Reservoir Simulation - Sensitivities

This module enables user to perform sensitivity analysis on one or more variables at once.

1. Input

There are four input cards, namely:

1. Well & Reservoir Data
2. Fluid Intialization
3. Relative Permeability
4. Sensitivities

It is not possible to modify input cards other than sensitivities. This is done to ensure consistency of the input variables between modules. If one wishes to edit it, this can be done in History Matching module.

1.1 Sensitivity Variables

1.1.1 Reservoir Properties

In general, all changeable variables in history matching can be used as sensitivity variables. A minimum of one variable is required and can be added as many as desired. To do this, simply check the box next to the variable.

Fig. 1: Sensitivity Type: Reservoir Properties

If you recall, the Numerical Model section has the following toggles -

Fig. 2: Toggles for h and x_e in numerical model settings

Here, if the toggles are switched on, the reservoir height and reservoir half-length are always enforced to be equal to fracture height (h_f) and fracture half-length (x_f) in all simulations - this includes simulation calls via cases in sensitivities and probabilistics.

The default behavior in the sensitivities feature when running sensitivities with x_e (Reservoir half-length) and x_f (Fracture half-length) -

1. If you have x_e=x_f in the model (toggle is on) - Then any specified x_e values are ignored for the given x_f in sensitivities and x_e is enforced to be equal to this x_f in the sensitivity case. Base case x_f is set as x_e if x_f is not provided.
2. If you have x_e not equal to x_f (toggle is off) - Then specified values of x_e are used, and if they are blank, the base case x_e is used.

Essentially, sensitivities and probabilistics cannot override these toggles. To freely adjust x_e and h, go to the history matching section and turn off these toggles on the Numerical Model card and click save before running sensitivities. Similar behavior when toggle is on/off for the other pair of variables - h_f | h

1.1.2 Well Control

User can also choose well control to do sensitivity analysis instead of reservoir properties. This can be done by adding at least one case with input of initial and final BHP, time to minimum BHP and total simulation time.

Fig. 3: Sensitivity Type: Well Control

1.2 Modify Cases

After sensitivity variables are chosen, one can modify each variable by clicking "Modify Cases" then "Save". To run, user can click three dots next to the case and click "Run Case" for individual run, or click "Run" button above the input cards.

2. Plot and Edit

All cases will be plotted automatically by default. To choose one or some of the cases, check or uncheck the show box for each case. Editting input can be done by clicking "Modify Cases" or "Edit Case". User has the ability to remove and/or add more variables to the sensitivity analysis.

3. How to Handle Simulation of Different pRi and GORi?

The black-oil PVT table is always generated in whitsonʳˢ from initial composition ($z_{i}$), reservoir temperature ($T_{R}$), equation of state (EOS), and surface process configuration. The black-oil PVT table is always regenerated locally at runtime, taking only a fraction of a second. This approach ensures flexibility and avoids delays previously encountered when downloading pre-generated BOT files from the cloud.

Current handling for variations in initial reservoir pressure ($p_{Ri}$) and initial GOR ($GOR_{i}$):

The black-oil PVT table is primarily a function of $GOR_{i}$ (through $z_{i}$) and ($T_{R}$). The $p_{Ri}$ is used to initialize the fluid as either single-phase or two-phase. This parameter is not a direct input in the generation of the black-oil PVT table but is used during its extrapolation to avoid numerical instabilities of negative compressibility and internal extrapolation as much as possible. Therefore, the extrapolated part of the black-oil PVT table (affected by $p_{Ri}$) is typically outside the region used in simulations and should not materially impact the quality of the results.

• Variations in $p_{Ri}$ with fixed $GOR_{i}$

  When $GOR_{i}$ is held constant, the same $z_{i}$ is used across all cases. Varying $p_{Ri}$ influences the initialization of the fluid system:

  • If $p_{Ri}$ ≥ $p_{sat,i}$, the fluid initializes as single-phase.
  • If $p_{Ri}$ ≤ $p_{sat,i}$, the fluid initializes as two-phase.

  Note

  If you compare the files of two History Matching cases with same $GOR_{i}$, but different $p_{Ri}$, there may also be some differences in the extrapolated part of the black-oil PVT table, but that should not impact the simulations.

• Variations in $GOR_{i}$ with fixed $p_{Ri}$

  Changing $GOR_{i}$ is equivalent to altering the $z_{i}$. For each case, black-oil PVT table will be generated using different composition. A new composition ($z_{i}^{*}$) is generated by taking the original $z_{i}$ obtained from Fluid Definition and recombining it to match the specified $GOR_{i}$. A new BOT is then constructed based on ($z_{i}^{*}$) and used in the simulation.

• Variations in both $p_{Ri}$ and $GOR_{i}$

  Both effects described in previous points are applied simultaneously.