Flow of particulate suspension in porous media with particle retention and consequent permeability reduction is discussed. Using analytical model for suspension injection via single well, the permeability damage zone size was defined and expressed by transcendental equation. Analysis of field data shows that usually the size of damaged zone does not extend more than one meter beyond the injector. The definition of damage zone size is used for design of well stimulation via deposition removal.


Deposition of solid phase and retention of particles from the moving fluids during flow in porous media result in permeability decline [1]. In the petroleum industry it happens in almost all processes of oil production: injection of sea or produced water with solid or liquid particles causes decline of injectivity, invasion of drilling fluid into formation rock yields decreased return permeability, precipitation of salts in the near well region causes well index decline, etc. [2, 3]. The above mentioned phenomena, called formation damage, can seriously impact on the economics of field development.

The retention and deposition phenomenon occurs also in disposal of industrial wastes, geothermal power production and in several environmental and chemical engineering processes [4, 5].

Different well stimulation technologies are used for damage removal and mitigation: acidizing, perforation, solvent or inhibitor injection, etc. Optimal planning of well stimulation requires knowledge of the deposit proximity relative to the wellbore [1, 2]. Area of solid phase retention and deposition can be found from mathematical modeling, field data or laboratory tests. Yet, a theoretical definition of the size of the formation damage zone, to the best of our knowledge, is not available in the literature.

In the current work we concentrate on well index decline during injection of seawater or produced water which is a wide spread phenomenon in waterflooding field projects. Solid and oily particles are captured by rock from the injected fluid resulting in permeability decline.

The traditional model for particulate suspension in porous media consists of mass balance for suspended and retained particles, equation of particle capture kinetics and modified Darcy's law accounting for permeability decline due to particle retention [5–10]. The problem of axi symmetric injection into clean bed allows for analytical solution [11, 12]. The model contains two phenomenological parameters - filtration and formation damage coefficients. The parameters can be found from either laboratory coreflood tests or well injectivity history by solving the inverse problems [11–15].

Several micro models for injectivity decline have been derived for pore scale: population balance equations [16, 17], random walk models [18–20], numerical network models [2, 4]. The traditional model for deep bed filtration can be derived from micro scale only for the case of mono dispersed suspensions [17].

In the current work we define size of formation damage zone using an analytical model for axi symmetric suspension flow in porous media. This size can be found from transcendental equation. It was shown that the formation damage size has an order of magnitude of the mean distance of deposition from the well. Calculations show that, with the exception of very low filtration coefficient cases, the damaged size almost always does not exceed one meter.

The defined damaged zone size is proposed for application in the design of well acidizing and perforation. Some field cases presented show that in successful applications the amount of injected acid has the same order of magnitude as that calculated by the proposed method.

It is also shown how the proposed damaged zone size can be used in well modeling during reservoir simulation and in defining the length of perforation holes.

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