Suppressing fluid loss in fractures
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Injected fluid losses in large subsurface channels can be suppressed with the use of low concentrations of viscoelastic surfactants which selectively retard flow in larger apertures. The effect is demonstrated by pumping viscoelastic surfactants through smooth capillaries. The choice of capillary diameters relate to fractures in oil or geothermal reservoirs as well as induced hydraulic fracturing operations in tight gas reservoirs. Selective retardation is favoured at a lower range pressure drops usually associated with oil recovery. The effective apparent viscosity contrasts between different capillary diameters are not as high as those previously observed in permeable flow because the measured effects in the smooth capillaries are mainly shear driven. We expect an elongation contribution to the apparent viscosity in real non-smooth fractures.
KeywordsHydraulic fracturing Geothermal Secondary oil recovery Fracture flow Viscoelastic surfactants
List of symbols
Lateral extent of matrix
Total resistance to flow
Shear viscosity from rheometer
Apparent viscosity from capillary
During the initial stages of hydraulic fracturing, the pressurised injected water “pad” needs to be selectively stopped from entering large fractures. This enables more volume to be directed into small fractures where more surface area needs to be created to enhance fracture conductivity.
In enhanced geothermal systems in granite basement, injected water is diverted via larger fractures. The diverted water is not heated and cools down the other hot streams from smaller fractures when they are combined at the producer well. These “short circuits” are thus limiting factors on efficient high quality heat recovery.
In secondary oil recovery, uneven advance of the displacing injected fluid arises from “short circuits” caused by large fractures diverting water around, and thereby bypassing, oil bearing zones.
Recent research (Golombok et al. 2008; Reuvers and Golombok 2009a, b; Golombok and van der Wijst 2012) has demonstrated the potential of viscoelastic surfactants (VES) in selectively retarding flow in regions of high rock permeability for application in oil recovery. So far these VES materials have not been studied in the other source of oil bypass i.e., fracture flow. This is the subject of the current paper.
Viscosity modifying additives are generally characterized by their response to changing shear in a standardised situation such as a Couette cell. The viscosity is mapped for a range of shear rates measured one at a time. Couette cell measurements with their constant applied shear rate do not extrapolate straight-forwardly to direct application in an idealized capillary or slit flow. In porous and aperture (fracture, capillary etc.) flow there is a distribution of shear rates within the openings. The apparent viscosity is different from measurements in Couette cells. A study of viscosity modifying additives in fractures, slits and capillaries is a logical intermediate step between Couette cells and porous media. Slits and capillaries have a well-defined geometry where the behaviour of fluid flow is simpler than for porous flow. Demonstrating selective retardation in capillaries is the focus of this paper i.e., the link between effects observed in Couette cells and in porous media. “Background” describes the physical processes and connects these with the application. An experimental description follows in “Experiment” and the results are analysed and discussed in “Results and discussions”.
The case of fracture diversion away from permeable porous flow is more difficult because of the much greater contrasting effective permeabilities. For example, if two competing fractures (Fig. 1a) have a width ratio w l /w s of 10, the ratio of permeabilities is 100. For fracture and matrix (Fig. 1b), the effective permeability ratio is higher—this can be as much (see “Appendix”) as 105. Fractured oil fields typically have dual porosity structure derived from porous matrix and fractures, respectively (van Golf-Racht 1982). Intergranular porosity is associated with primary matrix permeability K m. Secondary porosity arises from fractures and has an secondary (intrinsic) fracture permeability K f defined by Eq. (1). (Occasionally one sees references to an effective (conventional) fracture permeability which is a spatial average over a matrix block containing a fracture—see “Appendix”)
The rheology of VES fluids has also been studied in a number of flow configurations. Cheung et al. (2012) studied CTAB/NaSal solution through a microfluidic device containing an array of microposts (100 μm diameter, 10 μm apart). Yamamoto et al. (2008) described a 30/60 mM CTAB/NaSal solution flowing through a capillary with a diameter of 4.3 mm. This study focussed on the shear rate jump—the region where the shears stress is independent of the shear rate. The only pressure-driven flow study of VES solutions was through an array of cylinders by Moss and Rothstein (Moss and Rothstein 2010). Selective retardation has been demonstrated in permeable flow in a porous medium but not to our knowledge in aperture/capillary flow.
