Time-lapse gravity: A numerical demonstration ... - Semantic Scholar
GEOPHYSICS, VOL. 77, NO. 2 (MARCH-APRIL 2012); P. G33–G43, 8 FIGS., 1 TABLE. 10.1190/GEO2010-0412.1
Time-lapse gravity: A numerical demonstration using robust inversion and joint interpretation of 4D surface and borehole data
Richard A. Krahenbuhl1 and Yaoguo Li1
movement. Complex model construction and robust inversion show that time-lapse gravity surveys may contribute to improved production efficiency and reservoir management inbetween the more traditional, and expensive 4D seismic surveys. Results hint that the true value of time-lapse gravity as an additional tool for production efficiency and reservoir management may be greatly undervalued. Data simulated within current and ongoing sensor technologies, combined with advances in computing power and robust inversion, can extract much more meaningful information about fluid movement in reservoirs that are geometrically complex and relatively thin and deep. To illustrate these points, simulations are performed using a representation of the published Jotun Field in the Norwegian North Sea, a well-studied site demonstrating successful application of the time-lapse seismic method, and reconstructed for 4D gravity understanding.
ABSTRACT There are a number of ongoing developments in the 4D gravity method for time-lapse production and sequestration problems. Complex model construction is an essential component for meaningful feasibility studies and data interpretation in 4D. In the case of oil reservoirs, for example, the 4D gravity method must deal with very small density contrasts at depth, and overly simplistic model representations of a field site may not properly guide monitoring efforts for effective reservoir management decisions. The tracking of injected fluid through inversion can be significantly improved with the joint interpretation of surface and borehole gravity data. This is particularly relevant for time-lapse gravity problems where subtle changes in density contrast at depth may not produce surface data that alone contain the necessary information to recover the boundaries of fluid
County, Texas (Eckhardt, 1940; LaFehr, 1980). Within years of the Nash dome discovery, the advances and application of gravity to resource exploration grew significantly. The method was crucial for discovering hundreds of oil fields around the world in the 1920s and 1930s (Eötvös, 2010). Parallel to early surface gravity applications, experiments in determining densities with depth were likewise being made in vertical mine excavations as early as 1854 by Airy, and soon after by von Sterneck in the 1880s in Europe, Hayford in 1902 in the North Tamarack Mine in Michigan, and by Heinrich Jung (1939) in the Wilhelm Mine at Clausthal, Germany (Hammer, 1950). Soon after, Hammer (1950) carried out gravimeter observations in a vertical shaft to a depth of 2247 feet “with a standard-type gravimeter to simulate the data which would be obtained by a borehole gravimeter to aid in the anticipation and formulation of problems in the development and application of a borehole gravimeter for gravity
INTRODUCTION The first successful measure of fluid movement with time-lapse gravity experiments, although poorly documented, is generally credited to Loránd Eötvös in the early 1900s. By increasing sensitivity to one of his several ground-breaking instruments, the gravity compensator, he reportedly detected 1 cm variations in the water level of the Danube River from a distance of 100 m (Szabó, 2008). Soon after, the gravity method was introduced as a practical tool to the oil and gas industry in 1916 near Gbely, Slovakia. This time, the meter was the Eötvös torsion balance, also developed by Loránd Eötvös in 1888, and used by Eötvös himself to collect 92 stations over the Egbell oil field (Eötvös, 2010). But it wasn’t until the first geophysical discovery of an oil and gas field in the United States in 1924 that gravity surveying became widely used for exploration geophysics. That site was the Nash dome in Brazoria
Manuscript received by the Editor 20 December 2010; revised manuscript received 16 July 2011; published online 17 February 2012. 1 Colorado School of Mines, Center for Gravity, Electrical and Magnetic Studies, Department of Geophysics, Colorado, USA. E-mail: [email protected]; [email protected]. © 2012 Society of Exploration Geophysicists. All rights reserved. G33
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prospecting” (Hammer, 1950). These seminal works laid the foundation for future borehole gravimetry. Since that time, we have seen a dramatic shift in exploration strategy as younger technologies with higher resolution capability have come onto the scene. In particular, the 1940s and 1950s witnessed significant advances in the seismic method such as availability of portable multichannel systems, magnetic tape recording for large data volumes, common-depth-point (CDP) stacking, and synthetic seismograms for 2D and 3D model studies (Allen, 1980). The gravity method had become, to a great extent, eclipsed by the seismic method in petroleum exploration. However, gravity continues to remain an important, cost effective, and necessary complementary method in specific problems. We continue to see its successful application in salt provinces and for regional geologic mapping, mineral exploration and geothermal applications. More recently, and largely resulting from new advances in gravity meter technology, computing power and interpretation software, we are experiencing a sharp increase in the use of 4D gravity surveys, on the surface and in the borehole environment for dynamic systems. For example, it is now common to implement gravity surveys with micro-Gal accuracy (e.g. Scintrex, 2006) for land-based exploration and time-lapse problems. Recent developments are likewise demonstrating repeatability in measurements as low as 3 μGal using modified land-gravimeters on the seafloor for time-lapse applications (Zumberge et al., 2008). In the borehole environment, we are witnessing the development of gravimeters capable of gathering data in highly deviated boreholes (e.g. Nind et al., 2007), and more recently in the horizontal well environment (C. Nind and T. Niebauer, personal communication, 2011). Equally relevant to the engineering advances we are seeing are the developments in time-lapse gravity associated with survey design (Ferguson et al., 2007; Davis et al., 2008), noise estimation (Gettings et al., 2008; Glegola et al., 2009), understanding the influence of reservoir compaction (Battaglia et al., 2008), processing (Davis et al., 2008; MacQueen, 2010), inversion (Silva Dias Fernando et al., 2008; Krahenbuhl and Li, 2009), and resolution analysis (Kirkendall and Li, 2007; Davis et al., 2008). In response to these advancements, we are naturally witnessing many successful applications of the time-lapse gravity method for volcanic monitoring (Battaglia et al., 2008; Vigouroux et al., 2008), groundwater studies (Cogbill et al., 2006), artificial aquifer storage and recovery (Davis et al., 2008), waterflood surveillance (Meyer, 2008; Ferguson et al., 2008; Nind et al., 2007b; Hare et al., 2008), gas production (Eiken et al., 2008), CO2 sequestration (Gasperikova and Hoversten, 2008; Alnes et al., 2011), and numerous feasibility studies (Hare et al., 1999; Vasilevskiy and Dashevsky, 2008; Krahenbuhl et al., 2011). These combined gravity developments are playing an important role in transitioning the method from its traditional role as an exploration tool into the realm of production, a monitoring endeavor perceived by many as limited to seismic alone. This misconception is based largely on past applications and limited knowledge of continuous gravity sensor and software evolution, coupled with a belief that most reservoirs are either too thin, too deep, or both, for practical 4D gravity application. It is within this context that this paper is focused. We examine some of the latest developments in the 4D gravity method, develop an integrated approach to feasibility study, and determine the parameter limits within which 4D gravity monitoring through inversion can be effective in reservoir monitoring. In
particular, there are four relevant components that we seek to highlight. First, we demonstrate that the 4D gravity method can contribute to improved production efficiency and reservoir management, such as in-between the more traditional, and expensive, 4D seismic surveys. We show that a well-designed collection of surface and borehole gravity stations can successfully identify lateral fluidcontact movement during enhanced oil recovery (EOR). Resolution may never achieve the levels of 4D seismic at particular sites, but the bulk distribution of time-varying density due to fluid replacement can be successfully recovered for comparison with projected fluid-contact movement from reservoir simulations. Second, reservoir modeling for EOR and sequestration efforts has moved well beyond the simplistic 2D and 3D geometric representations of field sites. For initial feasibility studies and later field data interpretation, it is now common to use integrated models that can reproduce the geometrically and lithologically complex structures by taking full advantage of all prior information. Thirdly, we examine improved reservoir monitoring capabilities through joint inversion of surface and borehole gravity data. Gravity technology is continuously advancing toward smaller and cheaper sensors capable of monitoring minute changes in gravity due to time-varying density. In addition to micro-Gal accuracy on the surface, recent advances have led to first-generation sensors capable of collecting gravity data in the slim and horizontal well environment. As these technologies have continued to progress, it is viable now to jointly utilize surface and borehole gravity data for effective reservoir management. Over the long term, the approach should prove an effective, yet relatively cheap, means of filling the void of knowledge between the less frequent 4D seismic surveys at many sites. Finally, we illustrate that application of the 4D gravity method for reservoir monitoring may be greatly undervalued. We show that modern 4D gravity data — collected in the boreholes as well as on the surface and within current noise thresholds — can monitor fluid movement in reservoirs that are much thinner and deeper than previously perceived. To demonstrate the above-described components of 4D gravity developments, we simulate density change from brine injection over a realistic reservoir model created to mimic the Norwegian North Sea Jotun Field published by Gouveia et al. (2004). We utilize relevant parameters for the Jotun reservoir, such as geometry, thickness, depth and porosity. Using this model construction as a foundation for this study, we then illustrate that one can successfully monitor fluid movement within geometrically complex and relatively thin and deep reservoirs. We likewise demonstrate that an improved recovery of the fluid movement can be obtained by jointly inverting surface and borehole data, rather than focusing on one data set alone.
