Mejora Simulacion Teoria Catastrofe Espuma KAM 2007

Available online at www.sciencedirect.com Colloids and Surfaces A: Physicoch em. Eng. Aspects 318 (2008) 62–77 Improved mechanistic foam simulation with foam catastrophe theory Seung Ihl Kam ∗ Craft and Hawkins Department of Petroleum Engineering, Louisiana State University , 3523 Patr ick F . Taylor Hall, Baton Rouge, LA 708 03, USA Received 7 May 2007; received in revised form 4 October 2007; accepted 5 December 2007 Available online 23 December 2007 Abstract Recent experimenta l studies discovered that foam exhibits three different states (weak-foam, intermediate, and strong-foam states) reminiscent of catastrophe theory, and the strong-foam state consists of two distinct flow regimes (high-quality and low-quality regimes). No existing foam simulators can handle these concepts properly, especially when the simulation comes to near the limiting capillary pressure, P ∗ c (or the limiting water saturation, S ∗ w , equivalently) at which foam breaks down abruptly. Capturing the delicate feedback mechanism near P ∗ c has been a great challenge in mechanistic foam simulations. This study presents how to build a mechanistic foam simulator consistent with foam catastrophe theory and two steady-state strong-foam regimes. More importantly, this study for the first time resolves the issues on the instability and diverge nce of numerical simulation that take place near the physical discontinuity (i.e., P ∗ c or S ∗ w ) in foam simulation. Results showed that it was necessary to choose an appropriate lamella-creation function to ensure the stability and convergence. Specifically (1) the lamella-creation function should increase rapidly above a certain pressure gradient (P), known as a minimum pressure gradient (P min ) for lamella mobilization and division, to kick off active bubble generation, and (2) the function should also reach a plateau at high P at which foam rheology is governed by bubble coalescence rather than bubble generation. This new mechanistic simulator required five parameters to fit the steady-state foam catastrop he, the two flow regimes, and dynamic foam coreflood data, each of which was determined uniquely . The foam model in this study manifested that active (or, inactive ) lamella-creation mechanism could be compensated by active (or, inactive) lamella-coalesc ence me cha nis m in themodel ing pro ces s. Theleve l of ho w act iv e the se me cha nis mswe re,howe ver, hada signifi can t imp ac t on the shi ft from we ak- foa m to strong-foam propagation during dynamic foam displacement. Simulations were extende d not only to simultaneous injection of gas and surfactant solutions in a wide range of injection velocities, but also to alternating gas and surfactant solutions in which the dynamic mechanisms near P ∗ c is the key to field performance. Results were compared and verified with fractional flow analysis that was equipped with mechanistic foam mechanisms. © 2007 Elsevier B.V. All rights reserved. Keywords: Foam; Foam simulation ; Limiting capillary pressure; Limiting water saturation; Foam catastrophe 1. Intro ducti on Foam is an agglomeration of gas bubbles separated by thin liquid films [1]. These thin liquid films, called lamellae, are sta- biliz ed by surf ace acti ve agen ts, or surfa ctant s. Surfa ctant s allo w foams to be long-lived even though foam is thermodynamically unstable, and eventually breaks down to minimize its surface area [1,2]. Foam is a good example of complex fluids. Its flow char- acteristics are sensitive functions to the physical properties of external aqueous phase, the type and concentration of surfac- tants dissolved, and the size and shape of internally dispersed ∗ Tel.: +1 225 578 5216; fax: +1 225 578 6039. E-mail address: [email protected]. gas bubbles. Foam rheology also depends on the interactions between individual bubbles, bubbles and pore walls, and gas and liquid phases [2,3]. Many of these are yet to be fully under- stood, which becomes the major impediments to modeling and simulation of foams in porous media. The wide and consistent use of foams [4–8] in enhanced and imp rov ed oil rec ov ery and nea r wel lbo re tre atment s res ult s fro m two major advantages that foam exhibits: (1) the mobility of gas phase can be reduced by a few orders of magnitudes if a fine-textured foam is developed in the media, and (2) a large fraction of foams are trapped in porous media, which can divert sub seq uen t fluidsinto thelayerwith lowerperme abi lit y or hig her oil saturation. The terms, weak and strong foams, have been used in the literature to describe the degree of gas-phase mobility reduction [2,3,7,8]: strong foam is referred to as a state at which foam 0927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2007.12.017

Mejora Simulacion Teoria Catastrofe Espuma KAM 2007

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