Injection of water with oily particles happens during waterflooding by re-injection of produced water (PWRI). The injected oily particles are captured by porous rock causing decrease of permeability and consequent injectivity decline. Maintenance of the injection rate results in increase of pressure gradient near to well, snap-off the residual oil and additional formation damage due to released drops retention.

We study effects of residual oil mobilization in well vicinity due to pressure gradient increase and, consequently, the increase of capillary number. The mobilized oil ganglia perform snap-off, move together with the injected water; they are captured by rock causing additional formation damage.

The system of governing equations includes mass balances for oil, for particles and equation for desaturation curve. The analytical model derived includes expressions for suspended and deposited particle concentrations, for velocities of concentration fronts and for injectivity decline.

The main result is an additional formation damage induced by residual oil.

Comparison of the injectivity decline models with and without residual oil allows estimate the efficiency of the near-well area treatment by solvent in order to remove residual oil and to reduce injectivity decline.

Another important application of the model is determination of residual oil with PWRI from routine coreflood tests on relative phase permeabilities. If one injects produced water, the formation damage caused by the capture of injected particles and release of excessive residual oil fraction must be taken into account.


The produced water re-injection becomes an important option of water management during last 10–15 years, mainly for deep-water field developments. The produced water contains significant amounts of solid and liquid particles which is difficult and expensive to remove under sea platform conditions. Therefore, one expects drastic injectivity decline. The decline may result in significant cost increase in the waterflooding project. Reliable prediction of this decline is important for waterflood design as well as for the choice and preventive treatment of injected water 1,2. One of reasons for well injectivity decline is permeability decrease due to rock matrix plugging by solid/liquid particles suspended in the injected water 1–4 (The flow and deposition of particles in the rock matrix is called deep bed filtration).

The reliable injectivity prediction is based on mathematical modelling. Mathematical models of deep bed filtration consist of equations for mass balance of suspended and deposited particles, for kinetics particle capture by the rock and for permeability decline 1,2,5,6. Several analytical and numerical models are available in the literature 1,2,5–8.

The model parameters can be recovered from laboratory particle breakthrough curves and pressure drop on the core by means of inverse problems 1,2,5–10. The models fairly well reproduce the experimental data.

Produced water re-injection (PWRI) arise the problem of oily water transport in rocks 11.

The results of laboratory studies on deep bed filtration of oily particles are in a fairly good agreement with predictions by traditional suspension flow models 10–15.

The above-mentioned suspension transport studies do not account for the presence of residual oil in rocks.

Droplet generation from residual oil when the critical capillary number was exceeded has been observed in laboratory experiments 18. It was found out that the presence of residual oil had a profound effect on the measured permeability decline due to further retention of generated particles by porous medium. The permeability decline occurs in two stages, one associated with the injected droplets, when permeability declines slowly and breakthrough particle concentration does not exceed the injected concentration, followed by a second stage during which generation of droplets plays an important role and permeability declines faster.

The mathematical model developed captures effects of oil particle generation by residual oil, retention of injected and generated particles by rock and consequent permeability reduction 18. The simulated and experimental data are in a good agreement.

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