Local Equilibrium Mechanistic Simulation of CO2-Foam Flooding

Mechanistic modeling of the non-Newtonian CO2-foam flow in porous media is a challenging task that is computationally expensive due to abrupt gas mobility changes. The objective of this paper is to present a local equilibrium (LE) CO2-foam mechanistic model, which could alleviate some of the computational cost, and its implementation in the Matlab Reservoir Simulation Tool (MRST). Interweaving the LE-foam model into MRST enables users quick prototyping and testing of new ideas and/or mechanistic expressions. We use MRST, the open source tool available from SINTEF, to implement our LE-foam model. The model utilizes MRST automatic differentiation capability to compute the fluxes as well as the saturations of the aqueous and the gaseous phases at each Newton iteration. These computed variables and fluxes are then fed into the LE-foam model that estimates the bubble density (number of bubbles per unit volume of gas) in each grid block. Finally, the estimated bubble density at each grid block is used to readjust the gaseous phase mobility until convergence is achieved. Unlike the full-physics model, the LE-foam model does not add a population balance equation for the flowing bubbles. The developed LE-foam model, therefore, does not add much computational cost to solving a black oil system of equations as it uses the information from each Newton iteration to adjust the gas mobility. Our model is able to match experimental transient foam flooding results from the literature. The chosen flowing foam fraction (Xf) formula dictates to a large extent the behavior of the solution. An appropriate formula for Xf needs to be chosen such that our simulations are more predictive. The work described in this paper could help in prototyping various ideas about generation and coalescence of bubbles as well as any other correlations used in any population balance model. The chosen model can then be used to predict foam flow and estimate economic value of any foam pilot project.

Elementary Numerical Analysis of Wet Foam Formation and Study of Its Flow Structures and Physical Behavior

The purpose of this study is to analyze the flow of wet foam and to study the effect of volume fraction, velocity and surface tension and other physical parameters on the foam flow. The most numerical researches done in this area are for single-phase flows. The numerical simulation in this study is the first simulation in the foam flow, in which both the bubbles and the water are simulated as two-phase flow. In this study, fluid containing a surfactant and bubbles are flowing in a duct. The dimensions of the duct cross section is 15 × 60 in millimeters. The numerical solution is performed for three Reynolds numbers of 50, 100 and 1000, three volume fractions of 48, 41 and 28, and three Weber numbers of 0.405, 0.27 and 0.203 (27 different modes), and the effect of the above parameters on the flow behavior and its physical properties have been investigated. It was found that in foam flow, the velocity fluctuations, due to the movement of bubbles in the flow, is in the order of magnitude of the mean velocity. The same is true for wall shear stress. By increasing the Reynolds number, the pressure loss increases, the magnitude of the velocity fluctuations decreases and the frequency of the velocity fluctuations increases. By increasing the Weber number, the pressure loss and the magnitude of the velocity fluctuations decrease and the mean shear stress increases. By increasing the foam quality, pressure loss increases, the mean shear stress and the magnitude of the velocity fluctuations decrease and its frequency increases. And the phenomenon of coalescence causes a sudden increase in momentum speed.

Foam Flow in Different Pore Systems—Part 1: The Roles of Pore Attributes and Their Variation on Trapping and Apparent Viscosity of Foam

