It is well established within the Industry that water injection mostly takes place ... Water injection will generally result in rapid injectivity decline unless it takes ...
SPE 115204 Dynamic Induced Fractures in Waterfloods and EOR P.J. van den Hoek, B. Hustedt, M. Sobera, H. Mahani, R.A. Masfry, J. Snippe and D. Zwarts, SPE, Shell International Exploration and Production B.V. Copyright 2008, Society of Petroleum Engineers This paper was prepared for presentation at the 2008 SPE Russian Oil & Gas Technical Conference and Exhibition held in Moscow, Russia, 28–30 October 2008. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract It is well established within the Industry that water injection mostly takes place under induced fracturing conditions. Particularly in low-mobility reservoirs or when injecting contaminated water (e.g. PWRI), large fractures may be induced during the field life. This paper presents a new modeling strategy that combines fluid-flow and fracture-growth (fully coupled) within the framework of an existing ‘standard’ reservoir simulator. We demonstrate the coupled simulator by applications to a model five-spot pattern flood model, and to a number of actual field cases (waterfloods, produced water disposal) worldwide. In these field cases, validity checks were carried out comparing our results with available surveillance data. These applications address various aspects that often play an important role in waterfloods, such as shortcut of injector and producer, vertical fracture containment, and reservoir sweep. We also demonstrate that induced fracture dimensions can be very sensitive to typical reservoir engineering parameters, such as fluid mobility, mobility ratio, 3D saturation distribution (in particular, shockfront position), positions of wells (producers, injectors), and geological details (e.g. flow baffles, faults). The results presented in this paper are expected to also apply to (part of) EOR operations (e.g. polymer flooding). 1. Introduction Water injection will generally result in rapid injectivity decline unless it takes place under induced fracturing conditions (e.g. 1,2). Important risks associated with waterflooding under induced fracturing conditions are related to potential unfavorable areal and vertical sweep. These risks can be managed if one has a proper understanding of dynamic induced fracture behaviour as a function of parameters such as injection rate, voidage replacement, reservoir fluid mobility and reservoir / injection fluid mobility ratio 3. In order to enable building and using such an understanding as part of field development planning and of reservoir management, we developed an ‘add-on’ fracture simulator to our existing in-house reservoir simulator 4. In the past, several attempts were made to address the coupled problem of reservoir simulation and induced fracture growth. Common approaches can be grouped into fully implicit simulators (Tran et al.5) where both fluid flow equations and geomechanical equations are solved at the same time on the same numerical grid, and coupled simulators (Clifford et al.6) where a standard, finite-volume reservoir simulator is coupled to a boundary-element based fracture propagation simulator. Both approaches are not standard and currently not used in the industry mainly because reservoir models need to be purpose-built, and numerical stability is questionable. Our approach, as briefly described in 4, uses a ‘standard’ reservoir simulator, thereby enabling reservoir engineers to model induced fracturing around injectors using their ‘standard’ reservoir models (sector, full-field). Moreover, our specific methodology of coupling induced fractures to the reservoir via special connections 4 helped to eliminate most of the numerical instabilities that are generally encountered in the coupled (reservoir flow)-(fracture growth) problem. The current paper presents an important application of coupled reservoir flow and induced fracture growth. The focus is on demonstrating how dynamic fracture growth around injectors is largely driven by reservoir engineering parameters. It is shown that the degree of induced fracture growth / shrinkage in waterfloods depends strongly on oil-water mobility ratio and can vary strongly with time because of changing reservoir saturation distribution (e.g. shockfront position). For example, induced fracture growth in an injector can be strongly accelerated at the moment of water breakthrough in nearby producers. Once water has broken through, the induced fracture shrinks again. These results imply that an optimized waterflood strategy will generally require variable injection rates over the field life in order to prevent jeopardizing sweep by excessive induced fracture growth.
