•A simulation that runs with alternating periods of time step increase and convergence failure / time step chopping / small time steps, will normally be much less efficient than a run with albeit shorter average time steps, but with no convergence problems. The optimal time step is the largest possible with no problems, but as exemplified above, this may vary (strongly) during the run, so it is absolutely not a trivial question.
TUNING keyword summarized
TUNING has three records Record 1: Time step control
Record 2: Convergence tolerance parameters, recommended left at default values Record 3: Iteration control.
Each record contains a number of parameters and is terminated by a slash.
The keyword syntax, with record 2 left default is,.
TUNING
TSINIT TSMAXZ TSMINZ TSMCHP TSFMAX TSFMIN TSFCNV TFDIFF ... /
/
NEWTMX NEWTMN LITMAX LITMIN MXWSIT .../
TSINIT |
Max. length of next ministep (after this keyword) (default 1 day) |
TSMAXZ |
Max. length of any ministep (default 365 days) |
TSMINZ |
Min. length any ministep (default 0.1 day) |
TSMCHP |
Min. length any choppable ministep (default 0.15 day) |
TSFMAX |
Max. ministep increase factor (default 3) |
TSFMIN |
Min. ministep cutback factor (default 0.3) |
TSFCNV |
Cut factor after convergence failure (default 0.1) |
TFDIFF |
Max. increase factor after convergence failure (default 1.25) |
NEWTMX |
Maximum number of Newton iterations in a time step (default 12) |
NEWTMN |
Minimum number of Newton iterations in a time step (default 1) |
LITMAX |
Maximum number of linear iterations in each Newton iteration (default 25) |
LITMIN |
Minimum number of linear iterations in each Newton iteration (default 1) |
MXWSIT |
Maximum number of iterations within well flow calculation (default 8) |
In addition, the number of search directions stored for use in the linear solver procedure is defined by the NSTACK keyword in the RUNSPEC section.
The TUNING keyword can be used anywhere in the SCHEDULE section, and as many times as desired. The parameters will be valid until the next TUNING keyword is encountered.
If the user only wants to change TSINIT, the size of the next time step, the keyword NEXTSTEP is an alternative to re-including the entire TUNING keyword.
19. Non-neighbour Connections and System Structure
We return to the structure of the system matrix as in Figures 29 and 30. In this section we will discuss how the structure shown in Figure 30 is affected by a fault, or more generally, by the presence of nonneighbour connections. The model segment we will study is shown in Figure 33.
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Figure 33. A grid with ZYX ordering
This time we use the ordering most often used by Eclipse, where “direction 1” is Z, “direction 2” is Y, and “direction 3” is X. The cell ordering is then seen in Figure 33.
This configuration will result in the system matrix shown in Figure 34.
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Figure 34. System structure for grid in Figure 33
Next we look at what happens if there is a fault between the rows i = 2 and i = 3 in the grid. The configuration is shown in Figure 35. (When working through this example we assume the sand to sand contact is as in the figure.)
103
Figure 35. Grid as in Figure 33, but with fault
Note that some connections will disappear (cells are not in contact), while new contacts appear due to the fault. Connections which are present in Figure 33, but not in Figure 35 are marked with a “-” in the system, Figure 36, while new connections due to NNC-cells are marked with an “n”.
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Figure 36. System structure for faulted grid
The most important consequence of the presence of the non-neighbour connections is that the 7- diagonal structure has been destroyed. Some elements have disappeared, while others have been added. In this particular example the difference isn’t that large, but in general the NNC-entries can end up anywhere in the matrix, so techniques which utilise the 7-band structure can no longer be used. The zero-elements on the bands also pose problems.
Eclipse handles the NNC-entries as perturbations of the original structure, and project these entries onto the original bands. Effectively, the “alien” elements are moved to the right hand side of the
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equation and lags one iteration behind in the procedure. This approach works satisfactory when the number of “irregular” entries is small, but if the number of NNCs become large (like more than 10% of ordinary connections) it should come as no surprise that convergence rate is severely reduced.
Obviously fault throws generate non-neighbour connections. In addition, the most common sources for NNCs are wells, aquifers, and local grid refinements.
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