Effects of fines migration and reservoir heterogeneity on well productivity: analytical model and field cases

Formation damage due to fines migration after water breakthrough during oil and gas production results in significant well productivity decline. A recent study derived an analytical model for fines migration during commingled water-oil production in homogeneous reservoirs. Yet, reservoir heterogeneity highly affects well productivity. This paper develops an analytical model for layer-cake reservoirs. We develop a novel methodology of characterising productivity decline by the function of impedance versus water-cut, two quantities that are commonly measured throughout the production life of the well. The methodology is based on a new analytical model for inflow performance in layer-cake reservoirs under fines migration. The new model integrates pseudo phase-permeability functions for water-oil flow with equations for fines release and induced permeability damage. The analytical model reveals linear well impedance growth versus water-cut increase, where the slope is determined by a modified form of the mobility ratio which includes the extent of formation damage. This linear form is shown to arise when the formation damage factor is constant, regardless of the reservoir permeability distribution. The model is validated by comparison with production histories of five wells from three fields, which exhibit good agreement with the linear trend predicted by the new model. The explicit formulae allow for prediction of productivity at abandonment, determining the optimal well stimulation time, as well as reconstructing skin values during the early stages of production to better estimate the influences of other formation damage factors, like those induced during drilling and completion.