MODEL CONSTRUCTION Reservoir geometry For practical exploration and production efforts, gravity modeling for pre- and postdata acquisition stages has evolved, overall, to complex model representations of study sites. While simple 2D and 3D prismatic geometries — such that the structures approximate the lengths, widths, depths, depth extents and dips of a dynamic system — have demonstrated great success when appropriate, more complicated reservoirs require higher-quality and realistic representations to fully understand the applications and limitations of 4D gravity. For example, current algorithms can
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Time-lapse gravity now manage geometrically complex models; they can incorporate reservoir boundaries directly from surfaces derived from 3D seismic surveys, as well as realistically varying 3D porosity and permeability information, when available in advance. Gasperikova and Hoversten (2008) successfully demonstrate this point by implementing a realistic model of the Schrader Bluff reservoir, where variations of rock properties and resulting realistic spatial density variations are incorporated. As an alternative, Krahenbuhl et al. (2011) implement an algorithm that incorporates multiple dipping seismic surfaces directly into the 4D gravity inversion for a feasibility study at the Delhi Field sequestration site in Louisiana. The benefit of these growing algorithms, and therefore improved model constructions, is that we can now work more seamlessly with other geophysical and geological contributors to a project. The goal is to reproduce, as accurately as possible, a time-lapse density model representative of the site and consistent with other geophysical and geologic data, so that early feasibility studies and later interpretations are as meaningful as possible. To demonstrate a current application of the 4D gravity method as a potential interseismic monitoring tool, we begin by constructing a realistically complex reservoir model for maximum analysis when limited information is available. The model we employ is a representation of the Norwegian North Sea Jotun Field inspired from Gouveia et al. (2004). For this demonstration, digital data are not directly available on reservoir geometry, depths, or fluid movement during EOR. Therefore, to construct a meaningful 4D gravity study, we built the model utilizing parameters representative of the field obtainable from published literature. The information from which we build our physical reservoir model is limited entirely to the images extracted from the work of Gouveia et al. (2004), reproduced in Figure 1. In this figure, the top panel provides information on scale and lateral geometry for our model reservoir. The lower panel illustrates a cross section through the acoustic impedance change (positive in red), which the authors derived from their seismic difference inversion. In this case, fluid movement is baffled due to the presence of a shale layer at the base of the reservoir, and the resulting fluid movement is therefore dominated by a flank drive rather than a bottom drive. As a result of imperfect vertical sweep, a significant oil potential remains within the upper volume of this section of the field (between the yellow and green lines). For our demonstration here, we do not attempt to reproduce the complex history of fluid movement at Jotun. Rather, we build upon the concept of partial vertical fluid movement and increased lateral movement at the lower half of the reservoir for time-lapse gravity demonstration. Using the images in Figure 1, extraction of shape and scale provides the basic foundation for a model such that we can easily incorporate physical properties appropriate to the 4D gravity problem. For further detail into the production history and application of 4D seismic method at the Jotun field, the reader is referred to the original publication (Gouveia et al., 2004). We first use the images in Figure 1 to construct a model region representative of the Jotun reservoir geometry and depth. The result is illustrated in Figure 2, and it adequately reproduces the geometric complexities of the field for practical understanding when limited information is available. When seismic surfaces are directly incorporated, model construction is naturally simplified and structural accuracy improved even more (Krahenbuhl, et al., 2011). In Figure 2, the upper image shows a full vertical extent of our simulated reservoir model, and the lower panel provides the foundation
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for an alternative modeling scenario where time-lapse density changes are limited to the lower half of the reservoir model. This second scenario is inspired from the concept of partial vertical fluid movement within the Jotun field as described above. The model region is next discretized into 52,650 cuboidal cells, each with a dimension of 100 meters in the northing and easting direction, and 6 meters in depth. Each cell can have a time-varying density contrast value appropriate to fluid movement during EOR. These two models represent a means for conducting an early stage feasibility study and later interpretation of field data.
Physical properties We next focus on identifying a reasonable density change appropriate to the time-lapse gravity problem. Ideally, 3D variations of reservoir properties — such as porosity, permeability and saturation — should be incorporated, and specific inversion algorithms can now incorporate these varying properties as discussed above. However, this information is not always available, as we must assume here, and early time-lapse simulations may therefore only incorporate values representative of the site as a whole. For example, the Jotun reservoir is comprised of distal gravity flow deposits dominated by sandy turbidites (Gouveia et al., 2004), which we can approximate by a matrix density of 2.65 g∕cc in
Figure 1. Available information for reconstruction of the Jotun reservoir for time-lapse gravity simulations. The images shown here are reproduced from Gouveia et al. (2004). Data are not directly available on reservoir geometry, depths and fluid movement during EOR at Jotun. We use these images directly to construct a model representation of the Jotun reservoir illustrated in Figure 2. The top panel provides information on scale and lateral geometry for our simulated models. The lower panel illustrates a cross section through the acoustic impedance change (positive in red) which the original authors’ derived from their seismic difference inversion. Note that approximately half the vertical extent of the reservoir was being produced during EOR.
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our demonstration. Top of reservoir is at a depth of 2000 meters, average reservoir thickness is 30 meters, swept thickness of the reservoir is set to 18 meters from the base injector, and an average porosity of 28% can be reasonably used throughout our model. To calculate time-varying bulk density fluctuations, we use an oil density of 0.74 g∕cc and brine density of 0.98 g∕cc. The resulting change in bulk density from fluid-contact movement in our simulations is therefore 0.06 g∕cc within the swept zones. The parameters for this stage are site-dependent, and are subject to the availability of prior information. For example, if the oil density value above decreases for a site, the resulting change in density over time from fluid movement would increase, and the 4D gravity response would naturally follow for improved application. In contrast, if residual saturation is subsequently incorporated, the density change will decrease and the resulting 4D gravity response will likewise decrease, potentially precluding time-lapse gravity application at a site. The reservoir parameters that we incorporate into our model are provided above, and the resultant analysis of 4D gravity simulations would therefore be interpreted as an “end-member” solution to a feasibility study. By this, we mean that there is an assumption of piston-like sweep with full fluid substitution, and any data amplitudes and inversion results should be treated as a best-case scenario for the site. When more information on 3D distribution of reservoir properties is available (e.g., Gasperikova and Hoversten, 2008), a more accurate understanding of the utility and limitations of gravity at a site can be acquired. Regardless, all of the remaining steps which we present for 4D gravity applications are valid.
