Modeling Foam Displacement with the Local-Equilibrium Approximation: Theory and Experimental Verification

SPE Journal ◽  
2010 ◽  
Vol 15 (01) ◽  
pp. 171-183 ◽  
Author(s):  
Q.. Chen ◽  
M.G.. G. Gerritsen ◽  
A.R.. R. Kovscek
Keyword(s):  
Porous Media ◽  
Local Equilibrium ◽  
Population Balance ◽  
Entrance Region ◽  
Balance Model ◽  
Population Balance Model ◽  
Gas Bubble ◽  
Foam Generation ◽  
Foam Model ◽  
Bubble Sizes

Summary The gas-mobility-control aspects of foamed gas make it highly applicable for improved oil recovery. Gas-bubble size, often referred to as foam texture, determines gas-flow behavior in porous media. A population-balance model has been developed previously for modeling foam texture and flow in porous media. The model incorporates pore-level mechanisms of foam-bubble generation, coalescence, and transport. Here, we propose a simplified foam model to reduce computational costs. The formulation is based on the assumption of local equilibrium of foam generation and coalescence and is applicable to high- and low-quality foams. The proposed foam model is compatible with a standard reservoir simulator. It provides a potentially useful, efficient tool to predict foam flows accurately at the field scale for designing and managing foamed-gas applications. There are three main contributions of this paper. First, foam-displacement experiments in a linear sandstone core are conducted. A visualization cell is employed to measure the effluent foam-bubble sizes for a transient flow as well as to estimate the in-situ foam-bubble sizes along the length of the core during steady-state flow. These appear to be the first measurements of foam-bubble texture in the entrance region of a core. Additionally, the evolution of aqueous-phase saturation is monitored using X-ray computed tomography (CT), and the pressure profile is measured by a series of pressure taps. Second, the population-balance representation of foam generation by gas-bubble snap-off is modified to extend the capability of the population-balance approach to predict foam-flow behaviors in both the so-called high-quality and low-quality regimes. Third, a simplified population-balance model is developed and implemented with the local-equilibrium approximation. Good agreement is found between the experimental results and the predictions of the simplified model, with a minor mismatch in the entrance region.

Dynamic Simulations With an Improved Model for Foam Generation

SPE Journal ◽  
2007 ◽  
Vol 12 (01) ◽  
pp. 35-48 ◽  
Author(s):  
Seung Ihl Kam ◽  
Quoc Phuc Nguyen ◽  
Qichong Li ◽  
William Richard Rossen
Keyword(s):  
Steady State ◽  
Population Balance ◽  
Entrance Region ◽  
Balance Model ◽  
Population Balance Model ◽  
Displacement Front ◽  
Narrow Region ◽  
Foam Generation ◽  
Strong Foam ◽  
Injection Rates

Summary We present the first 1D simulations of dynamic foam displacements with a population-balance model incorporating bubble creation controlled by pressure gradient. For the first time, a population-balance model is fit to steady-state experimental data for both the three foam states (coarse foam, intermediate, and strong foam) and the two strong-foam regimes (low-quality and high-quality) observed in laboratory studies. Simulations confirm the stability of the coarse-foam and strong-foam states to small perturbations, and the instability of the intermediate state, at fixed injection rates. In dynamic displacements, the model shows foam generation as injection rates increase, or as liquid fraction of injected fluids increases, in agreement with laboratory observations. When coarse foam is created instead of strong foam, there is a narrow region of finer foam predicted near the gas displacement front. This region appears to play a role in foam generation. However, in the limited cases examined here, foam generation occurs at roughly the same injection rate as predicted by local-steady-state theory. Because of this narrow region of finer-textured foam, fronts can be sharper than estimated from fractional-flow theory assuming a constant effective gas viscosity at its steady-state value behind the displacement front. If a strong foam forms in the low-quality regime, the kinetics of foam generation and destruction affects the length of the entrance region in which foam forms. Therefore, the length of the entrance region can be used to calibrate the kinetic parameters in the model. The displacement front and the bank behind it, however, are essentially what one would have predicted from local-steady-state modeling. The complexities of population-balance modeling are not necessary, if it is known that strong foam will be created. Introduction Foam can improve sweep efficiency in gas-injection improved oil recovery (IOR) processes (Schramm 1994; Rossen 1996; Terdre 2003), redirect acid flow in matrix acid stimulation (Gdanski 1993; Cheng et al. 2002; Nguyen et al. 2003), and increase the efficiency of environmental remediation of aquifers (Hirasaki et al. 2000; Mamun et al. 2002). A continuing goal of foam research is the development of a fully mechanistic, predictive model. This paper describes efforts toward such a model and insights gained from application of the model to dynamic displacements. Before providing a detailed description of the model, it is worthwhile to review the mechanisms of foam in porous media and the experimental observations that the model attempts to reproduce.

scholarly journals Study on the regional characteristics during foam flooding by population balance model

2020 ◽  
pp. 014459872098361
Author(s):  
Zhongbao Wu ◽  
Qingjun Du ◽  
Bei Wei ◽  
Jian Hou
Keyword(s):  
Numerical Simulation ◽  
Simulation Model ◽  
Oil Recovery ◽  
Population Balance ◽  
Growth Zone ◽  
Balance Model ◽  
Population Balance Model ◽  
Liquid Ratio ◽  
One Dimensional ◽  
Foam Flooding

Foam flooding is an effective method for enhancing oil recovery in high water-cut reservoirs and unconventional reservoirs. It is a dynamic process that includes foam generation and coalescence when foam flows through porous media. In this study, a foam flooding simulation model was established based on the population balance model. The stabilizing effect of the polymer and the coalescence characteristics when foam encounters oil were considered. The numerical simulation model was fitted and verified through a one-dimensional displacement experiment. The pressure difference across the sand pack in single foam flooding and polymer-enhanced foam flooding both agree well with the simulation results. Based on the numerical simulation, the foam distribution characteristics in different cases were studied. The results show that there are three zones during foam flooding: the foam growth zone, stable zone, and decay zone. These characteristics are mainly influenced by the adsorption of surfactant, the gas–liquid ratio, the injection rate, and the injection scheme. The oil recovery of polymer-enhanced foam flooding is estimated to be 5.85% more than that of single foam flooding. Moreover, the growth zone and decay zone in three dimensions are considerably wider than in the one-dimensional model. In addition, the slug volume influences the oil recovery the most in the foam enhanced foam flooding, followed by the oil viscosity and gas-liquid ratio. The established model can describe the dynamic change process of foam, and can thus track the foam distribution underground and aid in optimization of the injection strategies during foam flooding.

Population balance model for solid state sintering II. Grain growth

2001 ◽  
Vol 27 (1) ◽  
pp. 63-71 ◽  
Author(s):  
S Sivakumar ◽  
Manjunath Subbanna ◽  
Satyam S Sahay ◽  
Vijay Ramakrishnan ◽  
P.C Kapur ◽  
...  
Keyword(s):  
Solid State ◽  
Grain Growth ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
Solid State Sintering
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