Micro-scale analysis of immiscible displacement in porous media Microanálisis del desplazamiento no miscible en medios porosos

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1 Micro-scale analysis of immiscible displacement in porous media Microanálisis del desplazamiento no miscible en medios porosos F. M. Francisca ()(2) and M. A. Montoro ()(2) () Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina (2) Universidad Nacional de Córdoba (UNC),FCEFyN, Área de Geotecnia, Argentina ABSTRACT Immiscible displacement depends on capillary, gravity and viscous forces. Capillary forces control menisci instability at micro-scale, restrict Non-Aqueous Phase Liquids (NAPL) recovery from porous media, and enhance residual saturation. At macro-scale, relative permeability is the most relevant property to analyze the displacement of immiscible fluids in porous media. In this work, a quasi-static pore scale network model is used to simulate wetting processes in porous media initially contaminated with NAPL. A new transparent cell is built to analyze ganglia generation in sand specimens during the immiscible displacement of paraffin oil by water. The influences of particle and pore size on the amount of ganglia in pore space and on residual saturation are established from numerical and experimental results. RESUMEN El desplazamiento de fluidos no miscibles en medios porosos y la saturación relativa de la fase orgánica no acuosa depende de fuerzas capilares, gravitacionales y viscosas. Las primeras controlan la inestabilidad y desplazamiento de meniscos e interfaces a nivel microscópico. A nivel macroscópico, el parámetro de mayor relevancia en el desplazamiento de fluidos no miscibles es la permeabilidad relativa. En este trabajo se presentan resultados de simulaciones numéricas y experimentales de fenómenos de mojado y desplazamiento de un fluido orgánico por agua dentro de un medio poroso. Los resultados obtenidos permiten determinar la influencia de la distribución de tamaño de poros y de partículas en la generación de ganglios y saturación residual en fenómenos de mojado. Keywords: porous media, simulation, numerical model, experiment, flow, NAPL, ganglia, residual saturation INTRODUCTION Immiscible displacement of fluids in porous media takes place during remediation of soils and rocks contaminated with Non-Aqueous Phase Liquid (NAPL) and at some stage during petroleum recovery processes. In both cases, the organic fluid or non-wetting phase is replaced by another fluid, air or water vapor during displacement. Interfaces develop between two immiscible fluids. Capillary, gravity and viscous forces govern the displacement of fluids inside porous media. However, capillary forces govern instability of interfaces in porous and fractured media (Mercer and Cohen 99, Dullien 992, Hardisty et al. 998), while gravity and viscosity prevail during steady state flow conditions (Corey 986). Capillary forces depend on interfacial tensions and contact angle between phases. Extraction of NAPL can be maximized by modifying the interfacial tensions (Pennell et al. 993, Rinaldi and Francisca 26). Displacement of immiscible fluids in porous media can be simulated by means of pore network models (Fatt 956, Lenormand et al. 988, Blunt 2, Francisca 26). In this case, the pore structure is characterized by a simplified representation of the pore space (Dullien 992) but capturing physical mechanisms at pore level (Lenormand et al. 988). In this work, formation of ganglia and residual saturation of NAPL is determined from a pore network model. On the other hand, three sand specimens were tested in a new transparent cell to evaluate immiscible displacement. The purpose of this work is to show that ganglia generation and NAPL residual saturation can be related to soil porous structure, particle size, and variability of pore size distribution.

