Abstract
In this work, we develop a new analytical solution for the problem of deep bed filtration under size-exclusion dominated particle capture. An uspcaled stochastic micro model has been derived that models individual particle-pore interactions. The solution is based upon mono-dispersed suspension injection into a medium with a known pore throat distribution. Ultimately, the model can be used for matching with laboratory corefloods, simulation of permeability decline or expected tracer breakthrough.
Size-exclusion particle capture during suspension transport in porous media takes place during drilling fluid penetration into oil bearing formations, sand production and the injection of poorly treated water. Straining particle capture can dominate over the particle attraction in cases of produced water injection, injection of produced water from aquifers, fines production in fractured wells and gravel packed horizontal wells. Deep bed filtration contributes highly to the problem of formation damage.
Planning and design of the above-mentioned oil production processes is based on reliable mathematical modeling. If compared with previous population balance models for the general case of particle capture, the current work discusses a particular case of pure straining. We show that in the case of particle-grain and particle-particle repulsion, the particles cannot be strained in pores larger than the particle size. The particles can be captured in thin pores only. These considerations change the expression for capture rate in the basic population balance model. In order to validate the proposed model by comparison with laboratory tests, we found a travelling wave solution. The comparison with 2 sets of laboratory data showed good agreement, which validated the proposed model.
The new solution has broad application to the petroleum industry. The developed model can be applied for: (1) Particle sizing for drilling fluids, (2) Log interpretation of filtrate penetration into the formation, (3) Design of injected water treatment and (4) The design of gravel packs to minimise fines production and formation damage.