Time-lapse simulations We next have an opportunity to add, subtract or cater our simulated models to reproduce specific time-lapse scenarios, possibly focused around planned injector wells. Or, we may likewise make
broader adjustments to the density distributions within these models, equivalent to ‘snap-shots’ in time, to answer general application questions about the 4D gravity method at a site, as is our aim here. In this case, we wish to validate the remaining points of which this paper seeks to address: (1) 4D gravity can provide valuable fluid movement information, potentially contributing as an interseismic monitoring tool for reservoir monitoring; (2) 4D gravity can be applied to relatively thin and deep reservoirs; and (3) we can improve recovery of fluid movement by jointly inverting surface and borehole 4D gravity data. To demonstrate these points, we next present a series of timelapse simulations designed to address two fundamental questions. The first question is: If the entire reservoir has been swept, can we detect the 4D gravity response with current sensors, and from these data, can we recover the regions that underwent density change? This is a logical first pass simulation, where the answer immediately justifies continuation, or precludes application of gravity as a monitoring tool on a project. For this first simulation, the true model is illustrated in Figure 3a as an areal perspective. Density contrast of 0.06 g∕cc is incorporated throughout the entire horizontal and vertical extent of our reservoir model due to fluid movement. The second question we pose is: Can 4D gravity identify significant deviations from flow patterns predicted by reservoir simulations, such as the unexpected partial vertical sweep experienced during the early production of Jotun? To address this later question, we next present two contrasting density models extracted from the original reservoir structures. The first simulation, Figure 3b, illustrates an areal perspective of density contrast distribution that represents complete oil displacement over a small portion of the reservoir. In this case, density contrast of 0.06 g∕cc is present throughout the entire vertical extent of our model, and the horizontal extent is identified in white. In contrast, the second simulation is illustrated in Figure 3c and it represents a density change from fluid movement limited to the lower 18 meters of the model. In this case, we have increased the horizontal extent of density change to the south, in white, such that the total volume of density change is approximately equal to the previous simulation in panel (b). The specific fluid flow pathways over time to reach these two density contrast models are not of interest. Rather, our goal is to utilize these two different models to determine if time-lapse gravity application can provide insight into unpredicted fluid movement based on recovery of bulk density distribution within the region.
4D SURFACE AND BOREHOLE GRAVITY DATA
Figure 2. Constructed model regions representative of the Jotun reservoir geometry for time-lapse gravity studies. The models successfully reproduce the 3D structure of the field. The models likewise provide the foundation for various 4D simulations based on the concept of partial vertical fluid penetration at the true Jotun site.
In the previous section, we discussed the need for geometrically complex site models for practical time-lapse applications, and demonstrated the ability to construct these reservoir models, even when limited prior information is available. We now focus our attention on numerically demonstrating that newer data, such as μGal-level measurements on the surface and in the horizontal wells, coupled with quantitative interpretation tools, such as a highly constrained inversion, can
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Time-lapse gravity contribute to an effective gravity-based monitoring tool for improved production efficiency. For this, we first generate two separate gravity data sets (gz ) for the various density models constructed for this demonstration. The first set is the surface data at 2000 meters above the field. The
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second is borehole data generated above the reservoir in two monitoring wells. We note that while the depth of the reservoir is representative of the Jotun field, the surface environment, such as terrestrial versus marine setting, and optimal survey design parameters incorporating these surface conditions are not a component of this paper. Our purpose is to illustrate that, provided a reasonable number of data are available, robust inversion algorithms can in fact extract subtle information from 4D gravity data during production of reservoirs that are geometrically complex, thin and relatively deep. We likewise seek to demonstrate that joint inversion of surface and borehole data will lead to improved recovery of fluid movement in the reservoir over surface data alone. Figure 4 illustrates the observation locations for all synthetic data relative to model location. In this example, there are 441 surface data (white dots) and 109 well-data (black dots) calculated above the full simulated density model. While the vertical separations between model, borehole, and surface have been adjusted for illustrative purposes, the horizontal positions are accurate. The data illustrated are the true response from the first simulation, full reservoir model, prior to the addition of noise for inversion.
Surface gravity data
Figure 3. Plan view of true models representing expansion of density change (swept zones) due to fluid movement over time. (a) Full sweep in vertical and horizontal directions of the reservoir model. (b) Full vertical sweep (30 meters) of the northern unit know as Elli to represent an early time during brine injection. (c) Partial vertical sweep (18 meters) of Elli over same interval of time nearly doubles horizontal movement of injected brine.
The generally accepted theory of potential field survey design (e.g., Elkins and Hammer, 1938; Reid, 1980; Murray and Tracey, 2001) identifies a station separation approximating the depth to target for many gravity applications. In practice, however, our data are always contaminated with noise, and one may prefer to consider this a maximum spacing and further tighten up station distances accordingly. For our simulations, the reservoir model is at a depth of 2000 meters, and we have opted to generate 441 surface data at a 1000 meter grid interval over a 20 × 20 km area. It is apparent by inspection of the noise-free data illustrated in Figure 4 that the outer 2 km (3 lines) could be safely removed from each end of our simulated grid, reducing the total number to 225 stations if desired. In practice, total data and station separation would be fine-tuned through further survey design analysis. We maintain the 20 × 20 km grid in our demonstration to present the complete gravity anomalies for each of our simulations. The final surface data for our three simulations are illustrated in Figure 5, and they are each contaminated with 5 μGal noise. In this figure, the inlaid models within the four data sets illustrate the density simulations from Figure 3 of which each data are calculated. The first panel, Figure 5a is the data assuming full vertical sweep of the entire reservoir as described in the previous section. This
Figure 4. Perspective view of data locations relative to the simulated reservoir models. In this example, there are 441 surface data (white dots) and 109 well-data (black dots) calculated above the full simulated density model from Figure 3a. The vertical separations between model, borehole and surface have been adjusted for illustrative purposes. The horizontal positions are accurate. The data illustrated are the true response from the first simulation, full reservoir model, prior to addition of noise for inversion.