2 2 IMMISCIBLE DISPLACEMENT IN SOILS 2. Micro-scale physics Pressure of the displacing fluid must be increased to surpass the capillary pressure in order to displace interfaces when inertial and gravity effects are negligible (e.g. fluid velocity tends to zero value and both fluids have similar density respectively) (Dullien 992). Necessary driven force, or pressure increase, is given by the Young-Laplace s equation as follow (Mercer and Cohen 99): 2γ wo cosθ P = () r Where P = P o P w = capillary pressure, P = pressure, γ wo = interfacial tension between the displacing and displaced phases, w and o represent wetting and non-wetting phases respectively, r = pore radius, and θ = contact angle (see Morrow 99 and Francisca et al. 23 for details on contact angle and wettability). Pore size and pressure of both fluid phases determine the interface curvature. Interfaces start to move when the pressure difference between the two liquid phases reaches the capillary pressure, defined by equation (). There are two possible mechanisms of immiscible displacement: a) wetting and b) drainage. Water and NAPL are the displacing and displaced phases respectively during wetting; the opposite occurs during drainage. Only wetting phenomena are considered in this work. Movement of interfaces defines the advancing front of water observed during wetting. Relative saturation of each phase changes while water penetrates inside pores. The smallest pores wet first because of capillarity (Dullien 992). Saturation of the non-wetting phase (S o ) can be determined as: S V o o = (2) VV Where V o = volume of oil or NAPL and V V = volume of voids. The lower possible value (or final quantity) of S o is known as residual saturation. The evolution of the advancing front and the prediction of ganglia generation can only be described by means of micro-scale analysis. 2.2 Macro-scale physics Porous media are heterogeneous mixtures of particles and fluids. However, soils and rocks can be considered as homogeneous for several practical purposes, at macro-scale and under certain circumstances (Sahimi 993). Even though micro-scale heterogeneities, behavior of macroscopically homogeneous systems is well predicted by average properties. Immiscible flow can be analyzed at macro-scale by means of equivalent continuous models based on the generalized Darcy s law (Corey 986): v K ρ g dh i i i i = (3) µ i dl Where v = Darcy s velocity, K = absolute permeability, = relative permeability, µ = dynamic viscosity, ρ = fluid density, g = acceleration of gravity dh/dl = gradient, and i refers to each phase. In addition, i = k(s i )/k(s i =) and S i = degree of saturation of the i phase. Values for relative permeability range from to. Note that both v i and S i change during immiscible displacement (Corey 986, Lenormand et al. 988). Relative permeability undergoes hysteretic behavior for wetting-drainage cycles (Fetter, 993). There are several models to compute relative permeability. Siddiqui et al. (999) and Montoro and Francisca (26) summarized the most used formula to determine. Relative permeability is usually related to saturation. A very simple and useful model to estimate the relative permeability of the aqueous phase ( w ) has been proposed by Brooks and Corey (964): w * η Sw S wi = ( Sw) = Swi η (4) Where S w * = effective saturation, S w = water saturation, S wi = irreducible water saturation, η = constant that depends on soil type. Note that S w =-S o. 2.3 Pore network models: from micro- to macroscale Fluid flow and multiphase flow in porous media are usually analyzed from a continuum point of view. Such approach ignores the effect of pore microstructure by considering only average macro-scale properties (Yiotis et al 2). Pore network models must be used in order to consider pore interconnectivity, interfaces movement and any other micro-scale process. Pore networks models consist of an array of pore bodies interconnected by pore throats. The number of pore throats connected to a pore body defines the coordination number of the network. These models have been extensively used to simulate immiscible flow in porous media (Fatt 956, Lenormand et al. 988, Hughes and Blunt 2, Francisca 26).

