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# Areal displacement in a waterflood

Before computer modeling was common, the 3D aspects of a waterflood evaluation were simplified so that the technical problem could be treated as either a 2D-areal problem or a 2D-vertical problem. To simplify 3D to 2D areal, either the reservoir must be assumed to be vertically a thin and homogeneous rock interval (hence having no gravity considerations) or one of the published techniques to handle the vertical heterogeneity and expected gravity effects within the context of a 2D-areal calculation must be used.

The primary areal considerations for a waterflood involve the choices of the pattern style (see Fig. 1[1]) and the well spacing. Maximizing the ultimate oil recovery and economic return from waterflooding requires making many pattern- and spacing-related decisions when secondary recovery is evaluated. This has been particularly true for onshore oil fields in the US in which a significant number of wells were drilled for primary production. For offshore oil fields where the maximum number of wells is limited, the optimal waterflood injection-well/production-well layout is best determined by the use of 3D numerical reservoir simulation.

This article describes various factors that affect waterflood performance and discusses some of the 2D-areal calculation methodologies that have been developed. This discussion does not cover the use of modern numerical reservoir-simulation models in a 2D mode for analyzing a reservoir’s waterflood performance, either for history matching or for future-performance projections. See Reservoir simulation for a review of numerical reservoir simulation.

## Waterflood displacement in a five-spot pattern

Because it has been studied extensively, taking a look at the five-spot pattern (Fig. 1) provides an effective review of the areal aspects of waterflooding. Fig. 2[2] plots the waterflood performance of a five-spot experimental homogeneous sandpack for range of water/oil viscosity ratios from 0.83 (slightly favorable) to 754.0 (very unfavorable). Fig. 3 shows the X-ray shadowgraphs of a waterflood of two five-spot homogeneous sandpacks, one whose mobility ratio is favorable ( M = 0.40) and one whose mobility ratio is unfavorable ( M = 1.43). Fig. 4 plots the breakthrough areal-sweep efficiency as a function of M for a five-spot-pattern flood.

Figs. 2 through 4 show that the water/oil viscosity ratio is critical to the efficiency of the waterflood displacement. When the oil is more viscous than the water, the water areally displaces the oil less efficiently. When the oil is less viscous than the water, the water areally displaces the oil very efficiently.

## Streamtube waterflood calculations

In the 1960s, Higgins and Leighton published a technique for analyzing waterfloods using what has been termed streamtubes, or stream channels, and using the concept of streamlines.[3][4] Streamlines are the paths that fluid particles follow when they move from the injector to the producer; a streamtube is the region between two streamlines. The Higgins and Leighton technique approximates the displacement problem by use of a set of streamtubes in which fluid flows from the injection well to the production well and in which no fluid flows perpendicular to the streamlines (Fig. 5). Streamlines for the steady flow of a single phase (unit mobility ratio) have been determined for regular displacement patterns. Streamlines for arbitrary arrangements of injection and production wells can be determined by superposition of numerical solutions (see Fig. 6).[5]

Streamtube techniques originally were developed for areal waterflood analysis. These techniques have continued to be popular with advancements in the mathematical techniques and computing power. (Also see the discussion about streamtube techniques in Streamline simulation). The more advanced streamtube models can handle stratified-layer systems. Many universities and oil companies have developed sophisticated streamtube models and applied them to waterflood calculations. Such models also are available from commercial software providers to the oil industry.[6]

Any 2D approach to waterflood analysis is an approximation. How accurate an approximation it is will depend on how vertically stratified the reservoir is and how significant the gravity considerations are in the real reservoir compared to what the numerical modeling assumes about them. For many situations, 2D-streamtube models have been used successfully to model historic waterflood performance and to project future waterflood performance.[7]

## Waterflood pattern and well spacing considerations

As Fig. 1 shows, a variety of geometric injector/producer pattern layouts can be used when waterflooding an oil reservoir. These geometric layouts are designed to produce an efficient waterflood for the whole of the reservoir, assuming the rock is homogeneous. The producer/injector ratio typically is chosen on the basis of the expected injection rates for the water injectors and the total fluid-production rates for the production wells. The goal is to have voidage replacement, with the injected volume equal to the produced volume. Injection and produced volumes will depend on the transmissibility of the system, the maximum pressure that can be applied at the injector, and the minimum pressure that can be achieved at the producer. It has been customary to limit injection pressures to lower than what would cause fracturing. As will be discussed later, this guideline can be relaxed in some circumstances.

