The inverse problem of determining the filtration function and permeability reduction in flow of water with particles in porous media

The original publication can be found at www.springerlink.comDeep bed filtration of particle suspensions in porous media occurs during water injection into oil reservoirs, drilling fluid invasion of reservoir production zones, fines migration in oil fields, industrial filtering, bacteria, viruses or contaminants transport in groundwater etc. The basic features of the process are particle capture by the porous medium and consequent permeability reduction. Models for deep bed filtration contain two quantities that represent rock and fluid properties: the filtration function, which is the fraction of particles captured per unit particle path length, and formation damage function, which is the ratio between reduced and initial permeabilities. These quantities cannot be measured directly in the laboratory or in the field; therefore, they must be calculated indirectly by solving inverse problems. The practical petroleum and environmental engineering purpose is to predict injectivity loss and particle penetration depth around wells. Reliable prediction requires precise knowledge of these two coefficients. In this work we determine these quantities from pressure drop and effluent concentration histories measured in one-dimensional laboratory experiments. The recovery method consists of optimizing deviation functionals in appropriate subdomains; if necessary, a Tikhonov regularization term is added to the functional. The filtration function is recovered by optimizing a non-linear functional with box constraints; this functional involves the effluent concentration history. The permeability reduction is recovered likewise, taking into account the filtration function already found, and the functional involves the pressure drop history. In both cases, the functionals are derived from least square formulations of the deviation between experimental data and quantities predicted by the model.Alvarez, A. C., Hime, G., Marchesin, D., Bedrikovetski, P

Effect of suspension fluid chemistry on fracture system stimulation using micro-sized proppant placement

The physical model and experimental data support the beneficial technology of graded proppant injection into naturally fractured reservoirs to stimulate natural fracture permeability. Injection of particles with increasing size, at poroelastic and hydraulic fracturing conditions, yield deeper penetration and gradual filling of natural fractures with a resulting increase in permeability. This work expands on the concepts and outlines steps to maximize the benefit of graded proppant injection to enhance coal seam gas stimulation by focusing on the effect of the chemistry of injected fluid on the overall performance and the use in conjunction with hydraulic fracturing. Low productivity indices can be observed in many moderate- to low-permeability coal bed methane (CSG) reservoirs due to low aperture and poor connectivity of natural cleats. Graded proppant injection in CSG environments can: stimulate a stress sensitive cleat system below the fracturing pressure as well as enhance a fracturing treatment by invading cleats, lowering fluid leakoff, and maintaining aperture during production. Further, periodic or remedial treatments could to counter effective stress on the cleats improving production by maintaining cleat aperture. Laboratory tests on coal core flooding by water under increasing pore pressure with proppant injection at the maximum pressure have been carried out under different salinities of the injected water. Proppantproppant and proppant-coal Derjaguin-Landau-Verwey-Overbeek (DLVO) total interaction energies were calculated to optimise the condition for successful proppant placement. Results on the DLVO total energy of interaction showed that conditions favourable for successful proppant placement in coal cleats are suspension ionic strengths between 0.05 M and 0.1 M NaCl. At these conditions no proppant agglomeration and proppant-coal attachment are observed, allowing deeper penetration of proppant into the natural coal cleat system. Lower suspension ionic strengths can lead to natural coal fines migration, cleat plugging and coal permeability reduction. Based on the experimental results and previously developed model a case study has been conducted to evaluate the productivity enhancement using this technique. The results show about four-fold increase in well productivity index at injections below fracturing pressures and may further improve the stimulated reservoir volume when used in conjunction with low permeability coal hydraulic fracturing treatments

Upscaling of stochastic micro model for suspension transport in porous media

© Springer The definitive version can be found at www.springerlink.comMicro scale population balance equations of suspension transport in porous media with several particle capture mechanisms are derived, taking into account the particle capture by accessible pores, that were cut off the flux due to pore plugging. The main purpose of the article is to prove that the micro scale equations allow for exact upscaling (averaging) in case of filtration of mono dispersed suspensions. The averaged upper scale equations generalise the classical deep bed filtration model and its latter modifications.P. Bedrikovetsk