Particle Transport In Sandstones

Abstract

@Copyright 1977, Amefican lnslltute of Mining; MeIallurglMl, and Petrol, nEngineers, inc. This paper was preaenterl at Ihe 52nd Annual FM Techmcsl Conference and Extnblt!on of the Society of Petroleum Engineers of AlME. held m Denver, Colorado, Oct. 9.12.1977. The material is sub;ect to Correchonbyt heauthor. Permission locopyia restdcted toanabstracl olnotmore lhan300 words. Write 6200 N. Central Expy. Dallas, Texas 75206. - ABSTRACT Particle transport within the Berea, NoxieandCleve-Iandsandstones having mean pore sizes of 10, 15and30 micronst respectively, was studied by infection of aqueous suspensions of sand particles hovingmean particle sizes of 4, 6and7 microns. Aconstarlt flow rate w~sused, and the pressure drop across the core wascontinuously monitored.The effluents were collected ina fraction collector, and the number of particles per milliliter and distribution of sizes of the particles were determined using apatiicle counter interfaced withc computer. These data were used to postulatea theory of discrete particle transport within porous media from a statistical point of view. A statistical random walk model was developed usinSPoiseuille's capillary flow equation and the actual pore size distribution of thecore to calculate the pressure drop across the core. Pa,-ticles areselecte6usin9a rondom number generator and the actual particle size distribution, and are tested for passage through the most probable c-pillary witha pressure threshold function.If the particle passes, another particle Isgenerated; however, ifthe particle lodges, onewpressure iscalwlated, andeach capillary is tested for particle breakout with the newpresxsre. This process is continued until ssplugging pressure i:~ttained ora ._ maximum number of particles pass through the core. The calculated pressures anddistributians of effluent particles close! y approximate the experimental Iy obsewed data. The process of particle transport, where COIIoidal forces are negl iglble, is a random statistical process which can be represented by a statistical mathematical model. ~RLECa f)oNALDsoN

Formation and ultrasonic removal of fouling particle structures in a natural porous material

“…Rege and Fogler (1987) proposed a network model to predict the permeability reduction due to particles. A comparison between their numerical results and the experimental results presented by Donaldson et al (1977) showed a good agreement.…”

“…The special interest for this fouling mechanism distinguishes the present work from earlier studies of the transport of particles through sandstones, see for instance Donaldson et al (1977) and Jiao and Sharma (1992). The occurrence of particle bridges in the near wellbore region of oil reservoirs was already mentioned by Batli and Risnes (1979) and Risnes et al (1982); however, a physical interpretation was not provided.…”

“…A mathematical description of the fouling mechanisms described above has been given by several authors. For instance, Donaldson et al (1977) proposed a statistical model to predict the decrease in permeability caused by particle deposition within a sandstone. Rege and Fogler (1987) proposed a network model to predict the permeability reduction due to particles.…”

Development of volume‐average theory for deep‐bed filtration

“…Work by Donaldson supports this conclusion, demonstrating that while the permeability of a sandstone formation declined by two orders of magnitude during filtration experiments, the porosity changed by only 0.3% Ž . Donaldson et al, 1977 . Therefore, the most important parameter in the permeability equation is the effective surface area, and it requires a more accurate model than the commonly accepted equation.…”

Effect of Clay Swelling and Fines Migration on Formation Permeability

“…Thus, the liquid diffusion into solid matrix is governed by the transient state diffusion equation ( 9) in which x is the distance measured from the pore surface, t the time, D the diffusivity coefficient and p 1 s the liquid mass concentration in the ' solid matrix.…”