This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that the longitudinal dispersion coefficient can be reasonably represented by a simple periodic unit cell (PUC), which consists of a single sphere in a cube. We present a slightly modified and simplified approach to derive the homogenized equations, which emphasizes physical aspects of homogenization. Subsequently, we give full dimensional expressions for the dispersion tensor based on a comparison with the convective dispersion equation used for contaminant transport, inclusive the correct dependence on porosity. For the PUC of choice, the dispersion relations are identical to the relations obtained for periodic media. We show that commercial finite element software can be readily used to compute longitudinal and transverse dispersion coefficients in 2D and 3D. The 3D results are for the first time obtained at relevant Peclet numbers. There is good agreement for longitudinal dispersion. The computed transverse dispersion coefficients for a single sphere in a cube are much too low. The effect of adsorption on the dispersion coefficient is also studied. Adsorption does not affect the transverse dispersion coefficient. However, adsorption enhances the longitudinal dispersion coefficient in agreement with an analysis of homogenization applied to Taylor dispersion discussed in the literature.

Remediation of dense nonaqueous phase liquids (DNAPLs) is recognized as one of the most difficult problems associated with ground water pollution. The pump‐and‐treat technique, usually consisting of a continuous operation of extraction‐injection wells, is widely used for ground water remediation. In a stratified or otherwise heterogeneous aquifer, however, this technique suffers from tailing and rebound problems, which limit its cleanup efficiency and result in higher operation costs. The tailing and rebound is usually due to slow diffusion of contaminants out of lower‐ permeability heterogeneities into the flow regime of the higher‐permeability zone. In this study, we conduct bench‐scale experiments to investigate a novel polymer system and injection method to improve the pump‐and‐treat technique for DNAPL trapped in a layer of porous media that has a relatively low permeability compared to the surrounding media. This technique might be useful, for example, to remove DNAPL from these low‐permeability zones after removal of DNAPL from the higher‐permeability zones by a more traditional remediation method. The polymer system consists of a mixture of anionic and cationic polyacrylamides in solution and the injection method is based on flow‐induced polymer adsorption, called bridging adsorption. The study includes single and parallel‐column experiments. The measured polymer penetration depths were compared with values predicted from a numerical simulation, which was developed previously by the authors of this paper. The experiments and simulations show that the polymer injection leads to a modification of the permeability contrast that favors a more efficient pump‐and‐treat process. These results suggest that additional research to upscale the technology to pilot scales is warranted.

The diffusion of ions in polyelectrolyte gels has been investigated both theoretically and experimentally. A simple phenomenological model was first developed, building upon the geometric obstruction theory developed originally for the diffusion of neutral and charged species in neutral gels. The electrostatic obstruction is accounted for by (a) adopting an effective chain diameter obtained from the Dobrynin scaling theory for polyelectrolytes and (b) adding an exclusion layer of thickness δ(c s) around the charged chains to describe the electrostatic interaction between the ions and the chains. Then the diffusion of water and organic ions in an organically cross-linked polyacrylamide gel was studied experimentally using nuclear magnetic resonance (NMR). The relative diffusion coefficients D r = D g/D 0 (D g = diffusion in gel, D 0 = diffusion in solvent) of the different species were measured for various polymer, cross-linker, and salt concentrations. The calculated predictions and the measured data were found to be in good agreement. For water molecules, we obtain D r = 0.92 ± 0.01 independently of salt content, which is consistent with a pure geometric obstruction. For monovalent anions and cations (butyrate, Bu-, and tetramethylamonium, TMA+) D r increases from about 0.5 to 0.75 when the ion concentration increases from 0 to 150 mol/m3. For the divalent cation (putrescine, Pu2+) the D r are generally higher and increase from 0.6 to about 0.92, indicating an almost complete elimination of the electrostatic obstruction, consistent with a more efficient screening of the charges in the chains.

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractPolymer and polymer gels are well suited for reducing water production during

An investigation of the adsorption of long flexible polymer chainlike molecules during flows in low permeability porous media under near-wellbore conditions is reported. The theory for this phenomenon (canonical filtration theory) previously developed is firstly surveyed. This theory encompasses four partial differential equations describing the overall mass conservation, the conservation of the longest chains and the layer and bridging adsorption kinetics. Simple analytical expressions were derived mainly for flow in flat cores (having a length that is much smaller than the diameter), for which the problem reduces to the adsorption kinetic equations. Numerical computations were conducted to predict the transport and sorption behavior in long cores. Experiments conducted using a high molecular weigh cationic polyacrylamide and siliceous cores have been performed. The flat core experiments were used to determine the kinetic adsorption coefficients, which were then used in the numerical computations. Long core flow experiments were used to determine concentration profiles. The theoretical prediction and experiments in the long cores are in excellent agreement, which proves the validity of the canonical filtration model. Introduction When adsorbed in the near-well region, polymers formed by long flexible chainlike molecules, like polyacrylamides, help reducing water production in mature wells suffering from excessively high water cut.1–3 The reduction of water cut using polymers relies primarily on the disproportionate reduction of water and hydrocarbon (oil and natural gas) relative permeabilities.4–6 Water control has also been achieved using weak7–10 and strong11,12 crosslinked polymer gels in conjunction with mechanical isolation of the oil layers. However, the selective placement of the polymer and blocking of the water bearing layers remains an important hindrance of bullhead water control treatments, i.e. of treatments performed without a mechanical isolation of oil layers. Resolving this issue is likely to widen the latitude of water control using polymers and gels.12,13 Several studies14–20 have shown that a bridging adsorption phenomenon occurs in low permeability porous media due to a combination of chain elongation and adsorption. Zitha20 developed a theory for polymer flow in porous media honouring the layer and bridging adsorption phenomena (canonical filtration theory) and proved that the bridging adsorption phenomenon induces a strong filtration of the longest polymer molecules. The epithet canonical filtration was adopted for this theory because it appears suitable to described filtration phenomena known to play a significant role in other polymer-based oilfield applications (e.g., leak off during drilling, hydraulic fracturing and fracture blocking using polymer gels). The filtration of the longest chains leads to a rapid increase in local flow resistance as has been reported earlier.15 Since such filtration is expected to occur mainly in low permeability layers14–17 it is believed to have the potential to divert the polymer flow towards the high permeability layers. This idea is consistent with laboratory experiments using parallel cores which showed that, for sufficiently high permeability contrasts, the bridging adsorption phenomenon diverts the polymer from the low permeability (oil-bearing) cores to high permeability (water-bearing) ones.14 For this reason the bridging adsorption is deemed capable of reducing the risk of clogging oil layers during bullhead treatments. The purpose of this paper is to gain further insight on the canonical filtration process and the underlying bridging adsorption phenomenon. First the canonical filtration model is briefly surveyed. This model condenses in a system of four partial differential equations describing the conservation of the polymer concentration, the conservation of the longest (stretched) also abusively called bridging probability, the layer adsorption kinetics and the bridging adsorption kinetics. Controlled experiments performed using cationic polyacrylamides and packs of silicious granular material are presented and discussed. These experiments are aimed at validating the canonical filtration model. The kinetic polymer adsorption was directly quantified using a specially designed flat-core arrangement. The filtration process was checked using more conventional long cores. The effects of the physical parameters (polymer concentration, injection rate, permeability) have been investigated. The adsorption profiles predicted numerically from the canonical filtration model were compared to those obtained experimentally.