MRST - MATLAB Reservoir Simulation Toolbox

Harmonic Upscaling

In this example, we will perform a simple harmonic permeability upscaling on a model from the project "Sensitivity Analysis of the Impact of Geological Uncertainties on Production Forecasting in Clastic Hydrocarbon Reservoirs" (SAIGUP). The model has faults, inactive cells, and disconnected components, but no pinch-out. To this end, we form an overlying coarse grid by partitioning the fine-grid uniformly in logical Cartesian space and then use a set of relatively simple calls to 'accumarray' to perform the upscaling.

Contents

Load the required modules

try
   require upscaling coarsegrid
catch %#ok<CTCH>
   mrstModule add upscaling coarsegrid
end

Load and process data

We assume that the data has been downloaded and placed in the appropriate data directory under the MRST root directory.

try
   grdecl = readGRDECL(fullfile(ROOTDIR, 'examples', 'data', ...
                                'SAIGUP', 'SAIGUP.GRDECL'));
   grdecl = convertInputUnits(grdecl, getUnitSystem('METRIC'));
   G      = processGRDECL(grdecl);
   G      = computeGeometry(G);
   rock   = grdecl2Rock(grdecl, G.cells.indexMap);
catch me
   error('SAIGUP model data is not available.')
end

Upscale model

Upscale the model by a factor 5x5x5 using a simple harmonic average for the permeability and arithmetic average for the porosity. (This demonstrates the power of the accumarray call..)

w  = G.cells.volumes;
p  = partitionUI(G, G.cartDims./[5 5 5]);
for i=1:size(rock.perm,2)
   K = accumarray(p,w./rock.perm(:,i))./accumarray(p,w);
   crock.perm(:,i) = 1./K;
end
crock.poro = accumarray(p, rock.poro.*w)./accumarray(p,w);

Visualize result

As expected, using such a naive upscaling will move the permeability values towards the centre of their fine-scale spectre.

clf
pargs = {'EdgeColor','none'};
subplot(2,2,1)
plotCellData(G,log10(rock.perm(:,1)),pargs{:});
view(-95,40); axis tight off; cx = caxis; title('original');

subplot(2,2,2)
plotCellData(G, log10(crock.perm(p,1)), pargs{:});
set(gca,'zdir','reverse');
view(-95,40); axis tight off; caxis(cx); title('upscaled');

subplot(2,2,3:4)
hist(log10(convertTo(rock.perm(:,1),milli*darcy)), 100);
hold on
hist(log10(convertTo(crock.perm(p,1),milli*darcy)), 100);
hold off
h=get(gca,'Children');
set(h(1),'FaceColor',[0 0 0.4])
set(h(2),'FaceColor',[0.7 0 0],'FaceAlpha',.4)
legend('original','upscaled');
title('permeability histogram'); xlabel('mD');

Harmonic upscaling of the permeability from a SAIGUP model

Published June 3, 2013