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with surface gravity permit more definite quantitative studies than could be made on the basis of the surface data alone.” (Smith, 1950). In addition to our long history of understanding the added benefits of jointly interpreting surface and borehole gravity data (Smith, 1950), it has also long been recognized that borehole gravimeters (BHGM) are a key factor for effectively characterizing reservoirs using gravity methods (Rasmussen, 1975; LaFehr, 1983; Herring, 1990; Popta et al., 1990). Perhaps the best-known early example is the detection of a gas reservoir near a dry hole in Michigan (Rasmussen, 1975). However, the practical application of the method to monitoring the dynamics of reservoirs has been severely limited by the large-diameter borehole gravimeters that can only operate in nearly vertical wells. Recent developments in this field are finally propelling borehole gravity monitoring into the realm of common practice. Nind et al. (2007) reported a slimhole gravimeter that is capable of operating in highly deviated wells. More recent, similar borehole gravimeters that can operate in horizontal wells have been deployed (C. Nind and T. Niebauer, personal communication, 2011). It is high time that we start understanding the information content and value of borehole gravity data from different well configurations in reservoir monitoring. With the advent of these new-generation gravimeters capable of collecting data in highly deviated to horizontal monitoring wells, one could design a monitoring array with a small number of wells, Borehole gravity data specifically emplaced to complement the geometry of the site. We limit the number of wells here to two and orient them such that “Supplement to Surface Gravity Data — It is obvious that borethey cross all three main reservoir structures as illustrated in hole gravity and borehole gradient would when used in conjunction Figures 4 and 6. Well heights are simulated 250 meters and 275 meters, respectively above the reservoir and sample data every 200 meters. Similar to surface data, the decision for gravity station separations comparable to target depth holds in the horizontal well setting above the source, and 200 meter spacing is a good approximation for our problem. The total number of borehole data from the two monitoring wells is 109. The data are contaminated with 10 μGal noise, because well environments are generally noisier than the surface. The data are presented in Figure 6 for the three model scenarios, and it is clear that they are successfully detecting, at the least, lateral density change from fluid movement. It is interesting to note in Figure 6 that we may be able to discern the extent of the fluid movement directly below the horizontal wells from the borehole gravity data because the wells are close to the reservoir. The surface data in Figure 5, however, lacks the high-frequency content as a result of the attenuation with the observation height and they may not be directly interpreted to define the 2D extent of fluid movement. Inversion is an effective way to combine the two data sets to obtain a more precise location of the flooded zone. Figure 5. 4D surface gravity data calculated 2000 m above the reservoir model for different recovery scenarios. Units are in μGal, and 5 μGal noise added to each data set. (a) Time-lapse data for full vertical sweep of entire reservoir. (b) Partial vertical sweep with INVERSION METHODOLOGY increased lateral fluid movement over Elli structure at early time. (c) Full vertical sweep within Elli structure at early injection time and slow fluid movement laterally. (d) Data Two inversion approaches are well suited for from panel (c) that contain correlated noise as might be expected for processed field data. time-lapse gravity problems. The first approach
represents the ideal end-scenario of 30 meters vertical fluid movement throughout the entire site. The peak gravity anomaly predicted for a full sweep is 29 μGal. The remaining panels, Figure 5b, 5c, and 5d, illustrate comparison of surface gravity responses for our later two density simulations at an early time, with different levels of vertical and horizontal sweep in the reservoir, and different noise characteristics in the data. Figure 5b illustrates the data for the scenario of poor vertical sweep and a larger horizontal extent for the water flood zone compared to panels (c and d). For this simulation, a less-defined surface gravity response is observed across the same area due to lateral spreading of the mass with decreased thickness. This level of response should be detectable, but interpretation of this surface data alone, as we will show, contains less detail about fluid boundaries and should be complemented with gravity data from wells. In contrast, Figure 5c and 5d show data calculated for the simulation first introduced in Figure 3b for complete oil displacement over a small portion of the reservoir. The peak gravity response on the surface is approximately 15 μGal and should likewise be detectable by surface gravity sensors. We demonstrate later the effects of inverting time-lapse gravity data for this simulation when the data are contaminated with uncorrelated noise (c) versus correlated noise (d) as one would expect for processed field data.
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is interface inversions. These methods assume a known density contrast and a simple topology for the boundaries of the reservoir, and construct the interface of the water flooded zone. Examples of these approaches applied to salt body problems include Cheng (2003) and Jorgensen and Kisabeth (2000). The methods are equally applicable to the time-lapse problem we demonstrate here, and they have the advantage that they may directly input the known density change due to injection and provide direct information about the fluidcontact surface. Another advantage of these techniques is that the recovered surfaces, representing fluid-contact movement over time, can be seamlessly transferred between seismic and gravity interpreters. A second approach is to implement a highly constrained generalized inversion approach, such as the formulation of Silva Dias Fernando et al. (2008), the compact growing body technique of Camacho et al. (2000), or the binary formulation of Krahenbuhl and Li (2006). For the EOR problem we designed here, the methods would enable one to incorporate density contrast values appropriate to the time-lapse problem, similar to the surface-based inversion, while retaining the flexibility and linearity of cell-based density inversions. When implementing the binary formulation for the current problem, the swept regions take on values of 1, indicating change in density due to fluid replacement, while nonswept zones will take on values of 0. Both approaches utilize density information appropriate to the dynamic processes of the problem, and they seek to resolve shape information or distribution of the anomalous regions — in our demonstration, these are the swept zones. To demonstrate one of the current approaches for time-lapse gravity interpretation, we naturally recover information on fluid-contact movement by inverting the surface and borehole gravity data using the binary approach.
Binary inversion Krahenbuhl and Li (2006) have formulated binary inversion by using explicitly the Tikhonov regularization approach (Tikhonov and Arsenin, 1977). The formulation was developed for the case of salt imaging at the presence of density reversal, but it is generally applicable and was subsequently demonstrated for the timelapse problem of aquifer storage and recovery (ASR) monitoring (Krahenbuhl and Li, 2009). The binary inverse problem is one of minimizing an objective function subject to restricting model parameters, ρ, to attain only one of two values at each location. The total objective function consists of the weighted sum of a model objective function, ϕm , and data misfit, ϕd . The minimization problem is then formulated as
minimize
ϕ ¼ ϕd ðρÞ þ βϕm ðτÞ;
subject to
ρ ∈ f0; ΔρðrÞg;
(1)
where ϕd is formulated as the χ 2 measure of our data misfit (Pearson, 1900; Fisher, 1924; Parker, 1977), and ϕm limits the solution of admissible models to those that are structurally simple (Li and Oldenburg, 1996). Although discrete physical property values can take on difference values in different cases, a general representation is to work with a binary model, τ, and scale it by expected density contrast at location x, y, z
τðrÞ ∈ f0; 1g;
Figure 6. Borehole gravity data generated for horizontal monitoring wells above the various reservoir models in Figure 3. Well 1 is 250 m above the field, and Well 2 is 275 m above. Data are sampled every 200 m and are contaminated with 10 μGal noise. The borehole data are clearly detecting changes in density related to fluid movement here.
(2)
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ρðrÞ ¼ τΔρðrÞ:
(3)
The density contrast model in equation 3 can be generalized to a constant value representative of the reservoir site as a whole, as we implement in the demonstrations to follow (0.06 g∕cc), or it can vary spatially (Krahenbuhl and Li, 2006) provided that adequate knowledge of 3D reservoir parameter distributions are available. When applied to the 4D gravity problem, a value of zero in the recovered model τ would represent regions of zero density change, such as background geology or unaltered reservoir volume, while a value of one corresponds to change in density over time associated with dynamic processes. As a result, inversion solutions using this formulation are often presented in black and white (zeros and ones) representing these respective regions. The minimization problem is then expressed in τðrÞ, where r is the location within the model, and we can work with 0 and 1 for the minimization problem. The actual density contrast values associated with dynamic processes are incorporated into the forward modeling of predicted data during the inversion.
RESULTS In the previous sections, we demonstrated that dynamic systems as thin and relatively deep as Jotun may generate a surface response in 4D gravity data well above the current noise thresholds of modern sensor and survey technologies. Likewise, we are moving into the realm of gravity data acquisition in the horizontal well environment for improved collection of time-lapse data. In this section, we illustrate that, given current sensors, inversion technologies, and the inclusion of realistic reservoir geometries, the previous dogma of appropriate sites for time-lapse gravity monitoring may be largely unfounded. We first illustrate that a robust inversion algorithm can reliably recover fluid movement in relatively thin and deep reservoirs, such as our Jotun representation. We likewise show that results are equally reliable for data contaminated with Gaussian noise — common to many geophysical studies — and for data containing correlated noise as would be expected if one were to process their field data. In our final simulation, we show that the joint inversion of surface and borehole gravity data significantly improves our ability to recover fluid movement over surface data alone, particularly when the dynamic regions of the reservoir continue to thin beyond the full thickness of our reservoir model at the given depth.