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The paper is organized as follows. Section 2 presents a brief recap of the methodology of 4. and an overview of the pattern flood model system as used in the computations. Sections 3 and 4 presents the results for a representative pattern flood cases with a variety of oil and water mobities and oil-water mobility ratio’s. Subsequently, section 5 presents and discusses a number of real field (waterflood) cases where induced fracturing was seen as one of the important issues. Finally, conclusions are given in section 6. 2. Methodology Coupling of reservoir simulation and dynamic fracture growth / shrinkage. Our simulator couples a standard, finite-volume reservoir simulator7 to a geomechanical modeling tool. The fracture and stress modeling is done using an in-house pseudothreedimensional fracture simulator8 and a stress computation on the reservoir simulator grid. As described in 4, we use a ‘two-way’ coupling strategy, where the fluid flow in the reservoir is influenced by the dynamic fracture propagation and visa versa. Variations of fracture dimensions over time are governed by a fracture propagation criterion that is based on a Barenblatt condition. For each of the fracture tips (length, height upward, and height downward), we evaluate the stress intensity factor (KI) against the rock toughness (KIc). The stress intensity factor for a given fracture tip, incorporates poro-elastic and thermo-elastic stress effects (backstress) as well as the fluid pressure in the fracture. Fluid flow from the fracture into the formation is further influenced by an external filtercake that builds up over time due to the particle content in the injection water. One of the main contributions to describe the effect of the fluid flow on the fracture propagation is the description of the reservoir stress over time. We calculate the stress field from the discrete pressure and temperature field on the grid that is used for the reservoir simulations. Fracture Representation. We introduce a dynamically growing planar fracture in the reservoir simulation grid by an explicit definition of a fracture grid block. For simplicity, we convert an unused block in the reservoir grid to the fracture grid block, such that the total number of grid blocks remains unchanged though a dynamic fracture is added to a given reservoir model. The approach using a special fracture grid block enables one to model induced fractures which are arbitrarily oriented with respect to the (local) reservoir grid. This is a clear advantage over methods that make use of modifying grid block transmissibilities. The planar fractures can be oriented arbitrarily which includes tilted or horizontal fractures. The fracture grid block is connected to the main reservoir grid by special connections. The area intersected by the fracture grid block and the reservoir grid blocks controls the amount of liquid that flows from the fracture into the surrounding matrix. The size of the fracture block is modified over time which is governed by the growing or shrinking of the fracture. Special attention is taken for the pressure and flow calculations for the reservoir gridblocks that contains the fracture tip. If a fracture tip is closer to the neighboring gridblock than the centre of the gridblock, the fracture represents a high conductive flow-path to the neighboring grid block. As it was shown by Dikken and Niko9, this effect may be captured by allowing a smoother transition of the pressure and flow profile when the fracture grows from one gridblock into the next. Fracture Propagation Criterion. At every time step during a coupled simulation we match the actual fracture size (fracture halflength, height upward and downward) to the reservoir pressure- and stress-field, such that a balance of the pressure inside the fracture and the in-situ minimum stresses around the fracture is achieved within a pre-defined error margin. In order to determine whether a fracture grows, shrinks (partially closes) or remains stationary during a given time step, we incorporate a fracture propagation criterion based on a stress intensity factor (KI) evaluation of all the fracture tips. We evaluate KI for each fracture tip with respect to the rock toughness (KIc). This leads to the following fracture propagation criterion: 1. KI > KIc: Fracture tip extension until KI = KIc 2. KI < 0: Fracture tip shrinkage until KI = 0 3. 0 ≤ KI ≤ KIc: No fracture tip extension / shrinkage 3. Pattern flood study The pattern flood reservoir model study focuses on the impact of reservoir engineering parameters on dynamic behaviour of induced fractures. This behaviour is demonstrated for a simple five-spot pattern flood without aquifer influx. The reason for choosing a pattern flood sector model is that induced fractures will be particularly important in low-mobility reservoirs, where a pattern-type development will be often the development concept of choice. In this paper we present both isothermal and non-isothermal calculations. Reservoir Model and Dimensions. To model and study induced fractures, an element of a 5-spot pattern (repeated pattern) was selected. Periodic boundary conditions at the model boundaries and special connections were used to enable the simulation pattern that contains fracture growth. Table 1 and Fig. 1 present the model dimensions and properties used for the 5-Spot pattern. The reservoir properties are uniform across the entire model and were kept the same for all simulations. The imposed periodic boundary conditions ensure translational invariance, i.e. the flows at the left and right boundaries of Fig. 1a are identical, just as the flows at the front and rear boundaries. Note