Other considerations with the injector/producer-pattern layout are the anisotropic permeability in the reservoir and the orientation of any natural-fracture systems that are within the reservoir interval. Fig. 7 shows the correct and incorrect orientation of lines of injectors and producers in this respect. The goal is to make these natural aspects of the reservoir improve the areal sweepout as the water displaces the oil, rather than allowing them to affect it negatively.

The choice of waterflood well spacing is primarily a function of four considerations:

• Incremental oil recovery
• Increased oil-production rate
• Reduced operating costs (producing more of the oil at lower water cuts)
• Costs to drill additional wells, including additional platform space at offshore locations

The initial well spacing typically is chosen on the basis of engineering studies, assuming that there will be a logical phased-development plan for the oil field, including possibilities for various levels of infill drilling and pattern realignments. Low-permeability reservoirs typically have closer well spacings than do high-permeability ones because of their reduced ability to move fluids rapidly between widely spaced injectors and producers. The initial well spacing usually is somewhat wider than what is likely to be used toward the end of field life. The number of injection and production wells also is tied to the capacity of the injection facilities and production fluid separation facilities.

The incremental oil recovery can be a function of the well spacing and depends on the continuity of the porous and permeable reservoir-rock layers. If the reservoir layers are highly continuous, then reducing the well spacing will not have much effect on the ultimate oil recovery by waterflooding; however, for layers that are discontinuous over the reservoir, closer well spacing will provide more reservoir continuity between injector/producer pairs. This aspect of waterflooding has been studied in depth for a variety of U.S. oil fields, mainly west Texas carbonate reservoirs, in which reservoir-layer continuity is a major issue. Many papers have been published on this topic.

For example, Barber et al.[8] reviewed nine sandstone and carbonate reservoirs’ responses to infill drilling. Figs. 8 and 9 show aspects of reservoir discontinuity in west Texas Clearfork and San Andres carbonate reservoirs. Fig. 9 shows that the San Andres reservoirs have significantly greater reservoir continuity at a 10-acre well spacing than at 20- and 40-acre well spacings. For these reservoirs, "[c]ontinuity calculations made after infill drilling indicated the pay zones to be more discontinuous than when calculations were made before infill drilling."[8] From the experience in those nine fields, the authors concluded that "the ultimate well density in any given field can be determined only after several years of field performance provide sufficient information on reservoir continuity and recovery efficiencies." [8]

Another paper on this topic is by researchers at Texas A&M U.,[9] who spent several years analyzing the impact of well-spacing reduction on west Texas Clearfork and San Andres waterflood performance from various geographic areas of the Permian Basin. The authors found infill drilling to be more effective for the San Andres units than for the Clearfork units. In the San Andres units, they determined the infill drilling to be more effective for the units in the Northern Shelf area than for those in the Central Basin Platform area. In those analyses, they calculated a 2 to 5% additional recovery of OOIP for a 9-acre well spacing, compared to a 22-acre well spacing.[9]

As noted above, many more papers have been published on this topic, but these two papers identify the key well-spacing issues. As both studies conclude, one does not know a priori what the optimal well spacing will be. The technical team must analyze the available data before starting a waterflood, then continue to evaluate the production and injection data to determine the waterflood’s efficiency and the extent to which infill-well locations should be drilled or patterns realigned.

## Horizontal wells, multilateral wells, and fracture orientation

Until the 1980s, all waterflood analysis assumed that the wellbores would penetrate the reservoir vertically and that water should not be injected above the formation parting pressure. Accordingly, mathematical formulations assumed areally that injection and production wells were point sources and sinks. This style of analysis is evident in the streamline patterns in Fig. 6.

The advent of horizontal-well and multilateral-well technologies has brought with it the ability to create line injection-well sources and line production-well sinks, which has changed how a waterflood pattern might be developed. Theoretical calculations show that parallel lines of horizontal injectors and horizontal producers will increase oil recovery and in the limit are the perfect line-drive pattern arrangement.