Simulation 1: Full reservoir model Inversion results produced by the binary technique are presented here for three scenarios of relevance to this demonstration. We first show inversion results for scenario one of full vertical and lateral sweep. The true model is presented in Figure 3a, the associated surface data with noise in Figure 5a, and the borehole data with noise in Figure 6a. Results are illustrated in Figure 7a in which a majority of the volume of the simulated reservoir is successfully recovered from the noisy gravity data simulated on the surface and in the borehole environment. The result illustrated in Figure 7a shows a plan view of the upper surface of the recovered model, and it is the same at each depth within the 30 meter thick reservoir volume. The percentage of volumetric recovery between the true and recovered models is provided in Table 1. Approximately 87% of the true model is recovered in this instance. The 13% difference is primarily the collection of unrecovered volumes concentrated along the outer edge of the reservoir. The inversion result is a good representation of our model field and confirms successful sweep of the entire reservoir. The value of this simulation is that it can justify moving forward with additional injection scenarios where smaller responses would naturally exist.
Simulation 2: Early time with full vertical sweep (Gaussian noise)
Figure 7. Inversion results illustrating horizontal swept regions predicted by joint surface and borehole gravity data. (a) Full sweep of the entire reservoir model at the end of production. (b) Full vertical sweep at early time with gravity data contaminated with uncorrelated noise. (c) Full vertical sweep at early time with data containing red noise, for comparison with panel (b).
The second scenario illustrates application of 4D gravity as a potential interseismic monitoring tool by identifying density change consistent with predicted reservoir simulations. Figure 7b shows that a full vertical sweep at early time, and therefore predicted horizontal movement of the fluid-contact, may be successfully recovered by jointly inverting the surface and borehole gravity data. The true model, surface gravity data and borehole data with Gaussian noise are presented in Figures 3b, 5c, and 6b, respectively. The recovered model is a good representation of the true model with a 93% volumetric recovery (Table 1). As with the previous example,
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Time-lapse gravity the concentration of unrecovered volumes occurs primarily along the outer edge of the reservoir model, and along the southern boundary of the water flooded zone, as expected.
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constructed from surface gravity data alone and the joint inversion of surface and well data. Simulation 4: Surface data inversion
Simulation 3: Early time with full vertical sweep (correlated noise) Effect of noise characteristics It is common to formulate synthetic studies with data that are contaminated with uncorrelated noise. One reason for such an approach is the lack of specific knowledge regarding the spectral content of the noise that might arise in practical applications. For this reason, we have used Gaussian white noise in all our simulations to avoid unrealistic assumptions. However, while the choice of noise does not necessarily alter the flow of well structured feasibility studies, the noise spectrum could have a profound impact on the performance of inversion algorithms in postacquisition interpretation. A robust algorithm should perform well regardless of noise characteristics. We therefore digress slightly to demonstrate that current time-lapse gravity interpretation techniques are equally reliable when data contain red noise (Gilman et al., 1963) as a natural consequence of data processing and filtering. Toward this end, we treat the data shown in Figure 5c as raw time-lapse data and apply a Wiener filter to attenuate the noise. The Wiener filter uses parameters estimated from the radially averaged power spectrum of the data without any prior information. The resulting processed data are shown in Figure 5d, which has a much cleaner appearance. The main anomaly shape, however, has been altered and the peak amplitude is reduced. We then invert these data using the same binary algorithm used thus far. The recovered model of density change is shown in Figure 7c. Comparison with the result in Figure 7b for the unprocessed data with white noise shows that the inversion algorithm has performed almost equally well on both data sets. There is a 4% difference in volumetric recovery between the two (Table 1). Therefore, for the purpose of our current study, it suffices to add white noise to the data. We will use this approach henceforth.
Simulations 4 and 5: Early time partial vertical sweep In the final simulations, we show that 4D gravity can distinguish between the previous model expected for full vertical sweep with slow horizontal movement, and the third scenario with partial vertical sweep and increased lateral fluid flow. With these simulations, we simultaneously show a comparison between inversion results
We first demonstrate interpretation results for the final 4D simulation when surface data are inverted alone. The results are illustrated in Figure 8a. The gray region outlines the horizontal boundary of the true simulated model, and the white region is the recovered zones of fluid movement. When only surface data are inverted for this problem, our ability to resolve this simulated density model is significantly reduced. With the current geometry, depth, physical properties, and an 18 meter thick sweep from base of the reservoir, the percentage of volumetric recovery here is 57% (Table 1). As with the previous simulations, the unrecovered volumes along the outer edge of the model account for nearly 10% of the differences, while the remaining unrecovered volumes inaccurately bisect the water flooded zone. The source of this poor result is that we are inverting data from a small portion of the reservoir in lateral and vertical directions, that there are no well-data close to the reservoir, and that the surface data no longer contain enough resolving power to properly recover the water flooded zone. The true model is only 18 meters thick on average and spans a small area of the total Jotun simulation. Additional information from well data is required to improve upon this result. Simulation 5: Joint inversion of surface and borehole data Figure 8b illustrates inversion results for the final time-lapse simulation when surface and borehole data are simultaneously inverted. In comparison to Figure 8a without well data, the recovered model shows a significant improvement. It is clear that the combination of thickness, depth, and density contrast for this scenario is straddling the detection limit of surface data alone, and that supplementary well data are necessary here. The borehole gravity data in our final example clearly supplement the surface observations with significant information and lead to a more meaningful understanding of fluid movement within our Jotun simulation. The percentage of volumetric recovery for this scenario is now 75% (Table 1), and it is an 18% improvement over the inversion with surface data alone. We note that the results are still less resolved than for the previous thicker simulations. However, the true value of the gravity inversion here is that it would instantly indicate that the bulk distribution of time-varying density change from fluid movement is not consistent with the projected water flood zone from reservoir simulations. It is progressing laterally far too fast,
Table 1. Percentage of volumetric recovery from the number of binary cells.
Simulation True (# cells) Recovered True (m3 ) Recovered (m3 ) % Recovered
1 Full reservoir
2 Gaussian noise
3 Correlated noise
4 Surface data only
5 Joint surface and well data
13,880 12,004 233 E6 201 E6 87%
3295 3070 55.4 E6 51.6 E6 93%
3295 2928 55.4 E6 49.2 E6 89%
3708 2113 62.3 E6 35.5 E6 57%
3708 2793 62.3 E6 46.9 E6 75%
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Figure 8. Comparison of inversion results from (a) surface data alone, and (b) joint surface and borehole data. The gray region outlines the horizontal boundary of the true simulated model, and the white region is the recovered zones of fluid movement. The model represents the concept of an early production time, where approximately half the vertical extent of the field experiences density change from brine injection (lower 18 meters), and a resulting increase in lateral change. It is apparent that surface data alone do not contain enough information about fluid movement when the lower 18 meters of the reservoir alone are being produced. Joint interpretation of surface and borehole data is essential for a meaningful inversion of 4D gravity data in this instance. hinting that there might be a problem with the extent of vertical sweep. This is valuable information that can raise legitimate concern during production, and thus warrant further investigation, possibly with a more timely seismic survey.