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that this does not necessarily imply zero flow at the boundaries because the latter will not be true for general fracture azimuth (Fig 1b). Injection and reservoir fluid properties. Table 2 presents the reservoir and injection fluid properties used for this model. Water and oil viscosity were kept independent of pressure. However, injection water and oil viscosity were varied as part of the sensitivity study (see below). A gas phase was included in the model, but the pressures are kept above bubble point so no free gas is present in the system. Relative Permeability and Mobility. Table 3 presents the relative permeability data for the base case scenario. The bulk of this study was geared toward studying the impact of the relative permeability and fluid mobility on induced fracture growth and overall reservoir behaviour. Note: For simplicity, we kept the reservoir characteristics fairly basic, for example it was assumed that there is no capillary pressure effect, in order to prevent an even more complex interference between the fluid flow and the fracture propagation. This means that there is no transition zone and hence the capillary pressure is fixed to 0 (i.e. no capillary pressure curves). Well location and Well Properties. Table 4 presents the location of the two wells within the box model, perforations interval and other key data that were used to perform the study. Rock Mechanics and Fracture properties. During the reservoir simulation, the fracture was fixed at an ‘unfavorable’ orientation, i.e. an orientation at which it grows directly from the injector to the producer (orientation= 45º relative to unit cell boundary). Table 5 presents the rock mechanics and fracture geometry data used for the simulation and sensitivities. 4. Results of pattern flood study Unit oil-water mobility ratio. As pointed out in 3, dynamic behaviour of induced fractures depends very much on oil-water mobility ratio (see also below). Broadly speaking, for constant injection rate, a favorable oil-water mobility ratio will result in growing fractures over time, whereas an unfavorable oil-water mobility ratio will lead to fracture shrinkage (after initial growth) and, eventually, potemtial complete fracture closure 3. However, even for unit mobility ratio, induced fractures can grow or shrink considerably over time, depending on the change of the shock front position in the reservoir. The shockfront for such a case is characterized by a leaky piston with varying effective permeability behind the front (Fig. 2). As a result, the overall “fluid throughput capacity” of the reservoir will change over time depending on the exact position of the shockfront. For constant injection rate under induced fracturing conditions, the fracture will ‘compensate’ for the changing reservoir throughput capacity over time –i.e. a lower reservoir throughput capacity results in a larger induced fracture and vice versa. Figure 3 illustrates the above for the relative permeability curves of Fig. 2 (which corresponds to the base case as defined by Tables 1-5). As indicated in the figure, the process of dynamic growth and shrinkage of the induced fracture can be divided in four different periods. During the first period (‘transient pressure build-up’) the fracture ‘rapidly’ grows to a steady-state size under the influence of transient fluid flow. The second period (‘dry oil production’) is characterised by a ‘stationary’ fracture because the overall reservoir throughput capacity does not change very much during this period. During the third period (‘water breakthrough P1’), the shock front enters the near-wellbore area around producer P1, where pressure gradients are comparatively large. Because the effective permeability behind the shockfront is lower, this will tend to increase the ‘high’ pressure gradient around the producer, resulting in a lower overall reservoir throughput capacity. Consequently, the induced fracture will grow until it reaches a maximum length. After water has broken through on all sides in P1, the effective permeability in the area around P1 will start to gradually rise as a result of rising water saturations, and consequently the fracture will start to shrink again (‘increasing watercut P1’). This shrinkage will be much slower than the initial growth during water breakthrough because the water saturation only slowly increases behind the shockfront. The above discussion illustrates how induced fractures in waterfloods can rapidly grow in response to a shockfront passing an area of high pressure gradient (e.g. near-wellbore area of producer). This only applies to immiscible displacement (‘non-straight-line relative permeabilities’). Therefore, in miscible tertiairy (e.g. polymer) floods, this effect is only expected to play a role at the second shock front between oil and mobilized connate water, but not at the shockfront between injectant and mobilized connate water. However, in the latter case fracture growth / shrinkage associated with non-unit mobility ratio between injectant and mobilized connate water (as discussed below) will definitely play a role. Dependency on injection rate. Fig. 3 also shows the fracture growth dependency on injection rate. It should be noted that, as above, all these calculations were carried out for constant producer BHP=20 bar. Consequently, for all different injection rates the reservoir voidage replacement ratio is equal to one (except for the duration of the first transient flow period). As can been seen in Fig. 3, the phenomenon of rapid fracture growth upon water breakthrough in the produces as discussed above becomes less pronounced for very low and for very high injection rates. Dependency on Corey exponent. The previous discussions around Fig. 3 strongly suggest that for higher Corey exponents, the effect of temporary fracture growth acceleration upon water breakthrough in the producer will be more pronounced. Figure 4 shows that this is indeed the case, and that the effect can be quite pronounced.
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Dependency on producer BHP. Figure 5 shows the dependency of induced fracture length on BHP of the producer P1 (assuming that this BHP can be fixed, for example, by using an artificial lift pump). As can be seen from this figure, a higher producer BHP will result in larger fractures, with potentially significant differences. The explanation for the longer fractures is that for the same injection and gross production rate, a higher producer BHP will result in a higher average reservoir pressure within the pattern. Via the poroelastic backstress this will result in a higher fracture pressure as well, but the latter increase is smaller (typically by a factor 0.6-0.8) than the increase in reservoir pressure. As a result, the difference between fracture pressure and reservoir pressure becomes smaller. Because it is this pressure difference that drives the water from the injector into the reservoir, the induced fracture will respond to a smaller pressure difference by extending itself. This is what is reflected in Fig. 5. From the above result, we can derive the general statement, that in low-mobility reservoir without aquifer, the risk of excessive induced fracturing from injectors can be reduced by minimizing the BHP of adjacent producers. Non-unit oil-water mobility ratio. In ref. 3 it was argued that for constant injection rate, a favorable oil-water mobility ratio will result in growing fractures over time, whereas an unfavorable oil-water mobility ratio will lead