Type Curves for Injectivity Decline

Abstract

Injectivity decline is a wide spread phenomenon for seawater injection, produced water re-injection, disposal of produced water in aquifers and whatever waterflood project with a poor quality injected water. The typical injectivity decline curves appear for impedance (normalised reciprocal to well index) versus PVI. They consist of linear growth interval for deep bed filtration, another interval for the linear growth during formation of external filter cake, ending up with the stabilised value. This paper discusses the stabilised impedance calculation. The mathematical model for the stabilised impedance is based on the torque balance of attaching (electrostatic and permeate) and detaching (drag, lifting and gravity) forces exerting upon a particle on the cake surface. If compared with the previous models, this paper accounts for electrostatic force and for varying non-unit value of the permeate factor. It was shown that the electrostatic force can exceed other forces and cannot be neglected. Moreover, the permeate factor can highly exceed one. Accounting for the two above factors completely change the order of magnitude for the lever arm ratio as obtained from the stabilised injectivity, if compared with previous works. The lever arm was also calculated from the particle deformation by permeate and electrostatic forces using Hertz theory, resulting in the same order of magnitude as that obtained from well data. It validates the model for stabilised injectivity. Analysis of 35 injector histories results in probabilistic distributions for 5 injectivity impairment coefficients, including the lever arm ratio. It provides with fully predictive tool for injectivity decline.