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PSEUDO UPSCALINGRock property data input to reservoir engineering models requires reliable special core analysis (SCAL) data which has been modified to account for the mathematical shortcomings of numerical simulation. The full value of SCAL has often not been realized because the rock relative permeability and capillary pressure are generally incorporated directly into the simulation model where they are subjected to a manual manipulation to fit observed production data.
The initial lack of attention to the effects of relative permeability is often one of the primary causes for the poor predictional capabilities of simulation models, even at later stages after the model has been "fully" history matched. This problem quite often is not rectified during the history matching due to the sheer number of variables matched.
Many oil companies do not have the time nor the expertise to perform a proper pseudo upscaling and this important area is therefore often ignored while much effort is put into other, and often, less important aspects of the model, resulting in considerable uncertainties in the output from the models. The overriding objective is to reduce the uncertainties in simulation of adapted dynamic SCAL data, thereby reducing one of the major causes for uncertainties in simulation model prediction.
Weatherford's pseudo upscaling services serves as an extension of our
SCALMAN services. We are therefore able to provide an integrated service covering the entire process from SCAL program design to pseudo upscaled dynamic pseudos.
Introduction To Pseudo UpscalingThere are three major reasons for the need to upscale pseudos:
- Capturing the geology
- Correcting for numerical dispersion
- Accounting for capillary pressure
Capturing The Geology
The traditional reason for pseudo upscaling is to capture fine heterogeneity in a coarse gridded system.
Quite often the fractional flow theory is used to create the pseudo curves. However, this method does not address the two other primary reasons for the need to upscale.
Correcting For Numerical Dispersion
A numerical simulator such as Eclipse considers each grid block as an element in which all properties are averaged. When water enters one side of such a grid block it is immediately dispersed throughout the gridblock due to the averaging of properties such as saturation. The water saturation at the far end of the grid block will be at the same as at the inlet instantaneously. The water can travel through a course gridded model more quickly than a fine gridded model. Consequently the water front becomes smeared causing a prematurely water break through in the coarse gridded model. This effect is called numerical dispersion. In practice there are other factors contributing to numerical dispersion such as the averaging of relative permeability and of saturations.
The effect of the upscaling, in relation to numerical dispersion, is directly related to the ratio between the number of grid blocks in the flow direction between the fine and the coarse gridded model. It is therefore important to start the upscaling at the core plug scale where the SCAL measurement has been made, in order to capture the full effect of numerical dispersion.
Figure 1: Numerical Dispersion
Accounting For Capillary Pressure
A numerical simulation program such as Eclipse uses the pressure difference across a grid block when calculating the flow through it. Under similar flow conditions the pressure difference across a grid block will be directly proportional to the size of this (in the flow direction). The direct effect of capillary pressure will therefore often be dominating in a core-sized grid block while it is negligible in a full field simulation formation scale grid block.
Figure 2: Balance of Forces at Core Plug Scale and Simulation Grid Block Scale
Therefore it is often claimed that the effect of capillary pressure is not important for the flow calculations in numerical simulation; however this is not correct.
In an offshore oil reservoir, where the frontal advance rate in the vast majority of the reservoir may be as low as 0.5-20 ft per day, the flow is often capillary-force dominated.
Figure 3: Balance of Forces
Oil recovery in the field is NOT dependent on the grid block size used in the simulation model. Therefore the effect of capillary pressure must be properly represented in the simulation model for it to capture the actual physics of the recovery.
If a correct pseudo upscaling is performed from core plug sized grid blocks and upwards in scale with a representative frontal advance rate, the effect of capillary pressure at the small scale is accounted for at the large scale by being gradually incorporated in the relative permeability curves as the upscaling progresses. This can be shown by upscaling two identical models with identical relative permeability at the small scale. If the capillary pressure is removed from one of these models the upscaled relative permeability curve at the next upscaling step will be different from that derived from the model incorporating capillary pressure.
Furthermore the true effect of gravity slumping will be captured using the procedure described above.
Pseudo Upscaling Services
Upscaling Design
It is often impractical to upscale directly from core plug sized grid blocks to full field simulation size grid blocks, due to the number of grid blocks such a model would require. Instead, a multiple step upscaling has to be designed. Weatherford ensures that the design of this upscaling will incorporate the full effect of heterogeneity in the different upscaling step.
Figure 4: Example of Upscaling Design
Upscaling Procedure And Considerations
When performing a pseudo upscaling Weatherford ensures that all aspects of the physics are taken into consideration. These include:- Incorporating the full effect of reservoir heterogeneity in the models
- Determining the proper length of each time step and the duration of the flood in the Upscaling models
- Upscaling in both horizontal and vertical directions when necessary
- Performing the upscaling so that the balance between viscous, capillary and gravitational forces is captured, i.e. starting at the core plug size and using representative frontal advance rates in the upscaling
- Merging the fully upscaled pseudo curves where applicable to facilitate practical use of the full field simulation model
Quality Control
Every single upscaling step is quality controlled during the upscaling by comparing recovery from the fine model with the recovery from the upscaled coarse gridded model incorporating the pseudo curves.
The merging of the fully upscaled curves is quality controlled by comparing recovery from identical models with and without merged curves.
Figure 5: Upscaling Accuracy
Figure 6: Upscaling Accuracy
Figure 7: Example of Upscale Pseudo Curves in a Pseudo Compositional Oil
Figure 8: Example of Recovery Accuracy Between Fine & Upscaled Coarse Gridded Model
Illustrating a nearly perfect match between the recovery of the fine and the upscaled coarsely gridded model