to fracture shrinkage (after initial growth) and, eventually, to possible complete fracture closure. Because the methodology of 3 was semi-analytical, a number of simplifying assumptions had to be made 3. However, with our coupled fracture-reservoir simulator 4 we were able to confirm the qualitative results of 3. An illustration of this is presented in Fig. 6 for unfavorable oil-water mobility ratio (endpoint M=3). This figure shows the computed fracture dimensions (length, upward and downward height) , plus oil and water production as a function of time. The results of Fig. 6 can be understood using the same concepts that were presented above in connection with Fig. 3. We can distinguish four different periods: 0-t1, t1-t2, etc (see Fig. 6). As before (Fig. 3), the first two periods can be identified with the transient pressure build-up and dry oil production, respectively. In the third period (t2-t3), water breaks through in P1 and although the lower effective permeability in the intermediate saturation zone will tend to enhance fracture growth (as in Fig. 3), this is more than compensated for by the mobility increase associated with (viscous) oil displacement by water. Therefore, the net result is a fracture shrinkage upon water breakthrough in P1 at time t2. As a result of the fracture shrinkage, watercut initially decreases in P1, until the shockfront catches up and P1 watercut starts rising again. This decreasing watercut causes the fracture shrinkage to stop initially. However, once the watercut rises again, it causes a further fracture shrinkage. Finally, at time t3 water breaks through in producer P2, which again leads to further fracture shrinkage. The example of Fig. 6 clearly illustrates how the presence of induced fractures in injectors can strongly influence the characteristics of oil and water production behavior over time in neighboring producers. The implication is that proper history-matching of production data in a waterflood will require adequate modeling of induced fractures in many field cases. Impact on production and recovery. In ref 3 it was argued that induced fractures generally have two opposite effects on recovery: (1) On the plus side, induced fractures can significantly improve injectivity in by-passing near-wellbore damage etc – in other words they significantly improve voidage replacement capacity, while (2) on the minus side, induced fractures will have a negative impact on areal sweep. From an economic perspective, one needs to find an optimum between (1) and (2). For the simple conceptual 5-spot pattern flood as presented above, the above points are illustrated in Fig. 7 (compare also Fig. 3). It can be seen that there is an optimum injection rate balancing enough voidage replacement on one hand without jeopardizing areal sweep on the other hand. The optimum in this case corresponds to an injection rate of around 4500 m3/d, for which the induced fracture length is about one third of the injector-producer spacing (Fig. 3). Further optimization is possible by allowing for variable injection rates over time. In such a scheme, rates will be reduced at moments that significant induced fracture growth is expected as a result of low ‘reservoir throughput capacity’, and vice versa. In particular, for favorable oil-water mobility ratio, this will result in an overall reduction of injection rate over the field life, whilst for adverse mobility ratio, it will result in an increase in injection rate 3,4. We found that especially when waterflooding ‘medium-heavy’ oil reservoirs (viscosity of the order 100 cp), ‘optimized’ injection rates will increase significantly during the first few years of field life 4,10. Inclusion of thermal effects. Injection of cold water will result in a cold front lagging behind the shockfront, where the magnitude of the lag depends on injection water and reservoir heat capacities4. For a waterflood situation, roughly two types of changes take place behind the cold front: fluid viscosities become higher, and thermo-elastic backstress lowers the fracturing pressure. We carried out thermal calculations for the five-spot of Fig 1. (see Tables 1-5 for base case input data), where the specific thermal data are given in Table 6. Below, we present the results for varying Corey exponents whilst keeping the other relevant parameters fixed: injection rate (2000 m3/d), producer BHP (20 bar) and fracture azimuth (ϕ=45°). Results are presented in Figure 8. When comparing this with the isothermal case (Figs. 3 and 4), it can be seen that a number of features (initial rapid fracture growth upon water breakthrough in P1, followed by fracture length stabilization and subsequent shrinkage) is also exhibited in the thermal case. After a number of years, however, the shockfront breakthrough in P1 is followed by the (higherviscosity) cold front breakthrough, which in turn can result in significant induced fracture growth. This is entirely in line with the concepts presented in3, which in the current paper have been discussed above in the paragraph about nonunit mobility ratio. Figure 8 shows another effect: with increasing fracture length at initial water breakthrough in P1, the ‘severity’ of additional fracture growth owing to the temperature effect becomes worse. This can be explained by the fact that longer fractures at water break-
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through in P1 will result in earlier cold front breakthrough as well, as can be clearly seen in Fig. 8. If he cold front breaks through early enough, the average effective permeability around P1 still is comparatively low, which may result in additional rapid facture growth until breakthrough in the producer, as can be seen for the case of Corey exponent equal to 1.75 in Fig. 8. 