 0°C) and will likely flash that will propagate down the wellbore. Depending on initial reservoir P, T and depth, two-phase conditions may or may not propagate into the reservoir.

You may run sensitivity simulations starting with high WHT (or WH enthalpy) and reducing them until two-phase conditions develop along the wellbore. This is what we did in the past to study the impact of different WH injection parameters with T2Well-ECO2M.

We also used TMGAS (Battistelli and Marcolini, 2009) to simulate the injection of CO2 in a natural gas reservoir (with CH4, ethane, propane) for the cases in which there is single CO2 flow along the wellbore. TMGAS is not coupled to T2Well, but it has internal single phase wellbore flow capabilities, with an approximate approach based on a steady-state flow assumption along each time step (Battistelli et al., 2011). Despite that, TMGAS results (right) are very close to those of ECO2M (left), even with a rather different approach for calculating thermodynamic equilibria and non-aqueous phase properties.

I mentioned 3 figures that were not uploaded.