Summary Lateral propagation of foam in heterogeneous reservoirs, where pore geometries vary laterally, depends on the roles of pore geometries on the foam properties. In this paper, the pore attributes of 12 different rock samples were characterized in terms of porosity, permeability, pore shape, pore size, throat size, aspect ratio, coordination number, and log mean of surface relaxation times (T2LM). These were measured from gas porosimeter and permeameter, X-ray microcomputed tomography (CT)-basedpore-network models, thin-section photomicrographs, and nuclear magnetic resonance (NMR) surface relaxometry. The samples have a wide range of porosity: 12 to 29%; permeability: 1 to 5,000 md; average pore size: 3.7 to 9 µm; average throat size: 2.4 to 8 µm; average aspect ratio: 1 to 1.7; average coordination number: 2.6 to 5.2; and T2LM: 9.4 to 740 ms. Nitrogen foam flow experiments (without oil) were then conducted on each rock sample using a specialized coreflood apparatus. A graphical analysis of the coreflood data was used to estimate the total saturation of trapped foam (10 to 66%), flowing foam (3 to 14%), and apparent viscosity of foam (3.2 to 73 cp). Trapped foam saturation and apparent viscosity values were then correlated with each of the measured pore attributes. The results revealed that all pore attributes, except aspect ratio, have positive correlations with foam trapping and apparent viscosity. The best correlation with trapped foam saturation was obtained when the most influential pore attributes (pore size, throat size, aspect ratio, and coordination number) were combined into a single mathematical function. Foam apparent viscosity also appears to be mostly influenced by trapped foam saturation, permeability, and coordination number of pore systems. Trapping is also likely enhanced by the presence of fenestral or channel pores. Furthermore, the shape and angularity of pores seem to facilitate snap-off and trapping of foam, because rock samples with angular pores trapped the highest foam saturation compared with other samples with rounded and subrounded pores. It was also shown that the correlation between trapped foam saturation (and foam apparent viscosity) and the absolute permeability of porous media may reverse at some high-permeability values (greater than several darcies), when one or both of the following conditions exist: (1) The aspect ratio of a lower-permeability porous medium is lower than that of a higher-permeability porous medium, and (2) the coordination number of a lower-permeability porous medium is higher than that of a higher-permeability porous medium. Finally, T2LM showed a good correlation with foam trapping, making NMR logging a prospective tool for pre-evaluating foam performance in targeted reservoir sections.

Effects of water salinity on the foam dynamics for EOR application

Factors limiting foam injection for EOR application are exceptionally low rock permeability and exceedingly high salinity of the formation water. In this regard, foam formation using internal olefin sulfonate is investigated over a wide salinity range (1, 5, 8, 10, and 12% NaCl) through 10 mD limestone. The relationships between pressure drop (dP), apparent viscosity, liquid flow rate, total flow rate, salinity, foam texture, and length of foam drops at the outlet used as an indicator of viscosity are studied. Foaming is observed up to 12% NaCl, compared to a maximum of 8% NaCl in similar core-flooding experiments with 50 mD limestone and 255 mD sandstone. Thus, the salinity limit of foam formation has increased significantly due to the low permeability, which can be explained by the fact that the narrow porous system acts like a membrane with smaller holes. Compared to the increasing dP reported for highly permeable rocks, dP linearly decreases in almost the entire range of gas fraction (fg) at 1–10% NaCl. As fg increases, dP at higher total flow rate is higher at all salinities, but the magnitude of dP controls the dependence of apparent viscosity on total flow rate. Low dP is measured at 1% and 10% NaCl, and high dP is measured at 5, 8, and 12% NaCl. In the case of low dP, the apparent viscosity is higher at higher total flow rate with increasing gas fraction, but similar at two total flow rates with increasing liquid flow rate. In the case of high dP, the apparent viscosity is higher at lower total flow rate, both with an increase in the gas fraction and with an increase in the liquid flow rate. A linear correlation is found between dP or apparent viscosity and liquid flow rate, which defines it as a governing factor of foam flow and can be considered when modeling foam flow.

Flow Characteristics of Foam in Fractures and Prediction of Preferred Paths

Foam is widely used in fractured reservoirs. The flow characteristics in complex fracture networks are still unclear, and there are few numerical simulations of foam fluid flow in fractures. In this study, a variety of combined visual fracture models were used to observe the flow characteristics of foam in the fracture. Firstly, based on the parallel fracture model, the foam flow characteristics under different fracture depths were explored, and then based on the complex fracture network model, the foam flow path and sweep efficiency are evaluated. Finally, the Dijkstra’s algorithm was used to determine the weighted graph of the fracture network nodes, and the preferred flow paths of the foam were predicted. The results show that when foam flows in parallel fractures with different depths, it preferentially flows in high permeability (100 μm) fractures, and there is gas trapping in low permeability (50 μm) fractures. In the irregular fracture network model, the sweep efficiency of the foam fluid is greatly affected by the foam quality, and the sweep volume is the widest when the foam quality is about 90%. The simulation results based on the Dijkstra’s algorithm can be fitted to the experimental results to a certain extent. By controlling the number of preferred paths and the weight of nodes, the plugging and regulating performance of the foam are characterized. These findings reflect the necessity of considering fractures when foam flows in reservoirs, and provide a certain experimental basis and theoretical guidance for the development of fractured reservoirs.