5. Examples of field applications Deep water disposal in the Middle East. The field background of this case was described in some detail before 2. Large quantities of very contaminated (unfiltered) produced water are being disposed into a subsurface aquifer under induced fracturing conditions. Typically, one well injects about 20,000 m3/d of production water with an average of 60 ppm Total Suspended Solids (TSS) and 200 ppm of Oil-In-Water (OIW) 2. An ongoing concern in these operations has been induced fracture breakthrough through overlying caprock shale into potable aquifer bearing carbonate formations. Previous fracture simulations using a simple reservoir model estimated that under these circumstances, water injection should take place at ca. 300 m below the caprock shale or deeper. This recommendation was duly followed up and all subsequent water disposal wells were completed with perforation intervals between 1200 and 1300m TVD, see Figure 9. A number of different surveillance techniques was tried to validate / calibrate the fracture simulations (especially with respect to fracture height), but results so far were fairly inconclusive 2. Early 2007, the technique of downhole tiltmeters was successfully applied in a trial to measure induced fracture height. This technique has been well-proven for propped fracture applications in tight rocks but applications in medium- to high-permeability waterflood applications are limited. Because none of the disposal wells had nearby observation wells, it was decided to use the technique of “treatment well tilt” in which the tiltmeters are deployed in the injection well itself. This allows for “optimal” measurement of fracture height (maximum tilt signal), although fracture length cannot be measured in this way. The tiltmeter measurements were combined with fall-off tests after each injection cycle, which were analyzed using a novel fall-off interpretation technique specially developed for fractured injectors 11. Figure 10 shows the injection / shut-in sequence during the tiltmeter trial. From the horizontal scale of this graph it can be seen that the well had already been injecting ca 4 years prior to the trial. Figure 11 shows an example of a raw tiltmeter signal alongside an “ideal” signal for the case of one planar vertical fracture. As can be seen, ideally the locations of fracture top and bottom are identified from the maxima in the tilt signal, but in our case four (instead of two) of such maxima were observed, leading to some ambiguity in the interpretation of fracture height. In the interpreted results we took this into account by indicating a range for fracture height rather than one value. Finally, Figure 12 shows an example of one of the injection fall-off test results. These results show a pronounced storage-dominated flow period, which is indicative of a large induced fracture 11. Figure 13 shows a summary of the interpreted fracture heights and lengths from tiltmeter and fall-off tests, together with the simulated fracture dimensions based on the 4 years injection history and the injection cycles as depicted in Fig. 10 (see Table 7 for summary of input data). During the later injection cycles, no reliable tiltmeter signals could be obtained owing to their detachment from the borehole wall (casing). As can be seen from Fig. 13, the computed and measured results are in fairly good agreement, especially when considering the large uncertainties both in the measurements and computations. Fig. 13 also shows that the maximum total fracture height during the injection trial is far less than the 300 m that was based on earlier simulations (see above). However, this turned out to be mainly the result of two essential differences between the trial on one hand and contiuous injection on the other hand: (1) During continuous injection, rates of ca 20,000 m3/d are applied, which was never achievd during the trial, and (2) the limited duration of the trial resulted in induced fractures which were still growing under the influence of transient pressure build-up in the reservoir. Without these two effects, induced fractures are likely to grow towards ca 300 m height, as is illustrated in Fig. 14 which shows the computed result of continuous injection fot 4 years at 20,000 m3/d. Summarizing the above discussion, the simulated sizes of the induced fracture were confirmed by surveillance data (tiltmeter, fall-off), endorsing the policy of perforating water disposal wells 300m below the caprock. North Sea waterflood. The second application example of our coupled fracture-reservoir simulator is a waterflood in a complex North Sea sandstone reservoir. The purpose of the simulation is to obtain a pressure history match such that fracture dimensions, vertical fracture containment, and potentially swept reservoir areas (where does the water go) can be estimated or identified. The field geometry is characterized by a salt diapir that is penetrating the reservoir formation. Seismic control is poor and only major geological features such as large faults are well localized. The reservoir model properties away from areas with well control (porosity, permeability, sand body connectivity) have been populated stochastically. The current well stock is characterized by four injectorproducer pairs that surround the salt diapir. Each injector-producer pair covers approximately one quarter of the area around the diapir. The coupled fracture-reservoir simulations were carried out to history-match the pressure behavior over time for an injector-producer pair, where fast water breakthrough in the producer was observed (see Figure 15). The reservoir model was set-up covering a sector of the full-field, history-matched simulation model. The model parameters are given in Table 7. The maximum horizontal stress field orientation was estimated to be radial around the salt diapir and the minimum horizontal stress field tangential, which, from a water injection point of view implies a non-favorable stress field orientation (dynamic fracture growing
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towards the producer). The fracture initiation point was chosen close to the top of the perforations at the heel of the highly deviated injector well since it is the weakest point of the well and has the lowest minimum horizontal stress. Note that we have simulated other fracture initiation points along the injector well as well, but the overall pressure behavior and fracture dimensions did not fit the observed data and, therefore, are not discussed here. Rock properties such as Young’s modulus and Poisson’s ratio have been estimated using data from analogue fields. The injection rate was varied in the model according to the averaged historical injection rate on a monthly basis (see Figure 16). As can be observed from the history match in Figure 16, during the 28 months injection period the dynamic fracture propagates to a total length of ca. 260 m and fracture height of 35 m. While the THP match is off during the initial injection periods (Dec 2005 to Mar 2006), at later times a good THP match is obtained. The simulated fracture dimensions are in the order of the injector-producer well spacing (see July 2006 and Feb 2007) and, therefore, a dynamically growing fracture may explain the fast water breakthrough in the producer well. The history-matched model is currently used to further investigate areas that have been swept by injection water and also what potential remediation activities could be executed to recover the