CONCLUSION There are different approaches to applying time-lapse gravity for monitoring efforts and no one approach fits them all. The geometry, physical properties, surface conditions, availability of borehole data, and prior information, such as seismic surfaces, are site dependent. There are many successful developments and applications, and each has contributed to the advancement of time-lapse gravity. We have implemented one monitoring scenario in this demonstration and one inversion technique adapted to time-lapse problems for recovering density change. In our study, we have aimed to provide researchers in the reservoir monitoring community with a glimpse into a few of the ongoing developments in the 4D gravity method and their potential value. In particular, there are four relevant components that we have addressed. First, we have demonstrated that the 4D gravity method may contribute to improved production efficiency and reservoir management in-between the more traditional, but much more expensive, 4D seismic surveys. While resolution of 4D gravity may never achieve the level of 4D seismic at particular sites, the bulk distribution of time-varying density due to fluid replacement
can be successfully recovered, at the least, for comparison with projected fluid-contact movement from reservoir simulations. Second, we have demonstrated how reservoir modeling for dynamic systems is moving beyond the simplistic 2D and 3D geometric representations of actual reservoirs. For pre- and postdata acquisition stages of a project, such as initial feasibility studies and later field data interpretation, respectively, it is now feasible to use detailed density models whose complexity is comparable to that of the engineering model used in reservoir simulations so that the structural complexities and physical property distributions of a site are incorporated. This ability to take full advantage of available reservoir information is imperative. These detailed models are the foundation for understanding the true application and limitations of the 4D gravity method at a production site. Thirdly, we have shown that the joint inversion of surface and borehole gravity data significantly improves our ability to recover fluid movement compared to using surface data alone. This is particularly clear for reservoirs that are extremely thin and at large depths. In our time-lapse simulations we have shown that an 18 meter thick section at 2000 meter depth will likely require the addition of borehole gravity data in conjunction with surface measurements. Finally, we have illustrated that the application of 4D gravity for reservoir monitoring may be greatly undervalued. When using robust inversion algorithms that incorporate available reservoir parameters, we can use modern 4D gravity data collected at the surface and in boreholes to effectively monitor fluid movement in reservoirs that are much thinner and deeper than previously perceived.
ACKNOWLEDGMENTS We gratefully acknowledge the advice and clarification for our constructed reservoir model by Martin Terrell of ExxonMobil. The concept of this study, based on the Jotun field, arose from his invited presentation to the gravity exploration community at the Workshop on 4D Gravity Monitoring of Reservoirs and Aquifers at the 2007 SEG Annual International Meeting. We would like to thank the reviewers of this manuscript for their constructive and necessary recommendations that ultimately led to this document. We thank Kristofer Davis and Misac Nabighian for helpful discussions. This work was supported in part by the industry consortium Gravity and Magnetics Research Consortium at the Colorado School of Mines. The current sponsoring companies are Anadarko, Bell Geospace, BG Group, BGP, BP, ConocoPhillips, Fugro, Gedex, Lockheed Martin, Marathon, Petrobras, Shell, and Vale.
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Krahenbuhl, R. A., and Y. Li, 2006, Inversion of gravity data using a binary formulation: Geophysical Journal International, 167, 543–556, doi: 10.1111/gji.2006.167.issue-2. Krahenbuhl, R. A., and Y. Li, 2009, Hybrid optimization for lithologic inversion and time-lapse monitoring using a binary formulation: Geophysics, 74, no. 6, I55–I65, doi: 10.1190/1.3242271. Krahenbuhl, R. A., Y. Li, and T. Davis, 2011, Understanding the applications and limitations of time-lapse gravity for reservoir monitoring: The Leading Edge, 30, 1060–1068, doi: 10.1190/1.3640530. LaFehr, T. R., 1980, Gravity method: Geophysics, 45, 1634–1639, doi: 10.1190/1.1441054. LaFehr, T. R., 1983, Rock density from borehole gravity surveys: Geophysics, 48, 341–356, doi: 10.1190/1.1441472. Li, Y., and D. W. Oldenburg, 1996, 3-D inversion of magnetic data: Geophysics, 61, 394–408, doi: 10.1190/1.1443968. MacQueen, J. D., 2010, Improved tidal corrections for time-lapse microgravity surveys: 80th Annual International Meeting, SEG, Expanded Abstracts, 1141–1145. Meyer, T. J., 2008, Monitoring water front advancements with down-hole gravity sensors: 78th Annual International Meeting, SEG, Expanded Abstracts, 721–725. Murray, A. S., and R. M. Tracey, 2001, Best practices in gravity surveying: GeoscienceAustralia, 3. Nind, C., H. O. Seigel, M. Chouteau, and B. Giroux, 2007, Development of a borehole gravimeter for mining applications: First Break, 25, 71–77. Parker, R. L., 1977, Understanding inverse theory: Annual Review of Earth and Planetary Sciences, 5, 35–64, doi: 10.1146/annurev.ea.05.050177 .000343. Pearson, K., 1900, On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling: Philosophical Magazine, 50, 157–175. Popta, J. V., J. M. T. Heywood, S. J. Adams, and D. R. Bostock, 1990, Use of borehole gravimetry for reservoir characterization and fluid saturation monitoring: SPE European Petroleum Conference, 151–160. Rasmussen, N. F., 1975, The successful use of the borehole gravity meter in northern Michigan: The Log Analyst (SPWLA), 16, no. 5, 3–10. Reid, A. B., 1980, Aeromagnetic survey design: Geophysics, 45, 973–976, doi: 10.1190/1.1441102. Scintrex Limited, 2006, CG-5 Ccintrex Autograv system: Operation manual, http://www.scintrexltd.com/. Silva Dias Fernando, J. S., C. F. Barbosa Valeria, and B. C. Silva Joao, 2008, Adaptive learning gravity inversion for 3D salt body imaging: 78th Annual International Meeting, SEG, Expanded Abstracts, 746–750. Smith, N. J., 1950, The case for gravity data from boreholes: Geophysics, 15, 605–636, doi: 10.1190/1.1437623. Szabó, Zoltán, 2008, Biography of Loránd Eötvös (1848–1919): The Abraham Zelmanov Journal, The Journal for General Relativity, Gravitation and Cosmology, 1, vii. Tikhonov, A., and V. Arsenin, 1977, Solutions of ill-posed problems: V. H. Winston & Sons. Vasilevskiy, A., and Y. Dashevsky, 2007, Feasibility study of 4D microgravity method to monitor subsurface water and gas movements: 77th Annual International Meeting, SEG, Expanded Abstracts, 816–820. Vigouroux, N., G. Williams-Jones, W. Chadwick, D. Geist, A. Ruiz, and D. Johnson, 2008, 4D gravity changes associated with the 2005 eruption of Sierra Negra volcano, Galápagos: Geophysics, 73, no. 6, WA29–WA35, doi: 10.1190/1.2987399. Zumberge, M., H. Alnes, O. Eiken, G. Sasagawa, and T. Stenvold, 2008, Precision of seafloor gravity and pressure measurements for reservoir monitoring: Geophysics, 73, no. 6, WA133–WA141, doi: 10.1190/ 1.2976777.
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Time-lapse gravity: A numerical demonstration using robust inversion and joint interpretation of 4D surface and borehole data
Richard A. Krahenbuhl1 and Yaoguo Li1
movement. Complex model construction and robust inversion show that time-lapse gravity surveys may contribute to improved production efficiency and reservoir management inbetween the more traditional, and expensive 4D seismic surveys. Results hint that the true value of time-lapse gravity as an additional tool for production efficiency and reservoir management may be greatly undervalued. Data simulated within current and ongoing sensor technologies, combined with advances in computing power and robust inversion, can extract much more meaningful information about fluid movement in reservoirs that are geometrically complex and relatively thin and deep. To illustrate these points, simulations are performed using a representation of the published Jotun Field in the Norwegian North Sea, a well-studied site demonstrating successful application of the time-lapse seismic method, and reconstructed for 4D gravity understanding.
