[1] A series of primary drainage experiments was carried out in order to investigate nonequilibrium capillarity effects in two-phase flow through porous media. Experiments were performed with tetrachloroethylene (PCE) and water as immiscible fluids in a sand column 21 cm long. Four drainage experiments were performed by applying large pressures on the nonwetting phase at the inlet boundary: 20, 30, 35, 38 kPa. Our results showed that the nonequilibrium local fluids pressure difference-saturation curves are above the capillary pressure saturation curve. Moreover, the nonequilibrium pressure difference showed a nonmonotonic behavior with an overshoot that was more pronounced at higher injection pressures. The dynamic capillarity coefficient was calculated from measured local pressures and saturations (the scale of sensor devices, 0.7 cm). Its value was found to vary between 1.3 Â 10 5 to 2 Â 10 5 Pa s. Within the saturation range of 0.50 > S w > 0.85, no clear dependency of the dynamic coefficient on the wetting saturation was observed. Also, no dependency of the dynamic capillarity coefficient on the applied boundary pressure was found. Averaged values of ½ at the length scales of 11 and 18 cm were also estimated from averaged pressures and saturations. The upscaled dynamic coefficient was found to vary between 0.5 Â 10 6 and 1.2 Â 10 6 Pa s at the average window size of 11 cm. This is one order of magnitude larger than the local-scale coefficient. Larger values were found for the length scale of 18 cm: 1.5 Â 10 6 and 2.5 Â 10 6 Pa s. This suggests that the value of dynamic coefficient increases with the scale of observation.
A two-dimensional pore-scale numerical model was developed to evaluate the dynamics of preferential flow paths in porous media caused by bioclogging. The liquid flow and solute transport through the pore network were coupled with a biofilm model including biomass attachment, growth, decay, lysis, and detachment. Blocking of all but one flow path was obtained under constant liquid inlet flow rate and biomass detachment caused by shear forces only. The stable flow path formed when biofilm detachment balances growth, even with biomass weakened by decay. However, shear forces combined with biomass lysis upon starvation could produce an intermittently shifting location of flow channels. Dynamic flow pathways may also occur when combined liquid shear and pressure forces act on the biofilm. In spite of repeated clogging and unclogging of interconnected pore spaces, the average permeability reached a quasi-constant value. Oscillations in the medium permeability were more pronounced for weaker biofilms.
Capillary pressure-saturation relationship plays an important role in the description of two-phase flow in porous media. Commonly, this relationship is determined in laboratory on a sample of few centimeters and it is then used in numerical modeling of two-phase in domain sizes of hundreds to thousands of meters. The correctness of such approach has been hardly ever questioned. In this study, an upscaled capillary pressure is determined from local pressure and saturation measurements employing a rigorous averaging procedure. Drainage and imbibition experiments were performed in a column of 21 cm long. The experiments were performed as a series of equilibrium steps; each time we changed the boundary pressures incrementally and then waited until an equilibrium distribution of fluids was reached. Phase pressures and saturation inside the column as well as external pressure and average saturation were recorded at each equilibrium step. Various averaging operators were considered: simple average, simple phase-average, intrinsic phaseaverage, and centroid-corrected average. Also, a potential-based average operator was introduced as reference curve to establish which operator gives the correct average pressure. Large differences were found for the average non-wetting phase pressure using different operators during primary drainage. However, when both phases were present throughout the domain (e.g. during main drainage) the differences between pressures obtained by various average operators were negligible. In such cases, the centroids of the two phases and the centroid of the averaging domain were close to each other. The comparison between averaged capillary pressure-saturation curves has shown that the centroid-corrected averaging operator is the most appropriate operator.
Formation damage as a result of hydraulic fracturing of unconventional gas reservoirs is known to occur by many speculated processes such as: filter cakes on fracture faces, matrix swelling, cleat plugging, gel damage and water blocking. In low permeability matrices, capillary forces can also prevent effective dewatering and result in water blocking of gas flow. Another type of formation damage that may be qualitatively understood but not quantified is the impact of biofilms. This paper combines two micro-scale modeling techniques to evaluate and predict the effects of biofilms on proppant packed fractures in unconventional gas reservoirs. Both a two phase flow model for gas and liquid and a modern cellular automaton biofilm model were combined to simulate the impact on gas flow rates in biofouled propped fractures. Initial simulations of just two phase flow without biofilms but varied proppant surface wettabilities, indicated that hydrophobic proppant surfaces provide better dewatering than hydrophilic surfaces. Gas flow rates dropped in half when biofilms were added to the model at a pore volume of approximately 10%. In addition, further modeling indicated even the same biofilm volume but different distribution within grains and pore-throats can impact gas flow rates as much as 10%. It is hoped that this work will help hydraulic fracturing engineers improve their fracture designs and subsequent treatments to maximize gas flow rates from their assets.
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