remaining oil. Moreover, the model is used to determine optimum injection rates as a function of time such that fracture dimensions do not exceed beyond the top seal or extend (shortcut) to the producer well. Finally, the modeling approach is being repeated on the other injector-producer pairs, to address these questions in the remaining sectors of the field. Gulf of Mexico waterflood. The third application example of our coupled fracture-reservoir simulator is a waterflood in a fairly complex Gulf of Mexico sandstone reservoir. A plan view of the relevant reservoir section is presented in Fig. 17. The injector which is subject of the current study is indicated in yellow. As can be seen from the figure, the reservoir area in which this injector is located is bounded on two sides by sealing faults. According to the field development design, this injector is supposed to sweep the oil from this particular “corner” into adjacent producers. The objective of the study is to determine an optimum injection rate profile over time such that “local” voidage is optimally replaced without excessive induced fracture growth (in particular, out-of-zone growth). Because cold seawater is injected, one expects thermal stresses to reduce the in-situ stress of the reservoir to a significant degree such that induced fractures will remain vertically contained. On the other hand, if injection rate becomes too high, limited reservoir connectivity (because of the faulting) may lead to excessive poro-elastic stress build-up around the injector, thereby increasing the risk of fracture breakthrough into adjacent non-reservoir zones. Figure 18 shows the results for high initial injection rate. As can be seen, the injection pressure is dominated by poro-elastic stress (rather than thermo-elastic stress) resulting in fracture breakthrough into the overlying layer. From this result, it can be concluded that the injection rate needs to be lowered, at least initially, to allow for proper cooling of the reservoir and prevent excessive poroelastic effects. The determination of the optimum injection rate as a function of time is subject of an ongoing study. 6. Conclusions This paper presents applications of a fracture model that is fully coupled to an existing reservoir simulator. The applications encompass both on a conceptual five-spot waterfood, and a number of real field examples. The conceptual five-spot waterflood study was carried out to obtain a better fundamental behaviour of induced fracture behaviour in waterfloods. This study yielded the following conclusions: • The degree of induced fracture growth / shrinkage in waterfloods depends strongly on oil-water mobility ratio and can vary strongly with time • In case of a favorable oil-water mobility ratio, the induced fracture grows over time when more of the oil-in-place is replaced by injection water • Conversely, in case of an unfavorable oil-water mobility ratio, the induced fracture shrinks over time (after initial growth) when more of the oil-in-place is replaced by injection water • Fracture growth can be strongly accelerated at the moment of water breakthrough in nearby producers. Once water has broken through, the induced fracture shrinks again. • The above implies that an optimized waterflood strategy requires variable injection rates over the field life in order to prevent jeopardizing sweep by excessive induced fracture growth. Continuous monitoring of induced fracture length and height during field operation will be required to enable proper and timely adjustment of injection rates to their ‘optimimum’ values. • In low-mobility reservoir without aquifer, the risk of excessive induced fracturing from injectors can be reduced by minimizing the BHP of adjacent producers. The field examples presented give an overview of the kind of issues that can be addressed by a fully coupled fracture-reservoir simulator. They illustrate, amongst others, the response of induced fractures to limited reservoir connectivity resulting from heterogeneities, such as faulting. The results presented appear to yield results (fracture dimension) which are in reasonably good agreement with sur-
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veillance results. Further reservoir study work is ongoing to improve the understanding of induced fracture behaviour for waterflood and EOR operations in real reservoirs, and to further “calibrate” the model to surveillance data. Acknowledgment The authors are grateful to Petroleum Development Oman, Shell Exploration & Production Europe, Shell Exploration and Production America and Shell International Exploration and Production B.V. for permission to publish this work. References 1. 2.
3. 4. 5. 6. 7. 8. 9. 10. 11.
Sharma, M.M., Pang, S., Wennberg, K.E., and Morgenthaler, L. Injectivity decline in water injection wells: An offshore Gulf of Mexico case study. SPE 38180 (1997). Van den Hoek, P.J., Sommerauer, G., Nnabuihe, L., and Munro, D. Large-Scale Produced Water Re-Injection Under Fracturing Conditions in Oman, ADIPEC 0963 (SPE 87267), presented at the 9th Abu Dhabi International Petroleum Exhibition and Conference held in Abu Dhabi, U.A.E., 15-18 October 2000. Van den Hoek, P.J. Impact of Induced Fractures on Sweep and Reservoir Management in Pattern Floods. SPE 90968 (2004). Hustedt, B., Zwarts, D., Bjoerndal, H.-P., Masfry, R., and van den Hoek, P.J. Induced Fracturing in Reservoir Simulations: Application of a New Coupled Simulator to Waterflooding Field Examples. SPE 102467 (2006). Tran, D., Settari, A. and Nghiem, L.: “New Iterative Coupling Between a Reservoir Simulator and a Geomechnics Module”, SPE 78192 (2002). Clifford, P.-J., Berry, P.J., and Gu, H.: “Modeling the Vertical Confinement of Injection-Well Thermal Fractures”, SPEPE (Nov. 1991), 377. Por, G.J., Boerrigter, P., Maas, J.G., de Vries, A.. A Fractured Reservoir Simulator Capable of Modeling Block-Block Interaction, SPE 19807 (1989). van den Hoek, P.J. New 3D Model for Optimised Design of Hydraulic Fractures and Simulation of Drill-Cutting Reinjection, SPE 26679 (1993). Dikken, B.J. and Niko, H.: “Waterflood-Induced Fractures: A Simulation Study of Their Propagation and Effects on Waterflood Sweep Efficiency”, SPE 16551 presented at the 1987 Offshore Europe Conference, Aberdeen, Sept. 8-11. Sæby, J., Bjoerndal, H.P., van den Hoek, P.-J.: “Managed Induced Fracturing Improves Waterflood Performance in South Oman”, IPTC 10843 presented at the 2005 IPTC Conference and Exhibition, Doha, Nov. 21–23. Van den Hoek, P.J. Dimensions and Degree of Containment of Waterflood-Induced Fractures from Pressure Transient Analysis, SPERE, October 2005, 377-387.