We used capillaries with inner diameters 0.25 and 0.60 mm, respectively. This size was chosen to reflect the applications as outlined in the introduction, and represents an intermediate value between the fracture short circuit oil recovery regime (ca. 100 μm) on one hand (van Heel et al., 2008) as in “Fracture/matrix flow” above, and the geothermal and hydraulic fracturing (Turcott and Schubert 1982) (ca. 1 mm) on the other. The capillaries are made of stainless steel and glued in flexible polyurethane tubing to prevent bending and for easy installation in the experiment. The CTAB and NaSal were dissolved in deionised water. We denote the concentrations as [CTAB]/[NaSal] where [CTAB] and [NaSal] are the concentrations CTAB and NaSal in milli-moles/l. A representative brine was 3 wt % NaCl (roughly seawater).
After placing the capillary in the setup, water is injected. Having flushed the system, the bypass of the core flooding system is opened and the pressure transducer piping is de-aired by opening the valves on top of the pressure transducer. After this step, all the air in the system is removed and the bypass valve is closed. The setup is now ready for measurement.
Results and discussion
In contrast to the above described rheometer measurements, a pressure driven flow in a capillary has no unique shear associated with a particular pressure drop and flow rate. The shear rate (for Newtonian fluids) at any point within the capillary is proportional to the radial distance from the centre. It varies from 0 at the centre line to a maximum value at the wall. In a 0.25 mm capillary, the smallest mean velocity reproducibly achievable was 44 mm/s. This means that the range of shear rates in the flow extends from 0 s−1 at the centre to 128 s−1 at the wall for water. In Figs. 3 and 4 the region of shear thickening and thinning encompasses 20–200 s−1, so we may expect a radially varying viscosity across the capillary. Similar arguments apply to the 0.6 mm capillary where the smallest achievable velocity was 17 mm/s. The shear thus varies between 0 and 227 s−1 and thus also encompasses part of the shear thickening and thinning region of the curves in Figs. 3 and 4. The net flow is determined by the range of shear rates convoluted with the rheometer viscous response shown in Figs. 3 and 4.
An apparent difficulty with this analysis is that we have used water estimates and then applied Couette responses of VES solutions. VES fluids are non-Newtonian and because of the complex behaviour it is not straightforward to calculate the wall shear rate in a capillary. However, a previous study (Yamamoto et al. 2008) suggests a plug flow profile for VES fluids which means a rapid shear rate decay near the wall. Therefore the maximal shear rates at the wall for VES solutions are expected to be higher than for water. Thus, we expect that the shear rate range at least includes that from 0 to 128 s−1. These shear rates overlap the shear rates (measured with the Couette cell) associated with the non-monotonic range of Figs. 3 and 4, although we will later show that this is not absolutely necessary for selective retardation in capillaries.
As explained above, the Couette cell applies a single shear rate whereas in a capillary there is a range of shear rates. The non-Newtonian VES solutions thus give different shear distributions in capillaries of different dimensions which result in different apparent viscosities. This is what causes the selective retardation in one of the capillaries. For our application the object is to have selective retardation in the larger aperture capillaries or fractures. This has been previously demonstrated (Golombok and van der Wijst 2012) in materials of contrasting matrix permeability: for a high permeability of 2200 mD and a low permeability of 45 mD, the water velocity ratio is 49 times whereas with low equimolar concentrations of VES (1.5 mM) it is reduced to 10.
