# SPE Comparative Solution Project description of model 1

### purpose

The purpose of this problem is to investigate performance of both upscaling and classical pseudoization approaches.

### description of the fine-grid model

The model is a 2-phase (oil and gas) model that has a simple 2D vertical cross-sectional geometry with no dipping or faults.

The dimensions of the model are 762 meters long by 7.62 meters wide by 15.24 meters thick. The fine scale grid is 100 x 1 x 20 with uniform size for each of the grid blocks. The top of the model is at 0.0 metres with initial pressure at this point of 100 psia. Initially the model is fully saturated with oil (no connate water).

The initial properties of the fine grid model is as follows:

Porosity, f= 0.2;

Grid block sizes, DX = 7.62 metres, DY = 7.62 metres and DZ = 0.762 metres;

Viscosities, mo= 1 cp, mg= 0.01 cp (constant throughout the run)

Densities, ro = 43.68 1b/ft3 or 700 Kg/m3,

rg = 0.0624 1b/ft3 or 1.0 Kg/m3.

The permeability distribution is a correlated geostatistically generated field.

The fluids are assumed to be incompressible and immiscible. The fine grid relative permeabilities are shown on the table on the right.

Capillary pressure was assumed to be negligible in this case. Gas was injected from an injector located at the left of the model and dead oil was produced from a well on the right of the model.

Both wells have a well internal diameter of 1.0 ft and are completed vertically throughout the model. The injection rate was set to give a frontal velocity of 0.3 m/d (about 1 foot/day or 6.97 m3 per day), and the producer is set to produce at a constant bottom pressure limit of 95 psia. The reference depth for the bottom hole pressure is at 0.0 meters (top of the model).

 Sg Krg Kro Pcog 0.000000 0.025000 0.050000 0.075000 0.100000 0.125000 0.150000 0.175000 0.200000 0.225000 0.250000 0.275000 0.300000 0.325000 0.350000 0.375000 0.400000 0.425000 0.450000 0.475000 0.500000 0.525000 0.550000 0.575000 0.600000 0.625000 0.650000 0.675000 0.700000 0.725000 0.750000 0.775000 0.800000 0.825000 0.850000 0.000000 0.000000 0.000000 0.000000 0.000001 0.000007 0.000031 0.000093 0.000232 0.000501 0.000977 0.001760 0.002980 0.004800 0.007416 0.011065 0.016028 0.022631 0.031250 0.042315 0.056314 0.073794 0.095367 0.121716 0.153590 0.191818 0.237305 0.291038 0.354093 0.427631 0.512909 0.611280 0.724196 0.853215 1.000000 1.000000 0.912530 0.830041 0.752410 0.679518 0.611238 0.547448 0.488020 0.432827 0.381737 0.334621 0.291345 0.251773 0.215767 0.183188 0.153893 0.127737 0.104573 0.084248 0.066609 0.051496 0.038746 0.028191 0.019658 0.012965 0.007925 0.004338 0.001995 0.000668 0.000103 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

Apply upscaling or pseudoization method in the following scenarios:

a. 2D -2D uniform 5 x 1 x 5 coarse grid model

b. 2D -2D nonuniform coarsening. Max 100 cells.

You are allowed to use directional pseudo relative permeability (if necessary).

### the rules

If you include capillary pressure in your coarse grid models, please report the same run without using pseudo capillary pressure.

Please state the upscaling or pseudoisation method used for both absolute and relative permeability.