Fractional-Flow Theory of Foam Displacements With Oil

SPE Journal ◽  
2010 ◽  
Vol 15 (02) ◽  
pp. 260-273 ◽  
Author(s):  
E.. Ashoori ◽  
T.L.M.. L.M. van der Heijden ◽  
W.R.. R. Rossen
Keyword(s):  
Oil Recovery ◽  
Flow Theory ◽  
High Water ◽  
High Water Content ◽  
Fractional Flow ◽  
Two Phase ◽  
Water Fraction ◽  
Speed Of Propagation ◽  
First Contact ◽  
Fractional Flow Theory

Summary Fractional-flow theory provides key insights into complex foam enhanced-oil-recovery (EOR) displacements and acts as a benchmark for foam simulators. In some cases with mobile oil present, the process can be represented as a two-phase displacement. We examine three such cases. A first-contact-miscible (FCM) gasflood with foam injection includes a chemical shock defining the surfactant front and a miscible shock defining the gas front. The optimal water fraction for the foam, that which gives the fastest oil recovery in 1D, maintains the gas front slightly ahead of the foam (surfactant) front. The success of a foam process with FCM CO2 and surfactant dissolved in the (supercritical) CO2 depends on the strength of foam at very low water fractional flow, such as for a surfactant- alternating-gas (SAG) process with surfactant dissolved in water. The speed of propagation of the foam front depends on surfactant adsorption on rock and on the partitioning of surfactant between water and CO2 but is always less than the velocity of the foam front in a SAG flood with surfactant ahead of the gas. A foam with surfactant that partitions preferentially into water rather than into CO2 would propagate slowly, regardless of the surfactant's absolute solubility or the level of adsorption on rock. An aqueous surfactant preflush can speed the advance of foam, however. An idealized model of a surfactant flood pushed by foam suggests that it is best to inject a relatively high water content into the foam to ensure that the gas front remains behind the surfactant front as the flood proceeds. Any gas that passes ahead of the surfactant front would finger through the oil and be wasted. We present simulations to verify the solutions obtained with fractional-flow methods and illustrate the challenges of accurate simulation of these processes.

The Application of Fractional Flow Theory to Enhanced Oil Recovery

1980 ◽  
Vol 20 (03) ◽  
pp. 191-205 ◽  
Author(s):  
Gary A. Pope
Keyword(s):  
Oil Recovery ◽  
Gas Flow ◽  
Local Equilibrium ◽  
Flow Theory ◽  
Simple Extension ◽  
Phase Flow ◽  
Constant Composition ◽  
Fractional Flow ◽  
Continuous Injection ◽  
Fractional Flow Theory

Introduction Fractional flow theory has been applied by various authors to waterflooding, polymer flooding, carbonated waterflooding, alcohol flooding, miscible flooding, steamflooding, and various types of surfactant flooding. Many of the assumptions made by these authors are the same and are necessary for obtaining simple analytical or graphical solutions to the continuity equations. Typically, the major assumptions, which are sometimes not stated explicitly, are:one dimensional flow in a homogeneous, isotropic, isothermal porous medium,at most, two phases are flowing,at most, three components are flowing,local equilibrium exists,the fluids are incompressible,for sorbing components, the adsorption isotherm depends only on one component and has negative curvature,dispersion is negligible,gravity and capillarity are negligible,no fingering occurs,Darcy's law applies,the initial distribution of fluids is uniform, anda continuous injection of constant composition is injected, starting at time zero. Several of these assumptions are relaxed easily. One of the most useful to relax is Assumption 12, continuous injection. The principles of chromatography can be applied to analyze the more interesting case of injecting one or more slugs. Most of these processes require slug injection of chemical or solvent to be economical. In fact, a lower bound on the slug size necessary to prevent slug breakdown can be obtained from a simple extension of fractional flow theory. In this and other extensions the common new feature is the need to evaluate more than one characteristic velocity. A second example of this is the extension of fractional flow theory from simultaneous immiscible two-phase flow (the classical Buckley-Leverett waterflood problem) to simultaneous immiscible three-phase flow (the classical oil/water/gas flow problem). A third example is the extension to nonisothermal cases. Here we need to consider the energy balance, mass balance, and velocity of a front of constant temperature. A fourth example is when one or more components are partitioning between phases. In all cases, mathematically, the extension is analogous to the generalization from the one-component adsorption problems (or two-component ion exchange problems with a stoichiometric constraint) to multicomponent sorption problems. The latter theory has been worked out in a very general way for many component systems using the concept of coherence. Pope et al. recently have applied this theory to reservoir engineering involving sorption problems. SPEJ P. 191＾

Applying Fractional-Flow Theory Under the Loss of Miscibility

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 661-670 ◽  
Author(s):  
Rouzbeh Ghanbarnezhad-Moghanloo ◽  
Larry W. Lake
Keyword(s):  
Numerical Simulation ◽  
Correlation Length ◽  
Linear Growth ◽  
Flow Theory ◽  
Mixing Zone ◽  
Fractional Flow ◽  
Water Alternating Gas ◽  
Simulation Results ◽  
First Contact ◽  
Fractional Flow Theory