3 3 MATERIALS AND METHODS Discrete numerical models and experimental tests were performed to investigate ganglia formation mechanisms during wetting. 3. Numerical model A two-dimensional pore network is used to simulate wetting processes. The model consists of a discrete network of cylindrical pores with a coordination number of four. Pore sizes are generated by using a lognormal probability distribution function. All developed models are characterized by a random distribution of pore sizes within the pore network. Porous structure is characterized by the mean (µ), standard deviation (σ) and Coefficient of Variation (CV) of pores size, where: CV σ = (5) µ The mean pore size was set as 5 µm. Pore diameter is related to particle size. The smaller the particles, the smaller the pore size for a given packing of particles. Pore-throat radius (r t ) can be estimated from particle diameter (d). Fetter (993) states that r t and d are related for well graded granular sediments with rounded particles, as: rt =.77 d (6) Wetting processes (also known as imbibition) are simulated. Hence, the initial state considers that the pore network is fully saturated with NAPL (Sr o = ). The NAPL is displaced as the pressure of the wetting phase increases. Water penetrates into the network and interfaces move when capillary pressure decreases until the critical value defined by equation (). Meniscus keep moving until a wither pore cross section is reached (see Dullien 992 for details). In order to move further the interface, the pressure of the displacing phase is again increased until a new capillary pressure is achieved, according to the new pore size and equation (). Simulation ends when the displacing phase breaks through the pore network. 3.2 Physical model Three sand specimens were tested. Figure shows the grain size distribution curves and Table summarizes the main physical properties of these sediments. Wetting and non-wetting phases were deionized water and colored paraffin oil (trademark Vaseplus 9) respectively. Table 2 presents the most relevant properties of these fluids. Passing Finer [%] Fine Sand Medium Sand Coarse Sand Grain Size [mm] Figure : Grain-size distribution of the sands.. Table : Main physical properties of tested sand samples (S = fine sand, S2 = medium sand, S3 = coarse sand). Property S S2 S3 Specific gravity , Effective particle diameter (mm) Passing sieve #2 (%) Uniformity coefficient, Cu Gradation coefficient, Cc.8.86 Table 2: Main physical properties of used fluids Property water Paraffin oil Color Colorless Colorless Relative density (2 C).85 Viscosity, Ns/m² (37,8 ºC) 6.85 x -4.5 x -2 Chemical formula H 2 O C n H 2n+2 (generic) Boiling point ( C) 4 2 Surface tension [N/m] Water solubility - Insoluble Figure 2 presents a schematic representation of test procedure which includes the following stages. Testing cell is filled out with sand contaminated with paraffin oil. Sample is permeated with the contaminant in order to obtain a saturation degree close to one. An auxiliary cell contains the water used to displace paraffin oil. A constant hydraulic gradient equal to one is used to force the penetration of water inside the sample. Flow direction is from bottom to top of the sample. Water and paraffin oil permeated through the sample are collected from the outlet port. The volume of fluids permeated trough the sample is taken as a reference parameter to monitor oil displacement, relative permeability, and water and paraffin oil saturations. 4 RESULTS Numerical and experimental results were used to understand the behavior of immiscible fluids in porous media.

4 Constant head water supply system (Mariotte's bottle) Figure 4 presents the influence of the coefficient of variation (CV) of pore sizes on the residual saturation of the non-wetting phase. The higher the CV, the higher the residual saturation. From equation (4), specimens with high CV have an extended range of pore sizes (well-gradation of pore sizes). Figure 2: Test devices Specimen under test Porous Stone Cell Recovered oil Recovered water 4. Numerical simulations Figure 3 shows the evolution of the advancing front during wetting, simulating a decontamination process. Each image corresponds to a particular equilibrium position and capillary pressure (equation ()). Note that the advancing front moves step by step describing a characteristic quasi-static behavior. Number and size of ganglia that appear during flushing (Figure 3) determine the residual saturation of NAPL. Several models were run varying the CV of pore size in order to study the effect of gradation of pores on ganglia formation and residual saturation. In addition, various models were tested in order to obtain general trends. NAPL Residual Saturation [%] % % % Sr o =.63 CV.24 R 2 =.85 E-2 E- E+ CV of pore size Figure 4: Influence of the CV of pore size on the residual saturation of NAPL 4.2 Experimental tests Figure 5a presents a high resolution image of the fine sand specimen, captured from the transparent cell when a volume of water equal to V V pass through the sample. Figure 5b shows the same image after processing. A sequence of images captured during the immisicible displacement provided a useful way to monitor the advancing front and to identify the presence of ganglia. A small dispersion is expected from anomalous reflections of light produced by some minerals (muscovite in our tests), which can be filtered by means of image processing. Figure 3: Simulated advance of the displacing phase (Black = water, white = paraffin oil)

