Upscaling of Foam Mobility Control to Three Dimensions

The applications of foam are 3-D on a field scale. However, most previous research focuses only on properties of foam in 1-D. Experiments were performed in 3-D, and the compositional reservoir simulator UTCHEM was modified to predict foam flow in 3-D. The 3-D experiments demonstrated that, under similar experimental conditions, the mobility of foam in a 3-D tank is greater than that in a 1-D column. They also showed that foam greatly increases lateral gas distribution along the bottom of the tank and the average gas saturation for both homogeneous and heterogeneous packings with the effects being significantly larger in the latter case. The reservoir simulator UTCHEM was modified for foam flow. The foam simulation parameters were measured in 1-D sand columns and the simulator was modified to match the 1-D and 3-D experiments. The proposed model successfully history matched the homogeneous and heterogeneous 3-D sand tank experimental results for average gas saturation, gas injection rate, gas distribution and pressure profile along the tank diagonal 6 inches from the bottom. The results of this study represent an advance in understanding of foam flow in 3-D. The simulator could be used to design a foam process in 3-D. Introduction Foam mobility difference in 1-D and 3-D. Foam is used for mobility control in aquifer remediation processes and oil recovery operations. Gas has low density and viscosity compared to other fluids like oil and water. So when gas is injected into the porous media, the gravity force will dominate its flow and the injected gas will tend to flow directly to the top of the porous media, results in a poor gas sweep in the horizontal direction along the bottom (Fig.1). Foam can reduce the mobility of gas by reducing the relative permeability and increasing the apparent viscosity thus increasing the gas sweep efficiency. However, though there were some field applications of foam, most of the previous laboratory researches on foam were in 1-D. The properties of 3-D foam have not been investigated yet. Tanzil observed that the apparent viscosity of foam is greater in 3-D than in 1-D. His observation was based on a rough comparison between a 3-D field scale foam application and some 1-D column experiments in lab. No strict experiments were performed by him to demonstrate the difference between 1-D and 3-D. Nevertheless, the observed mobility difference of foam between 1-D and 3-D revealed how much error would result if one uses 1-D column foam experimental results to predict 3-D field application results. A foam simulation model developed from 1-D experimental results would not be applicable to simulate 3-D foam results. 3-D foam experiments are important for us to understand the flow properties of foam and a simulation model is also indispensable to simulate and predict 3-D foam flow behavior considering the complexity and difficulty of performing 3-D foam experiments in lab. Foam generation and coalescence. Hirasaki et al defined that foam in porous media is a dispersion of gas in liquid such that the liquid phase is continuous and at least some part of the gas phase is made discontinuous by lamellae. Previous studies showed that the main generation mechanisms of foam in porous media are capillary snap-off, lamella division and leave behind. Among them, lamellae generated from the former two mechanisms are mainly perpendicular to the gas flow direction and can block the gas flow, greatly reduce the gas mobility. So these two mechanisms are considered to be able to generate strong foam. Pressure gradient is important in strong foam generation process. Higher can mobilize more stationary lamellae, set off the lamellae division process and generate more new lamellae which will block more of the gas flow paths. In porous media, the main coalescence mechanism of foam is capillary suction. Foam lamellae would break when capillary pressure reaches a limiting value p ∇ , which is named the “limiting capillary pressure” . The value of the limiting capillary pressure depends on many parameters including surfactant concentration, permeability and gas and liquid velocities. * c P Mobility of water and gas when foam is present. The relative permeability function of water is not directly influenced by the presence of foam. Foam can only change the water mobility indirectly by changing the water saturation in porous media. For the flow of gas, foam can greatly reduce 2 Busheng Li, George J. Hirasaki, and Clarence A. Miller SPE 99719 the mobility of gas from two aspects. When foam is present, the gas relative permeability will be smaller than in conventional two-phase flow and gas apparent viscosity is larger because of the resistance to movement of lamellae. The reduction of gas relative permeability arises because only a fraction of the gas phase is actually flowing when foam is present, i.e., some gas is trapped. The increase of apparent gas viscosity comes from the flow of