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Table 1. 5-Spot pattern dimensions and reservoir properties Description Symbols Quantities Units Total Grid Numbers
NX, NY, NZ
Grid Size Δx, Δy, Δz Pattern Total Dimensions
40, 40, 10
m
20, 20, 5 800 x 800 x 50
m m
Porosity Absolute Permeability
φ k
0.3 100
mD
Reservoir Compressibility
c
15.0 x 10-10
Pa-1
- 560
m
- 658
m
Original Model Top Depth/Height Oil Water Contactbelow reservoir (No transition zone)
OWC
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Table 2. 5-spot reservoir and injection fluid properties Description Quantities Units Water density
kg/m3
1002
Oil density
920
kg/m3
Gas density
0.797
kg/m3
Water viscosity
0.00059
Pa s
Oil viscosity
0.00059
Pa s
·10-10
Pa-1
Oil compressibility
3.5 ·10-10
Pa-1
Initial Reservoir Pressure
7500
kPa
Reference Depth
585
m
Water compressibility
4.4
Table 3. 5-spot base case Relative Permeability Data Description Quantities Connate Water Saturation (Swc)
0.2
Residual Oil Saturation (Sor)
0.1
End Point Relative Permeability to Water
1.0
End Point Relative Permeability to Oil
1.0
Corey Exponent of Water (nw)
1.3
Corey Exponent of Oil (no)
1.3
Capillary Pressure –Pc (no transition zone)
0
Table 4. 5-spot wells dimensions and properties Description Symboles Quantities Units Injection Well Locations
x, y
390, 390
m
Producer Well Location
x, y
790, 790
m
Injector –Producer Spacing
I-P
565.685
m
Perforation intervals for Injector and Producer (i.e. full reservoir height)
560 - 610
m
Bottom Hole Pressure for Producer (fixed)
20
bar
Maximum Injection Pressure
1000
bar
Injection and production wells depths- center height of reservoir
585
m
Table 5. 5-spot rock mechanics and fracture geometry data Description Quantities Stress Gradient Youngs modulus
15.8 · 103 1.8 ·
109
Poisson Ratio
0.2
Fracture Toughness
1.0· 106
Units Pa/m Pa Pa/√m
Minimum Fracture Height
0.1(small rate), 1.0 (high rates)
m
Maximum Fracture Height
25 (=50 for up & bottom)
m
Minimum Fracture Length
0.1 (small rate), 5.0 (high rates)
m
Maximum Fracture Length
560
m
45
deg
Fracture Orientation, relative to unit cell boundary
SPE 115204
9
Table 6. 5-spot thermal data Description Quantities
Units
Reservoir temperature
60
Degree C
Injection water temperature
40
Degree C
Rock heat capacity
2560
kJ/m3/K
Injection water heat capacity
4185
kJ/m3/K
Thermo-elastic constant
1
Bar / K
Cold-warm water viscosity ratio
1.5
Cold-warm oil viscosity ratio
2.0
Table 7. Field cases: summary of reservoir parameters. Middle East Deep water disposal
North Sea waterflood
Gulf of Mexico waterflood
Sandstone 1300 m ca. 300 mD 0.5 cP 0.40 cP Vertical well 60 1495 days 41 x 41 x 5 0-20000 m3/d 5 GPa 0.25
Sandstone 9000 ft ca. 15 mD 1.26 cP 0.30 cP Horizontal inj.-prod. pair 10 28 months 29 x 29 x 33 0 – 1600 m3/day 8 GPa 0.2
Sandstone 14000 ft ca. 120 mD 1.0 cP 0.36 cP Deviated 5 84 months 80 x 80 x 11 0 – 15000 bbls/day 500,000 psi 0.3
Formation: Depth: Permeability: Water viscocity at inj. Temp.: Formation fluid viscosity: Injection: TSS: Simulation time: Nr. of grid blocks: Injection rate: Young’s modulus Poisson’s Ratio
Producer
50 m
Injector
80 0m
0 80
m
Figure. 1a. Five-spot element with one producer and one injector
10
SPE 115204
P2
P1
I
Fracture
Fig. 1b. Five-spot geometry with base-case fracture orientation.