When fracturing injection wells, a concern has been that a fracture might extend from the oil-reservoir intervals into adjacent porous and permeable layers, into which considerable injection brine could be lost (i.e., thief zones); however, given that the principal orientation of any hydraulic fracture is known and that the fractures can be restricted to the oil-reservoir interval, hydraulic fractures can improve the areal sweepout during waterflooding in much the same way that horizontal wells can. This is true of fractures from the injection wells and the production wells, given that an appropriate pattern style is used. On the other hand, if they are oriented so that the fracture tips are significantly closer to each other than the vertical wellbores are, hydraulic fractures from the injectors and producers will yield poorer areal sweepout of the reservoir during waterflooding than would unfractured vertical wells.

An excellent example of a situation in which fracturing was needed is the waterflooding of diatomite reservoirs in California, US. These reservoirs have high porosity, but permeabilities of 0.1 md or less. Conventional injection methods yielded uneconomic rates; however, positioning the injectors and producers normal to the induced-fracture orientation established reasonable rates without significant loss of injected water to adjacent porous and permeable intervals and without premature water breakthrough.[10][11]

## References

1. Rose, S.C., Buckwalter, J.F., and Woodhall, R.J. 1989. The Design Engineering Aspects of Waterflooding, Vol. 11. Richardson, Texas: Monograph Series, SPE.
2. Willhite, G.P. 1986. Waterflooding, Vol. 3. Richardson, Texas: Textbook Series, SPE.
3. Higgins, R.V. and Leighton, A.J. 1962. Computer Prediction of Water Drive of Oil and Gas Mixtures Through Irregularly Bounded Porous Media Three-Phase Flow. J Pet Technol 14 (9): 1048–1054. http://dx.doi.org/10.2118/283-PA.; Trans., AIME, 225.
4. Higgins, R.V. and Leighton, A.J. 1974. Matching Calculated With Actual Waterflood Performance by Estimating Some Reservoir Properties. J Pet Technol 26 (5): 501–506. SPE-4412-PA. http://dx.doi.org/10.2118/4412-PA
5. Baek, M. and Hewett, T.A. 2000. A Hybrid Streamtube Simulator Using A Semianalytical Method. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 1–4 October. SPE-63151-MS. http://dx.doi.org/10.2118/63151-MS
6. Emanuel, A.S. and Milliken, W.J. 1997. Application of Streamtube Techniques to Full-Field Waterflood Simulation. SPE Res Eng 12 (3): 211–218. SPE-30758-PA. http://dx.doi.org/10.2118/30758-PA.
7. Grinestaff, G.H. and Caffrey, D.J. 2000. Waterflood Management: A Case Study of the Northwest Fault Block Area of Prudhoe Bay, Alaska, Using Streamline Simulation and Traditional Waterflood Analysis. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 1–4 October. SPE-63152-MS. http://dx.doi.org/10.2118/63152-MS
8. Barber, A.H. Jr., George, C.J., Stiles, L.H. et al. 1983. Infill Drilling To Increase Reserves—Actual Experience in Nine Fields in Texas, Oklahoma, and Illinois. J Pet Technol 35 (8): 1530–1538. SPE-11023-PA. http://dx.doi.org/10.2118/11023-PA
9. Lu, G.F., Brimhall, R.M., and Wu, C.H. 1993. Geographical Distribution and Forecast Models of Infill Drilling Oil Recovery for Permian Basin Carbonate Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. SPE-26503-MS. http://dx.doi.org/10.2118/26503-MS
10. Fast, R.E., Murer, A.S., and Zambrano, L.G. 1993. Lost Hills Diatomite Simulation Study: Predicting Waterflood Performance in a Low-Permeability, Compacting Reservoir. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. SPE-26627-MS. http://dx.doi.org/10.2118/26627-MS
11. Wright, C.A. and Conant, R.A. 1995. Hydraulic Fracture Reorientation in Primary and Secondary Recovery from Low-Permeability Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 22–25 October. SPE-30484-MS. http://dx.doi.org/10.2118/30484-MS