foam bubbles. Resistance to flow of the bubbles is greater than resistance to flow of gas when no lamellae are present because of the dragging of lamellae along the pore walls. Combining these two effects, gas mobility is reduced significantly when foam is present, the stronger the foam, the lower the gas mobility. Foam modeling. Foam texture (lamella density) determines the strength and mobility of foam and itself depends on many factors such as pore structure, heterogeneity, surfactant formulation, capillary pressure, flow rates, presence of nonwetting phase, etc. It is very difficult and complex to investigate the relation between foam mobility and these factors. There are many ways to model foam flow in porous media. Most of the models modify gas mobility when foam is generated. These foam models can be classified into four major groups. They are empirical and semi-empirical models, fractional-flow theory models, percolation (statistical networks) models and population balance models. Among all these foam models, the population balance method is the most comprehensive approach to fully describe foam mechanisms. Several investigators have used this approach in modeling foam in porous media. The significant achievement of the method is accounting for non-Newtonian gas mobility with respect to bubble population dynamics. In this approach, foam texture is explicitly taken into account. They solve a number of equations to describe lamella generation and destruction processes. The effective foam viscosity is determined by the calculated lamella density. The shortcoming of this model is its complexity: many parameters need to be determined in this approach by performing corresponding experiments. Attempts were performed to simplify the population-balance model by some other investigators. Hatziavramidis et al proposed a simplified population-balance model. In their model, when the foam is weak, only the relative permeability of the gas was modified. In the case of strong foam, the viscosity of the gas was also modified. Their model was applied on steam foam and incorporated into a thermal simulator, THERMS. Bertin et al offered a simplified model of the full population balance model of Kovscek et al. Foam texture was calculated using a bubble-population correlation and represented as a function of porosity, permeability, gas saturation, the limiting capillary pressure and the flowing foam fraction. The effective gas viscosity was modified when foam was present. This model was shown to give satisfactory results in modeling transient core experiments. Friedmann et al proposed a foam model in which the calculation of foam viscosity including a geometric factor and a reference velocity. In later sections of this paper, a foam model will be discussed based on the discussion of the models proposed by Bertin et al and Friedmann et al. Objective of this research. The purpose of this paper is to investigate the flow behavior of foam in 3-dimensions, compare the difference between air/water and foam cases and develop a foam model to simulate both 1-D and 3-D foam flow. Experimental Configuration of the 3-D tank. A 3-D sandpack was designed and constructed for the 3-dimensional foam experiments. Fig.2 shows a photograph of the empty tank with wells and sampling tubes. The tank has glass walls for its four sides. Steel frame is used in the corners and edges to make the tank strong enough to hold the experimental pressure. The actual scale of the tank is 2ft×2ft×2.5ft with a height 2.5ft. But we still call it ‘2x2x2 ft tank’ because the extra 0.5 ft in its height was not packed by sand in our 3-D experiments. The term ‘2x2x2 ft’ here only means the porous media size inside the tank. There are nine sampling tubes and four injection/production wells in the tank. Fig. 3 gives sketches of the side and top views of the sand tank. The sampling tubes are placed in lines and in each line, they are 0.5 ft from each other. The distance from line to line is also 0.5 ft. In each of these sampling tubes, there are four sample openings. The heights of these openings are 0, 0.5, 1 and 1.5 ft from the bottom of the tank. Four individual plastic tubes connect these openings to the outside of the tank. During experiments, these sampling tubes can be used to get information such as gas and surfactant solution distribution inside the tank. The tank has one injection well and three production wells as shown in Fig. 3. The diameter of these wells is 1.75 inch. To keep sand out of these wells, these wells are wound with 200 mesh stainless steel screen. The injection well is 3.5 inches high, and the three production wells are 2 ft high. All the production wells have their outlets at the bottom of the tank but use a 1⁄4” inch stainless steel tube to make the flow outlet to be at the same level as the height of the sand pack. This is just to keep the pressure potential inside the production wells at hydrostatic pressure and simulate an unconfined aquifer. A 150 mesh screen and