Doctrines vs. Realities in Reservoir Engineering
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The appreciation of empirical realities permits the improvement of commercial depletion planning and enables a greater number of projects. The concepts articulated here are applicable in almost all heavy-oil reservoirs and may be applicable also for lighter oils that possess oil chemistry typical of heavier oils (e.g., high acid content). This paper reviews the evidence for and against three doctrines in current use to develop depletion plans: (1) optimal recovery is obtained using a voidage-replacement ratio (VRR) of unity, (2) the Buckley-Leverett (BL) formulation (phase slippage) applies uniformly to heavier oils, and (3) viscous fingering dominates unstable multiphase flows.
- Doctrine: Optimal Waterflood Response Occurs With VRR=1
- Reality: Periods of VRR<1 Increase Oil Recovery
Though initially viewed with some suspicion, waterflooding has demonstrated multifold greater recovery than primary depletion for many reservoirs. It is, by far, the most important oil-recovery process. One visualization of the process is that of a leaky, deformable water piston displacing a fraction of the oil to the production wells. Maximum recovery occurs when the voidage created by the produced fluids (oil plus water) at reservoir conditions (pressure and temperature) is replaced fully by an equal volume of the injected water also at reservoir conditions (i.e., the waterflood VRR=1). In this way, reservoir pressure is maintained. The waterflood initial production is pure oil until water breakthrough. Subsequently, water is produced along with the oil, resulting in an increasing water/oil ratio (WOR). This simple visualization is intuitively attractive and has dominated the thinking of the industry.
This “leaky, deformable piston” visualization is simplistic and neglects or sidelines complex physical and chemical properties of the reservoir. If the waterflood is operated below the oil bubblepoint pressure through a continued VRR<1, a gaseous phase forms, creating three-phase-flow conditions and more-complex displacement possibilities. Furthermore, reservoir oils can have widely different physical and chemical properties, varying by many orders of magnitude in viscosity and substantially in interfacial activity as described by metrics such as the total acid number. Despite the full recognition of these complications, over time, the now almost universal practice developed of operating waterfloods with VRR=1.
Analytical and Numerical VRR Simulations. VRR<1 activates many recovery mechanisms. Some mechanisms can be enumerated and examined, and others may exist that are yet to be identified. What is the possible upside of operating a waterflood with VRR<1? Making a rough estimate is not too difficult if we limit the number of mechanisms. With VRR<1, two dominant recovery mechanisms exist, solution-gas drive (VRR=0) and water displacement (VRR=1). As a first approximation, at an intermediary VRR<1, the two mechanisms may be additive: Oil Recovery (at Optimal VRR)=Oil Recovery by Pure Waterflood (VRR=1)+Pure Solution-Gas Drive (VRR=0).
A percolation-theory connectivity model—where connected volumes can be either on the backbone or on the dangling ends—suggests that this recovery prediction should be substantially correct. Solution-gas drive displaces oil from the dangling ends to the backbone that is swept by the waterflood. Though unquestionably simplified, this model has heuristic value.
To a surprising degree, this additive model makes an accurate prediction of the value of optimal VRR<1 for viscous and heavy oils. It is in agreement with laboratory VRR experiments and consistent with empirical field observations that indicate an optimal VRR≈0.7.
Slipping Vs. Embedding
- Doctrine: Phases Slip Past Each Other
- Reality: Phases Embed Within Each Other
The first doctrine deals with macroscopic balance of volumes injected into and produced out of the reservoir. The second proposition deals with the pore-scale movement of the phases within the reservoir. The dominant visualization is that of a wetting phase, typically water, that coats the rock, with the other nonwetting phases, oil and gas, in the center of pores slipping past the wetting phase (Fig. 1a). In his classic 1938 paper, M.C. Leverett quantified the relative slipping of each phase by the multiphase extension of Darcy’s law including the relative permeability curve of each phase. He concluded that “the relative permeability of an unconsolidated sand to oil/water mixtures is substantially independent of the viscosity of either liquid.” Despite the limited laboratory data, this deduction became the fundamental building block of petroleum reservoir engineering. Extensive efforts have been made to develop this visualization mathematically, to quantify it through laboratory testing, and to make predictions on the basis of it using numerical simulators. In particular, the BL mathematical formulation is incorporated as the default—and typically the only available—reservoir-fluid-flow model for use in commercial reservoir simulations. By the 1960s, computers permitted the BL formulation to be applied to large-scale finite-difference simulations, and slippage flow became a doctrine.
