Optimal Injection Strategies for Foam IOR

Summary

Miscible-gas foam field trials have employed a variety of injection strategies, with mixed results. Using simulation, we compare foam-injection strategies in homogeneous reservoirs with a variety of foam models. The optimal injection strategy for overcoming gravity override with foam in a homogeneous reservoir is alternating injection of separate, large slugs of gas and liquid at fixed, maximum-allowable injection pressure. This strategy minimizes both gravity override and time of injection, with minimal rise in injection-well pressure. Injection of gas at maximum pressure can partially reverse the effects of gravity slumping of surfactant during injection of liquid. The process is remarkably insensitive to the detailed properties of the foam, as long as foam does not collapse abruptly and completely at a "limiting water saturation" S_w*. However, care is needed to exclude the effects of numerical artifacts in simulating such a process, especially if foam collapses abruptly and completely at S_w*.

An idealized model for the process reveals the mechanisms responsible for process success, why injection at fixed injection pressure is better than injection at fixed rate, why details of foam behavior play a secondary role in sweep efficiency, and why numerical artifacts can be difficult to identify.

Introduction

Since 1900, gas, such as steam, carbon dioxide, nitrogen, and reinjected field gas, has been widely used as a driving fluid to improve oil recovery.^1,2 However, reservoir heterogeneity, low gas density, and high gas mobility cause poor sweep efficiency, which limits the application of gas in improved-oil-recovery (IOR) processes. Because of low gas density, gas tends to rise to the top of the reservoir and override the oil-rich zone. High mobility of gas in the formation leads directly to viscous instability in the reservoir, and makes gravity override and heterogeneity much worse by forming high-mobility channels. Fortunately, foam can improve the sweep efficiency of injected gas by reducing gas mobility and the effects of reservoir heterogeneity.^3,4 Foams have been used in IOR processes and achieved some success in field applications.^5-18

Foam does not alter the water relative permeability function or liquid viscosity.^19-22 Foam greatly reduces gas mobility by trapping some bubbles and resisting the movement of flowing gas bubbles.^23-26 Trapped gas reduces mobility by reducing gas relative permeability, while in flowing bubbles, gas has a large effective viscosity. Gas mobility in the presence of foam is dominated by foam texture, or bubble size.^23-26 Smaller bubbles reduce gas mobility more than large bubbles.

Lower capillary pressure P_c favors foam generation^24,27 and stability,^28,29 and higher capillary pressure causes foam collapse. In fact, foam appears to suffer abrupt collapse at a single "limiting" value of P_c , P_c*.²⁸ This mechanism holds P_c close to P_c* and water saturation S_w constant at S_w* identical S_w (P_c*) over a range of flow rates and foam qualities (gas volume fraction).³⁰ Gas mobility and water fractional flow change abruptly over a narrow range of values of S_w near S_w* because of foam collapse. It is not yet clear whether foam collapses completely at this saturation. At lower foam qualities, there exists a second foam-flow regime,³¹ but it plays a small role in the discussion to follow.

In reality, the relative permeability and viscosity effects of foam are inextricable.³² Computationally, it is equivalent to alter gas mobility for foam by modifying either gas viscosity or relative permeability or both. In the models described here, gas relative permeability alone is altered to account for all effects of foam on gas mobility.

Methods of Foam Injection.

Foam can be placed in the reservoir by either coinjection of liquid and gas at fixed quality (gas volume fraction), or surfactant-alternating-gas (SAG) injection, where alternating slugs of surfactant solution and gas are injected. For CO₂ projects, SAG processes may be preferred to minimize corrosion to surface facilities and piping.^33,34 Continuous foam injection should be used if one wants to create and maintain foam in the near-well region, or to ensure that both gas and liquid enter the same zones in a heterogeneous reservoir.

Different foam-injection strategies have been used in field trials because of stratigraphic differences, foam behavior, and operational concerns. Shan³⁵ lists 11 foam field trials with CO₂, N₂, air, or hydrocarbon-gas foam.^{5-11,13-15,17,18} Six employed coinjection of gas and liquid, seven SAG injection at fixed injection rates, and two SAG injection at fixed injection pressure. (Some field trials tested more than one method of injection.) Determining the optimal injection strategy is a major goal of this work.

For continuous foam injection at fixed injection rate, the only way to improve sweep efficiency with continuously injected foam is by raising the injection-well pressure.^36,37 In such a process, low-mobility foam extends from the displacement front back to the injection well, where most of the pressure drop occurs. The required rise in injection-well pressure could fracture the injection well, rendering a continuous-injection foam process impractical.

Shi and Rossen³⁸ show that foam processes employing SAG injection at fixed injection pressure control gravity override better than continuous foam injection or SAG at fixed injection rate, based on numerical simulations. They limited their study to gas injection following injection of a large (infinite) slug of liquid. The effects of liquid-slug size or multiple slugs were not considered.

Here we extend that study of gravity override in homogeneous reservoirs to finite, multiple slugs of liquid and gas, with particular focus on optimal injection strategies for both fluids. Fractional-flow analysis indicates the reasons for the success of this process: Most of the well-to-well pressure drop is focused near the displacement front, where sweep efficiency is determined. An idealized model based on this concept shows why the process works, why it is relatively insensitive to the details of behavior of the foam formulations, and why real foam formulations may not live up to the ideal process efficiency.

For simplicity, this report focuses on foam mobility in the absence of oil, and "liquid" and "water" are used interchangeably to designate the aqueous phase.

Fractional-Flow Analysis of SAG Processes

Fractional-flow methods are useful in analyzing foam^39,40 and other IOR processes.¹ The assumptions made include incompressible phases; Newtonian mobilities; one-dimensional displacement; absence of dispersion, gradients of capillary pressure, and viscous fingering; and immediate attainment of local steady state. In spite of its simplifying assumptions, others⁴¹ have found fractional-flow theory to be accurate and useful in analysis of field data in the foam field test at the Snorre field. The application of fractional-flow theory to foam displacements is discussed more fully elsewhere.^39,40