From a waterflooding perspective (matrix), crossflow effects can improve the recovery performance at favorable mobility ratios and the reverse is true if the mobility ratio is unfavorable. The mobility of a fluid is the effective permeability of that fluid divided by the fluid viscosity. For example, water mobility is k_w/m _w and oil mobility is k_o/m _o. Mobility is saturation dependent. Mobility ratio has been defined as:

The subscript "d" denotes the displacing phase. In PWRI, the displacing phase is water and we can approximately consider the mobility ratio to be:

The water permeability is that in the water-contacted portion of the reservoir and the oil permeability is that in the oil bank (two different and separated points). These are simplifications if there is a saturation gradient behind the water front. Changes in mobility ratio can also occur after breakthrough. As a rule-of-thumb, Craig, 1971, suggested that the most commonly encountered values of mobility ratios during waterflooding range from 0.02 to 2.0. Most existing waterflooding operations involve unfavorable mobility ratios.

As another rule-of-thumb, in conventional waterflooding, using very elementary considerations, crossflow effects can improve the recovery performance (vertical coverage) at favorable mobility ratios (M < 1) and the reverse can occur for unfavorable mobility ratios (M > 1). BUT - this presumes that vertical coverage is desirable - that all zones have unswept oil. If this is not the case, it may be desirable to inhibit vertical coverage.

Figure 1 is a schematic of how flow might occur in a layered PWRI injector. Presume that all zones are "perforated" and initially open at the wellbore. "Normalized" values of permeability are shown for each layer. Presume that the in-situ stress (s) is the same in all zones. Figure 1 is a situation where there is negligible crossflow. Penetration is greater in the higher permeability zones and for the purposes of illustration, plugging at/near the wellbore is assumed to occur earlier in the lower permeability intervals.

Figure 1.

Multi-layered formation assuming no crossflow, but also demonstrating reduced recovery in lower permeability intervals and the potential for rapid breakthrough.

There will likely be some degree of crossflow (pressure and fluid-flow communication between layers). Figure 2 is a schematic of how crossflow can occur.

Figure 2. Suppose that there are two adjacent layers with permeability k1 and k2 (more precisely, mobility needs to be considered). Do not consider plugging at this time. If k1 >> k2, the radial pressure gradient "wants" to be higher in Layer 1 than in Layer 2 after injection has occurred for some time. This is because most of the flow has been going into the higher permeability layer. The spreading pressure increase in Layer 1 can create a vertical flow gradient into Layer 2 (i.e., at least away from the wellbore, instantaneous crossflow is assumed to occur between the layers to keep the pressure gradient the same in all layers at any distance). If k2/k1 £ 0.01 the direction of flow in Layer 2 would be almost vertical.

With crossflow, such as shown schematically in Figure 2, and also in Figure 3, flow can be diverted to zones where there is no hydrocarbon to be swept. Figure 3 shows incipient crossflow from higher to lower permeability zones at a relatively short distance from the wellbore.

Figure 3.

Incipient, near-wellbore crossflow is schematically shown where flow is diverted to a lower permeability zone.

Water breakthrough in the high permeability layer has serious consequences. The water mobility and transmissibility will skyrocket in the high permeability layer due to relative permeability effects. Then, oil recovery and sweep efficiency can be seriously impacted.

To the PWRI specialist, crossflow can have three manifestations. There can be horizontal crossflow on shut-in, occurring at the wellbore. This has been demonstrated on Heidrun. There can be near-wellbore vertical interlayer flow, as is shown in Figure 3. There can also be crossflow deep in the reservoir due to permeability contrasts, or in-situ inhomogeneities. Figure 4 is an example, showing movement of fluid to the water zone (perforated only in the oil zone) because of more favorable relative permeability and gravity. Note in this example that flow is to a higher permeability zone.

Figure 4.

Impaired sweep in the oil zone because of the more favorable relative permeability in the zone with higher water saturation. Injectivity may be adequate but hydrocarbon recovery is drastically reduced and impaired.

The situation in PWRI is frequently more complicated since some form of vertical fracture may have often formed. Figure 5 schematically shows diversion of fluid to a lower permeability zone because of fracturing. Injectivity may appear to be adequate, but this cannot be considered exclusive of sweep efficiency, [i.e., you may be able to inject all of the water that is produced, but because of the diversion of fluid to the lower permeability zone (possibly not containing hydrocarbons) sweep in the higher permeability zone can be less effective]. The inverse situation can also occur after water breakthrough in a high permeability layer.

Figure 5.

Impaired sweep in the higher permeability zones because of fracture growth into the overlying lower permeability material.

Yes. There is a simple (if not simplistic) tool, for commingled reservoirs (communication only possible in the wellbore).

It is desirable to be able to compare available field information with a closed form, analytical simulation, to emphasize any differences in procedures that may occur with the injection of produced water. The simplest representation is completely familiar to anyone who is used to dealing with conformance issues in conventional flooding situations. It is a radial flow analytical model, with no vertical crossflow. Thermal stress alteration is considered. This is incorporated in the PWRI Toolbox. If you have not already, you can download the PWRI Toolbox, and the associated User's Guide and Technical Manual.

You can also download the minutes of a Workshop held on Layered Formations. There is useful information here but remember that it is a workshop and as such it was an open forum for exchange of ideas and that there may have been disagreements among the participants on some issues.

You can select relevant downloads below.