ABSTRACT There are a number of ongoing developments in the 4D gravity method for time-lapse production and sequestration problems. Complex model construction is an essential component for meaningful feasibility studies and data interpretation in 4D. In the case of oil reservoirs, for example, the 4D gravity method must deal with very small density contrasts at depth, and overly simplistic model representations of a field site may not properly guide monitoring efforts for effective reservoir management decisions. The tracking of injected fluid through inversion can be significantly improved with the joint interpretation of surface and borehole gravity data. This is particularly relevant for time-lapse gravity problems where subtle changes in density contrast at depth may not produce surface data that alone contain the necessary information to recover the boundaries of fluid
County, Texas (Eckhardt, 1940; LaFehr, 1980). Within years of the Nash dome discovery, the advances and application of gravity to resource exploration grew significantly. The method was crucial for discovering hundreds of oil fields around the world in the 1920s and 1930s (Eötvös, 2010). Parallel to early surface gravity applications, experiments in determining densities with depth were likewise being made in vertical mine excavations as early as 1854 by Airy, and soon after by von Sterneck in the 1880s in Europe, Hayford in 1902 in the North Tamarack Mine in Michigan, and by Heinrich Jung (1939) in the Wilhelm Mine at Clausthal, Germany (Hammer, 1950). Soon after, Hammer (1950) carried out gravimeter observations in a vertical shaft to a depth of 2247 feet “with a standard-type gravimeter to simulate the data which would be obtained by a borehole gravimeter to aid in the anticipation and formulation of problems in the development and application of a borehole gravimeter for gravity
INTRODUCTION The first successful measure of fluid movement with time-lapse gravity experiments, although poorly documented, is generally credited to Loránd Eötvös in the early 1900s. By increasing sensitivity to one of his several ground-breaking instruments, the gravity compensator, he reportedly detected 1 cm variations in the water level of the Danube River from a distance of 100 m (Szabó, 2008). Soon after, the gravity method was introduced as a practical tool to the oil and gas industry in 1916 near Gbely, Slovakia. This time, the meter was the Eötvös torsion balance, also developed by Loránd Eötvös in 1888, and used by Eötvös himself to collect 92 stations over the Egbell oil field (Eötvös, 2010). But it wasn’t until the first geophysical discovery of an oil and gas field in the United States in 1924 that gravity surveying became widely used for exploration geophysics. That site was the Nash dome in Brazoria
Manuscript received by the Editor 20 December 2010; revised manuscript received 16 July 2011; published online 17 February 2012. 1 Colorado School of Mines, Center for Gravity, Electrical and Magnetic Studies, Department of Geophysics, Colorado, USA. E-mail: [email protected]; [email protected]. © 2012 Society of Exploration Geophysicists. All rights reserved. G33
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prospecting” (Hammer, 1950). These seminal works laid the foundation for future borehole gravimetry. Since that time, we have seen a dramatic shift in exploration strategy as younger technologies with higher resolution capability have come onto the scene. In particular, the 1940s and 1950s witnessed significant advances in the seismic method such as availability of portable multichannel systems, magnetic tape recording for large data volumes, common-depth-point (CDP) stacking, and synthetic seismograms for 2D and 3D model studies (Allen, 1980). The gravity method had become, to a great extent, eclipsed by the seismic method in petroleum exploration. However, gravity continues to remain an important, cost effective, and necessary complementary method in specific problems. We continue to see its successful application in salt provinces and for regional geologic mapping, mineral exploration and geothermal applications. More recently, and largely resulting from new advances in gravity meter technology, computing power and interpretation software, we are experiencing a sharp increase in the use of 4D gravity surveys, on the surface and in the borehole environment for dynamic systems. For example, it is now common to implement gravity surveys with micro-Gal accuracy (e.g. Scintrex, 2006) for land-based exploration and time-lapse problems. Recent developments are likewise demonstrating repeatability in measurements as low as 3 μGal using modified land-gravimeters on the seafloor for time-lapse applications (Zumberge et al., 2008). In the borehole environment, we are witnessing the development of gravimeters capable of gathering data in highly deviated boreholes (e.g. Nind et al., 2007), and more recently in the horizontal well environment (C. Nind and T. Niebauer, personal communication, 2011). Equally relevant to the engineering advances we are seeing are the developments in time-lapse gravity associated with survey design (Ferguson et al., 2007; Davis et al., 2008), noise estimation (Gettings et al., 2008; Glegola et al., 2009), understanding the influence of reservoir compaction (Battaglia et al., 2008), processing (Davis et al., 2008; MacQueen, 2010), inversion (Silva Dias Fernando et al., 2008; Krahenbuhl and Li, 2009), and resolution analysis (Kirkendall and Li, 2007; Davis et al., 2008). In response to these advancements, we are naturally witnessing many successful applications of the time-lapse gravity method for volcanic monitoring (Battaglia et al., 2008; Vigouroux et al., 2008), groundwater studies (Cogbill et al., 2006), artificial aquifer storage and recovery (Davis et al., 2008), waterflood surveillance (Meyer, 2008; Ferguson et al., 2008; Nind et al., 2007b; Hare et al., 2008), gas production (Eiken et al., 2008), CO2 sequestration (Gasperikova and Hoversten, 2008; Alnes et al., 2011), and numerous feasibility studies (Hare et al., 1999; Vasilevskiy and Dashevsky, 2008; Krahenbuhl et al., 2011). These combined gravity developments are playing an important role in transitioning the method from its traditional role as an exploration tool into the realm of production, a monitoring endeavor perceived by many as limited to seismic alone. This misconception is based largely on past applications and limited knowledge of continuous gravity sensor and software evolution, coupled with a belief that most reservoirs are either too thin, too deep, or both, for practical 4D gravity application. It is within this context that this paper is focused. We examine some of the latest developments in the 4D gravity method, develop an integrated approach to feasibility study, and determine the parameter limits within which 4D gravity monitoring through inversion can be effective in reservoir monitoring. In
particular, there are four relevant components that we seek to highlight. First, we demonstrate that the 4D gravity method can contribute to improved production efficiency and reservoir management, such as in-between the more traditional, and expensive, 4D seismic surveys. We show that a well-designed collection of surface and borehole gravity stations can successfully identify lateral fluidcontact movement during enhanced oil recovery (EOR). Resolution may never achieve the levels of 4D seismic at particular sites, but the bulk distribution of time-varying density due to fluid replacement can be successfully recovered for comparison with projected fluid-contact movement from reservoir simulations. Second, reservoir modeling for EOR and sequestration efforts has moved well beyond the simplistic 2D and 3D geometric representations of field sites. For initial feasibility studies and later field data interpretation, it is now common to use integrated models that can reproduce the geometrically and lithologically complex structures by taking full advantage of all prior information. Thirdly, we examine improved reservoir monitoring capabilities through joint inversion of surface and borehole gravity data. Gravity technology is continuously advancing toward smaller and cheaper sensors capable of monitoring minute changes in gravity due to time-varying density. In addition to micro-Gal accuracy on the surface, recent advances have led to first-generation sensors capable of collecting gravity data in the slim and horizontal well environment. As these technologies have continued to progress, it is viable now to jointly utilize surface and borehole gravity data for effective reservoir management. Over the long term, the approach should prove an effective, yet relatively cheap, means of filling the void of knowledge between the less frequent 4D seismic surveys at many sites. Finally, we illustrate that application of the 4D gravity method for reservoir monitoring may be greatly undervalued. We show that modern 4D gravity data — collected in the boreholes as well as on the surface and within current noise thresholds — can monitor fluid movement in reservoirs that are much thinner and deeper than previously perceived. To demonstrate the above-described components of 4D gravity developments, we simulate density change from brine injection over a realistic reservoir model created to mimic the Norwegian North Sea Jotun Field published by Gouveia et al. (2004). We utilize relevant parameters for the Jotun reservoir, such as geometry, thickness, depth and porosity. Using this model construction as a foundation for this study, we then illustrate that one can successfully monitor fluid movement within geometrically complex and relatively thin and deep reservoirs. We likewise demonstrate that an improved recovery of the fluid movement can be obtained by jointly inverting surface and borehole data, rather than focusing on one data set alone.