Summary This paper examines the limits of the Walsh and Lake (WL) method for predicting the displacement performance of solvent flood when miscibility is not achieved. Despite extensive research on the applications of fractional-flow theory, the prediction of flow performance under the loss of miscibility has not been investigated thoroughly. We introduce the idea of an analogous first-contact miscible (FCM) flood to study miscibly degraded simultaneous water and gas (SWAG) displacements using the WL method. Furthermore, numerical simulation is used to validate the WL solution on one oil/solvent pair. In the simulations, the loss of miscibility (degradation) is attributed to either flow-associated dispersion or insufficient pressure to develop the miscibility. 1D SWAG injection simulations suggest that results of the WL method and the simulations are consistent when dispersion is limited. For the 2D displacements, the predicted optimal water-alternating-gas (WAG) ratio is accurate when the permeable medium is fairly homogeneous with a limited crossflow or is heterogeneous with a large lateral correlation length (the same size or greater than the interwell spacing). The results suggest that the accuracy of the WL method improves as crossflow is reduced. In addition, linear growth of the mixing zone with time is observed in cases for which the predicted optimal WAG ratio is consistent with the simulation results. Hence, we conclude that the WL solution is accurate when the mixing zone grows linearly with time.

scholarly journals Application of Fractional Flow Theory for Analytical Modeling of Surfactant Flooding, Polymer Flooding, and Surfactant/Polymer Flooding for Chemical Enhanced Oil Recovery

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2195
Author(s):  
Lei Ding ◽  
Qianhui Wu ◽  
Lei Zhang ◽  
Dominique Guérillot
Keyword(s):  
Enhanced Oil Recovery ◽  
Oil Recovery ◽  
Analytical Modeling ◽  
Flow Theory ◽  
Polymer Flooding ◽  
Surfactant Flooding ◽  
Fractional Flow ◽  
Oil Saturation ◽  
Polymer Retention ◽  
Fractional Flow Theory

Fractional flow theory still serves as a powerful tool for validation of numerical reservoir models, understanding of the mechanisms, and interpretation of transport behavior in porous media during the Chemical-Enhanced Oil Recovery (CEOR) process. With the enrichment of CEOR mechanisms, it is important to revisit the application of fractional flow theory to CEOR at this stage. For surfactant flooding, the effects of surfactant adsorption, surfactant partition, initial oil saturation, interfacial tension, and injection slug size have been systematically investigated. In terms of polymer flooding, the effects of polymer viscosity, initial oil saturation, polymer viscoelasticity, slug size, polymer inaccessible pore volume (IPV), and polymer retention are also reviewed extensively. Finally, the fractional flow theory is applied to surfactant/polymer flooding to evaluate its effectiveness in CEOR. This paper provides insight into the CEOR mechanism and serves as an up-to-date reference for analytical modeling of the surfactant flooding, polymer flooding, and surfactant/polymer flooding CEOR process.

Fitting Foam-Simulation-Model Parameters to Data: II. Surfactant-Alternating-Gas Foam Applications

2014 ◽  
Vol 18 (02) ◽  
pp. 273-283 ◽  
Author(s):  
W. R. Rossen ◽  
C. S. Boeije
Keyword(s):  
Steady State ◽  
Capillary Pressure ◽  
Oil Recovery ◽  
Water Saturation ◽  
Field Application ◽  
Model Parameters ◽  
Fractional Flow ◽  
Sweep Efficiency ◽  
Water Fraction ◽  
Foam Model

Summary Foam improves sweep in miscible and immiscible gas-injection enhanced-oil-recovery processes. Surfactant-alternating-gas (SAG) foam processes offer many advantages over coinjection of foam for both operational and sweep-efficiency reasons. The success of a foam SAG process depends on foam behavior at very low injected-water fraction (high foam quality). This means that fitting data to a typical scan of foam behavior as a function of foam quality can miss conditions essential to the success of an SAG process. The result can be inaccurate scaleup of results to field application. We illustrate how to fit foam-model parameters to steady-state foam data for application to injection of a gas slug in an SAG foam process. Dynamic SAG corefloods can be unreliable for several reasons. These include failure to reach local steady state (because of slow foam generation), the increased effect of dispersion at the core scale, and the capillary end effect. For current foam models, the behavior of foam in SAG depends on three parameters: the mobility of full-strength foam, the capillary pressure or water saturation at which foam collapses, and the parameter governing the abruptness of this collapse. We illustrate the fitting of these model parameters to coreflood data, and the challenges that can arise in the fitting process, with the published foam data of Persoff et al. (1991) and Ma et al. (2013). For illustration, we use the foam model in the widely used STARS (Cheng et al. 2000) simulator. Accurate water-saturation data are essential to making a reliable fit to the data. Model fits to a given experiment may result in inaccurate extrapolation to mobility at the wellbore and, therefore, inaccurate predicted injectivity: for instance, a model fit in which foam does not collapse even at extremely large capillary pressure at the wellbore. We show how the insights of fractional-flow theory can guide the model-fitting process and give quick estimates of foam-propagation rate, mobility, and injectivity at the field scale.

Hysteresis in Flow in Porous Media With Phase Transitions

1999 ◽  
Author(s):  
Pavel Bedrikovetsky ◽  
Dan Marchesin ◽  
Paulo Roberto Ballin
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Oil Recovery ◽  
Initial Boundary ◽  
Oil Reservoirs ◽  
Flow In Porous Media ◽  
Fractional Flow ◽  
Two Phase ◽  
Initial Boundary Problem ◽  
Gas Drive

Abstract Two-phase flow with hysteresis in porous media is described by the Buckley-Leverett model with three types of fractional flow functions: imbibition, drainage and scanning. The mathematical theory for the Riemann problem and for non-self-similar initial-boundary problem is developed. The structure of the solutions is presented and the physical interpretation of the phenomena is discussed. We obtain the analytical solution for the injection of water slug with gas drive into oil reservoirs. The solutions show that the effect of hysteresis is to decrease gas flux (in the case where the drainage relative permeability lies below the imbibition relative permeability). This effect increases oil recovery for Water-Alternate-Gas injection in oil reservoirs.

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