Modeling of polymer adsorption under near-wellbore flow conditions

Abstract

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.