5 Figure 6 shows the evolution of NAPL saturation (S NAPL ) with the number of flushing for the three tested sand specimens. The observed decrease of S NAPL is associated with the displacement of paraffin oil by water within the pores of the specimen under test. The importance of the decrease of S NAPL increases as the effective particle diameter of the specimen decreases. pores interfering with each other and reducing. Finally, NAPL forms a trapped phase (ganglia) when the water saturation approaches to one. In this case only water flows within soil pores w o Sw (a) w o (a) (b) Figure 5: a) Picture of the fine sand specimen initially contaminated with paraffin oil after flushing; b) Processed image (Black = water, white = paraffin oil) Saturation of paraffin oil, S o Fine Sand Medium Sand Coarse Sand Number of pore volumes of flushing Figure 6: Evolution o f the NAPL saturation during flushing The fine sand was easier cleaned up than medium and coarse sand. This tendency was attributed to the lower water pressure needed to displace interfaces in smallest pores during wetting processes. Figure 7 shows the influence of the degree of saturation on. The relative permeability respect to water is extremely low when the degree of saturation of this phase is lower than.8 for fine sand, and.6 for medium and coarse sands. The opposite trend is observed for the relative permeability respect to NAPL. In this case, NAPL forms a continuous phase while water only fills the smallest pores. At higher saturations, the two immiscible fluids coexist inside Sw w o (b) Sw (c) Figure 7: Influence of water saturation (Sw) on relative permeability respect to water ( w ) and paraffin oil ( o ): a) Fine Sand, b) Medium Sand, c) Coarse Sand. 5 DISCUSSION Porous media can be considered homogenous at macro-scale, and characterized by average properties (e.g. porosity). However, micro-scale heterogeneities (e.g. spatial distribution of pore sizes) determine the non-homogenous pattern of ganglia shown in Figures 3 and 5. Results confirm that number and size of ganglia are inversely related each other as:

6 NGS φ (7) Where φ = size of ganglion and N GS = number of ganglia with size equal to φ. Similar qualitative behavior was observed in the experiments. Form Figures 6 and 7 it can be observed that the sudden decrease of saturation correlates with the increase of w (and decrease of o ). This explains the greater increase of w observed for the fine sand specimen in respect to the medium and coarse sand (Figure 7). A more uniform displacement of the non-wetting phase was observed for the fine sand specimen in respect to the medium and coarse sands. This result correlates with the higher volume of paraffin oil recovered from fine sand as shown in Figure 6. The effective particle size of the sample can influence the expected residual saturation of NAPL during wetting since particle and pore sizes are related each other (equation (6)), and because of residual saturation is related to pore properties (Figure 4). Brooks and Corey s model (Brooks and Corey 964) was calibrated for the experimental results shown in Figure 7. Variable η was determined from least square fit technique in order to attain the optimum fit of equation (4) to the measured data. The obtained values were η = 2.84,.94 and.85 for the fine, medium and coarse sand respectively. Results indicate that η can be related to the grain-size distribution of the samples (e.g. effective size, uniformity coefficient, etc.) 6 CONCLUSIONS Numerical and experimental tests have been performed to analyze the physics of immiscible displacement in porous media. The main conclusions of this research can be summarized as follows: - Ganglia generation and NAPL residual saturation depend on micro-scale porous media properties. Micro-scale heterogeneities are responsible for the ganglia formation, even though the system may be considered as homogeneous at macroscale. - Residual saturation of non-wetting fluids depends on the coefficient of variation (CV) of pore sizes. A lower oil recovery is obtained in porous media with a well-gradation of pore sizes. - Residual saturation decreases with the effective particle diameter of the sand sample, in absence of preferential flow paths. - Relative permeability can be related to the grainsize distribution of sediments. Soils with fines particles develop a faster increase of the water relative permeability than coarse sediments. The larger the effective size of particles, the smaller the value of the parameter η in the Brooks and Corey s model. ACKNOWLEDGEMENTS Authors thank CONICET, SECyT-UNC and Agencia Cordoba Ciencia for the support of this research. 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