Water and Oil Mobility ratios 2 1.8 1.6
Mobility Ratio
1.4 1.2
Mw Mo
1
Total Mobility
0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1
sw
Figure 2. Water and Oil mobility-total mobility (no=nw = 1.3) scenario
Water breakthrough P1 Dry oil production
Increasing watercut P1
Producer
600
1
Water injection rate:
0.9
5500 m3/d
0.8
Transient pressure build-up
Fracture length (m)
500
0.7
400
0.6
5000 m3/d
300
0.5
P1 watercut for 4000 m3/d injection rate
0.4
200
0.3
4500 m3/d 100
0.2
4000 m3/d 3000 m3/d
0.1
0
0 0
5
10
15
20
25
30
Time (years)
Figure 3. Induced fracture length as a function of time (unit mobility ratio, no=nw=1.3)
SPE 115204
11
Producer 600
Corey exponent:
Fracture length (m)
500
1
1.3
0.9
1.4
0.8
1.5
400
1.6
0.7
1.7
0.6
1.8
300
1.9
0.5
2.0
0.4
BSW
200
0.3 0.2
100
0.1 0
0 0
5
10
15
20
25
30
Time (years)
Figure 4. Impact of Corey exponent (no=nw) on induced fracture length for 4000 m3/d injection rate.
Fracture length (m)
600 500
Producer BHP
400
15 bar 20 bar 25 bar
300
35 bar 40 bar
200
45 bar 100 0 0
5
10
15
20
25
30
Time (years) Figure 5. Impact of producer BHP on induced fracture length for 4000 m3/d injection rate. 500
2500
Length O il ra t e
400
2000
W a t e r ra t e
(m)
1500
200
1000
100
(m3/d)
WBT P2
300
500
WBT P1 0
0 0
5
t1 t2
10
t3
15
20
T im e (ye a r s )
Figure 6. Fracture dimensions and oil / water production for unfavorable oil-water mobility ratio (M=3) and 2000 m3/d injection rate.
12
SPE 115204
Cum. oil production (m3)
8000000 7000000 6000000 5000000
2000 m3/d
4000000
3000 m3/d 4000 m3/d
3000000
4500 m3/d 2000000
5000 m3/d
1000000
5500 m3/d
0 0
5
10
15
20
25
30
Time (years)
Figure 7. Oil recovery for different injection rates (case of Fig. 3)
Producer 600
Fracture breakthrough P1
Fracture length (m)
500
400
Corey exponent:
300
1.3 1.4 1.5
200
1.6 1.7
100
1.72
Cold front reaches P1
1.75
0 0
5
10
15
20
25
30
35
40
Time (years)
Figure 8. Thermal fracturing: Impact of Corey exponent (no=nw) on induced fracture length for 2000 m3/d injection rate.
Fig. 9. Middle East disposal well: Simplified completion diagram
SPE 115204
13
25000
Fall-off
Injection rate (m3/d)
20000
Fall-off
Fall-off
Fall-off
15000
10000
5000
0 1492.4
1492.9
1493.4
1493.9
1494.4
1494.9
Time (days)
Fig. 10. Middle East disposal well: Injection cycles of tiltmeter test
9850
Measured Tilts
α = 0.2° α = 1.0° 9900
α = 10.0°
α
Depth ( ft)
9950
“Ideal” Tilts
10000
10050
10100
10150 0
1000
2000
3000
4000
Downhole tilt (Microradians)
Fig. 11. Middle East disposal well: Example of tiltmeter data
Fracture closure
Fracture storage
Fig. 12. Middle East disposal well: Example of fall-off test data
14
SPE 115204
180 Tiltmeter: H= 82-137 m Fall-off: L = 48 m H = 126 m
160 140
(m)
120 100
Tiltmeter: H= 58-113 m Fall-off: L=39 m H=92 m
Tiltmeter: No data Fall-off: L = 42 m H = 100 m
Tiltmeter: No data Fall-off: L = 38 m H = 87 m
Length Hup Hdown
80 60 40 20 0 1492.4
1492.9
1493.4
1493.9
1494.4
1494.9
Time (days)
Fig. 13. Middle East disposal well: Summary of tiltmeter test results. Colored curves represent computed results: Length (L), Hup (=upward fracture height), and Hdown (downwards fracture height). H=total fracture height = Hup+Hdown. Length
350
Hup
300
Hdown
(m)
250
20000 m3/d
200 150 100 50 0 0
200
400
600
800
1000
1200
1400
1600
Time (days)
Fig. 14. Middle East disposal well: Computed fracture dimensions for high-rate disposal injection
SPE 115204
15
Producer Injector Figure 15: Injector-producer pair for North Sea case
Figure 16. North Sea case: History match of THP and corresponding fracture sizes
16
SPE 115204
Producer
Injector
Producer Producer
Producer
Producer
Producer
Producer Producer
Injector Producer
Figure 17. Gulf of Mexico case: Plan view. The injector of the current study is indicated in yellow.
70
Poroelastic stress disappears because frac grows out of zone
50
9500 9000 8500 8000
40
Frac grows out of zone 30 20
7500
Fracture half-length
7000
Fracture upwards height
6500
BHP, stress (psi)
Length / height (metres)
60
10000
Fracture downwards height Injection BH pressure
10
6000 5500
Initial stress 0
5000 0
500
1000
1500
2000
2500
Time, day
Figure 18. Gulf of Mexico case: Computed fracture dimensions for high injection rate