WOR≈1—The Rosetta Stone of (Heavy Oil) Reservoir Engineering. The most striking observation in waterflooding of some viscous and heavy oils is that, after water breakthrough, the WOR rises to near unity and then this ratio (WOR≈1) persists for an extended period of time. The flattening is often surprisingly abrupt. This observation is pervasive for heavy-oil waterfloods.
Data strongly suggest that the WOR≈1 regime is a property of the fluids (oil and water) and not of the specifics of the container’s (i.e., reservoir’s) heterogeneity. Analytical and numerical studies for stratified reservoirs have demonstrated WOR plateaus, but their values range over orders of magnitude, as would be expected from conventional simulations where permeability ratios determine the WOR ratios. But this is not what is observed empirically. Commercial production data for individual wells, particularly from heavy-oil reservoirs, display a remarkable preponderance of a WOR≈1 regime early in the well production life.
Fingering and Sweep
- Doctrine: Mobility Ratios Determine Fingering and Sweep in Petroleum Reservoirs
- Reality: Slow Pressure Diffusion and Reservoir Heterogeneity Determine Fingering and Sweep
Compared with light oils, viscous- and heavy-oil waterfloods are characterized by lesser oil-production rates and lesser total recoveries. The greater oil viscosity of heavy-oil reservoirs readily explains their lower production rates. The reasons for the generally lower total recovery of heavy-oil waterfloods are more complex. One common empirical observation is early communication between the water injectors and the producers, resulting in early water breakthrough that significantly reduces the sweep (conformance) of the injected water. This early communication has been attributed to water fingers that quickly connect the injectors to the producers. The invoked mechanism for the fingering is the intrinsic instability of the fluid/fluid interface when a less-viscous fluid (water) pushes against a more-viscous fluid (heavy oil). The ratio of the displaced fluid to the displacing fluid viscosity (M) has become an important metric for characterizing and discussing the unstable-interface mechanism.
The laboratory visualizations of how M affects sweep were dominated initially by the use of the Hele-Shaw cell—two transparent rigid flat plates separated by a uniform spacer with no-flow boundary conditions at the bounding edges, except at the injection and production locations. Experiments from the 1950s onward, using both miscible (hydrocarbon solvent) and immiscible (water) displacing fluids, provided the key observation: The sweep declines with increasing M.
Though attractive in its simplicity, the Hele-Shaw model is conceptually limiting and can mislead. In fact, the Hele-Shaw cell is not even a porous medium because it lacks pores and constrictions. For real reservoirs, with their inherent heterogeneity, is it really M that limits the reservoir conformance? Areal numerical simulations have been used to demonstrate that, for sufficiently heterogeneous reservoirs, the flow paths through the formation, in fact, were independent of M, regardless of whether M was 1 or 20. But, for relatively homogeneous reservoirs, the sweep was very much dependent on the value of M, in accordance with the Hele-Shaw analog. The transition between the two states depends on the nature of the heterogeneity, and so the value of the insight is more conceptual than quantitative. At a minimum, the simulations suggest that the conventional doctrine overestimates the role of M in reducing reservoir sweep.
This paper presented three reservoir-engineering doctrines that developed early in the evolution of petroleum-recovery technology and were quickly adopted. These doctrines were intuitively appealing, simply articulated, and initially useful. They were based, however, on a very limited database drawn from conventional reservoirs, and, over time, their continued use began to limit commercial oil recovery, particularly for heavy-oil systems.
Optimal voidage management is the most leveraged technology for increasing waterflood recovery from heavy-oil reservoirs. The current doctrine dictates VRR=1, both instantaneously and cumulatively; this significantly underestimates the possible recovery levels from heavy-oil reservoirs and thus limits their economic attractiveness. Similarly, the continued use of the theory of immiscible continuous phase slippage, when emulsion flow would be more appropriate, overestimates the polymer concentration required for heavy-oil polymer floods. The limitations of mobility ratio as a doctrine are currently better understood than the limitations of the other two doctrines. Nonetheless, M continues to be used widely as a metric of the likely reservoir sweep, again to the detriment of reservoir recovery potential.
Doctrines vs. Realities in Reservoir Engineering
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