Comparison with the rheometer response in Fig. 3 for this 5/5 mM VES solution in brine answers two of the questions raised earlier. First of all, despite the lack of a “hump” (i.e., region of shear thickening followed by shear thinning) in the rheometer plot, we still see a selective retardation at lower (and realistic for oil reservoirs) pressure drops as shown by the higher viscosity in the larger (0.6 mm) capillary. Second, we may regard the plot in Fig. 7 as a kind of flow analogue to the Couette plot of Fig. 3. This is a function of the well-known phenomenon that viscosities of non-Newtonian solutions have different values dependent on how they are measured. However, at least for Newtonian fluids, the pressure drop is directly proportional to the shear rate in capillaries and slits. Of course there is a distribution of shear rates moving radially across the capillary and the apparent viscosity reported in Fig. 7 actually represents an average taken across the corresponding plot shown in Fig. 3. We do not actually have any knowledge (or indeed need to know) about the shear rate distribution in the solution in the capillary. The capillary plot in Fig. 7 does not show any non-monotonic “hump” and this correlates with our previous conclusion that selective retardation can be observed even without any shear thickening and then thinning region in the Couette plot.
These effects are also considerably less than the viscosity contrast obtained in permeable flow studies (Golombok and van der Wijst 2012). In that case even for much lower VES equimolar concentrations (1.5 mM) the viscosity contrast was 5 which is two times higher than observed in capillaries in the current studies at considerably higher concentrations (7.5/5 mM). This is due to the nature of the flow. In the capillary we have fully developed flow. However, in permeable flow in a porous medium we have developing flow—or rather, continuously redeveloping flow. The term “developing flow” is normally associated with entrance effects. By contrast, continuously redeveloping flow is what happens inside the porous medium due to the continuous changes in pore geometry and the associated aperture available for fluid flow. This brings in other fluid resistance factors such as extensional viscosity and is the subject of current study.
Using Eq. (6) above, we have been comparing the selective velocity retardation in larger apertures. In the energy recovery systems associated with geothermal and oil, there is a fixed pressure drop between injector and producer so the comparisons need to be made between different sized apertures operating at the same pressure drop. In fact the pressure drop (in the order of 0.1 bar/m for oil recovery and about ten times higher for geothermal systems), is not spread uniformly between injector and producer. Most pressure is lost in the well bore regions leaving only around a quarter of the remaining pressure for driving fluid flow in fractures far from the well bore. This is different for hydraulic fracturing where the flow is also pressure driven but where the constant resistance is provided by the geomechanical strength of rock under confinement by the lithostatic pressure. Figure 5, 6 and 7 have pressure drops relevant to the oil displacement case and show the desired higher capillary flow contrast at lower pressure drops.
Low concentrations of viscoelastic surfactant and co-solute in water can selectively retard flow in larger openings of parallel aperture systems. Applications are short circuits in geothermal and oil recovery systems, as well as during hydraulic fracturing.
Adding salt removes the non-monotonic effect in a rheometric measurement, however the selective retardation effect is maintained. Such a non-monotonic “hump” is therefore not required for selective retardation in aperture flow (capillaries or fractures).
The selective retardation is dependent on the pressure drop and is favoured at the lower values associated with oil recovery. At higher pressures, selective acceleration with respect to water is observed.
Viscosity contrasts of up to ten were observed. These were observed up to velocities around 0.1 m/s. Different formulations may yield even larger results.
The viscosity contrast is not as high as in permeable flow through porous material. The reason is that in this study the flow is steady state whereas in permeable flow, the flow can be classified as continually redeveloping because of pore geometry variations. Real fractures have continually varying geometries (wall roughness, tortuosity etc.) and are expected to show higher viscosity contrast. This is the subject of further study.
The authors thank Dr. Gerald Glasbergen and Professor Cor van Kruijsdijk of Shell Global Solutions b. v. for illuminating discussions and pointers.
- Golombok M, van der Wijst R (2012) Permeability thickening fluids for improved secondary oil recovery. J Petroleum Sci Eng 110(2013):22–26Google Scholar
- Turcott D, Schubert G (1982) Geodynamics: applications of continuum physics to geological problem. Cornell University Press, IthacaGoogle Scholar
- van Golf-Racht TD (1982) Fundamentals of fractured reservoir engineering. Elsevier, AmsterdamGoogle Scholar
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