MODEL CONSTRUCTION Reservoir geometry For practical exploration and production efforts, gravity modeling for pre- and postdata acquisition stages has evolved, overall, to complex model representations of study sites. While simple 2D and 3D prismatic geometries — such that the structures approximate the lengths, widths, depths, depth extents and dips of a dynamic system — have demonstrated great success when appropriate, more complicated reservoirs require higher-quality and realistic representations to fully understand the applications and limitations of 4D gravity. For example, current algorithms can
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Time-lapse gravity now manage geometrically complex models; they can incorporate reservoir boundaries directly from surfaces derived from 3D seismic surveys, as well as realistically varying 3D porosity and permeability information, when available in advance. Gasperikova and Hoversten (2008) successfully demonstrate this point by implementing a realistic model of the Schrader Bluff reservoir, where variations of rock properties and resulting realistic spatial density variations are incorporated. As an alternative, Krahenbuhl et al. (2011) implement an algorithm that incorporates multiple dipping seismic surfaces directly into the 4D gravity inversion for a feasibility study at the Delhi Field sequestration site in Louisiana. The benefit of these growing algorithms, and therefore improved model constructions, is that we can now work more seamlessly with other geophysical and geological contributors to a project. The goal is to reproduce, as accurately as possible, a time-lapse density model representative of the site and consistent with other geophysical and geologic data, so that early feasibility studies and later interpretations are as meaningful as possible. To demonstrate a current application of the 4D gravity method as a potential interseismic monitoring tool, we begin by constructing a realistically complex reservoir model for maximum analysis when limited information is available. The model we employ is a representation of the Norwegian North Sea Jotun Field inspired from Gouveia et al. (2004). For this demonstration, digital data are not directly available on reservoir geometry, depths, or fluid movement during EOR. Therefore, to construct a meaningful 4D gravity study, we built the model utilizing parameters representative of the field obtainable from published literature. The information from which we build our physical reservoir model is limited entirely to the images extracted from the work of Gouveia et al. (2004), reproduced in Figure 1. In this figure, the top panel provides information on scale and lateral geometry for our model reservoir. The lower panel illustrates a cross section through the acoustic impedance change (positive in red), which the authors derived from their seismic difference inversion. In this case, fluid movement is baffled due to the presence of a shale layer at the base of the reservoir, and the resulting fluid movement is therefore dominated by a flank drive rather than a bottom drive. As a result of imperfect vertical sweep, a significant oil potential remains within the upper volume of this section of the field (between the yellow and green lines). For our demonstration here, we do not attempt to reproduce the complex history of fluid movement at Jotun. Rather, we build upon the concept of partial vertical fluid movement and increased lateral movement at the lower half of the reservoir for time-lapse gravity demonstration. Using the images in Figure 1, extraction of shape and scale provides the basic foundation for a model such that we can easily incorporate physical properties appropriate to the 4D gravity problem. For further detail into the production history and application of 4D seismic method at the Jotun field, the reader is referred to the original publication (Gouveia et al., 2004). We first use the images in Figure 1 to construct a model region representative of the Jotun reservoir geometry and depth. The result is illustrated in Figure 2, and it adequately reproduces the geometric complexities of the field for practical understanding when limited information is available. When seismic surfaces are directly incorporated, model construction is naturally simplified and structural accuracy improved even more (Krahenbuhl, et al., 2011). In Figure 2, the upper image shows a full vertical extent of our simulated reservoir model, and the lower panel provides the foundation
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for an alternative modeling scenario where time-lapse density changes are limited to the lower half of the reservoir model. This second scenario is inspired from the concept of partial vertical fluid movement within the Jotun field as described above. The model region is next discretized into 52,650 cuboidal cells, each with a dimension of 100 meters in the northing and easting direction, and 6 meters in depth. Each cell can have a time-varying density contrast value appropriate to fluid movement during EOR. These two models represent a means for conducting an early stage feasibility study and later interpretation of field data.
Physical properties We next focus on identifying a reasonable density change appropriate to the time-lapse gravity problem. Ideally, 3D variations of reservoir properties — such as porosity, permeability and saturation — should be incorporated, and specific inversion algorithms can now incorporate these varying properties as discussed above. However, this information is not always available, as we must assume here, and early time-lapse simulations may therefore only incorporate values representative of the site as a whole. For example, the Jotun reservoir is comprised of distal gravity flow deposits dominated by sandy turbidites (Gouveia et al., 2004), which we can approximate by a matrix density of 2.65 g∕cc in
Figure 1. Available information for reconstruction of the Jotun reservoir for time-lapse gravity simulations. The images shown here are reproduced from Gouveia et al. (2004). Data are not directly available on reservoir geometry, depths and fluid movement during EOR at Jotun. We use these images directly to construct a model representation of the Jotun reservoir illustrated in Figure 2. The top panel provides information on scale and lateral geometry for our simulated models. The lower panel illustrates a cross section through the acoustic impedance change (positive in red) which the original authors’ derived from their seismic difference inversion. Note that approximately half the vertical extent of the reservoir was being produced during EOR.
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our demonstration. Top of reservoir is at a depth of 2000 meters, average reservoir thickness is 30 meters, swept thickness of the reservoir is set to 18 meters from the base injector, and an average porosity of 28% can be reasonably used throughout our model. To calculate time-varying bulk density fluctuations, we use an oil density of 0.74 g∕cc and brine density of 0.98 g∕cc. The resulting change in bulk density from fluid-contact movement in our simulations is therefore 0.06 g∕cc within the swept zones. The parameters for this stage are site-dependent, and are subject to the availability of prior information. For example, if the oil density value above decreases for a site, the resulting change in density over time from fluid movement would increase, and the 4D gravity response would naturally follow for improved application. In contrast, if residual saturation is subsequently incorporated, the density change will decrease and the resulting 4D gravity response will likewise decrease, potentially precluding time-lapse gravity application at a site. The reservoir parameters that we incorporate into our model are provided above, and the resultant analysis of 4D gravity simulations would therefore be interpreted as an “end-member” solution to a feasibility study. By this, we mean that there is an assumption of piston-like sweep with full fluid substitution, and any data amplitudes and inversion results should be treated as a best-case scenario for the site. When more information on 3D distribution of reservoir properties is available (e.g., Gasperikova and Hoversten, 2008), a more accurate understanding of the utility and limitations of gravity at a site can be acquired. Regardless, all of the remaining steps which we present for 4D gravity applications are valid.
Time-lapse simulations We next have an opportunity to add, subtract or cater our simulated models to reproduce specific time-lapse scenarios, possibly focused around planned injector wells. Or, we may likewise make
broader adjustments to the density distributions within these models, equivalent to ‘snap-shots’ in time, to answer general application questions about the 4D gravity method at a site, as is our aim here. In this case, we wish to validate the remaining points of which this paper seeks to address: (1) 4D gravity can provide valuable fluid movement information, potentially contributing as an interseismic monitoring tool for reservoir monitoring; (2) 4D gravity can be applied to relatively thin and deep reservoirs; and (3) we can improve recovery of fluid movement by jointly inverting surface and borehole 4D gravity data. To demonstrate these points, we next present a series of timelapse simulations designed to address two fundamental questions. The first question is: If the entire reservoir has been swept, can we detect the 4D gravity response with current sensors, and from these data, can we recover the regions that underwent density change? This is a logical first pass simulation, where the answer immediately justifies continuation, or precludes application of gravity as a monitoring tool on a project. For this first simulation, the true model is illustrated in Figure 3a as an areal perspective. Density contrast of 0.06 g∕cc is incorporated throughout the entire horizontal and vertical extent of our reservoir model due to fluid movement. The second question we pose is: Can 4D gravity identify significant deviations from flow patterns predicted by reservoir simulations, such as the unexpected partial vertical sweep experienced during the early production of Jotun? To address this later question, we next present two contrasting density models extracted from the original reservoir structures. The first simulation, Figure 3b, illustrates an areal perspective of density contrast distribution that represents complete oil displacement over a small portion of the reservoir. In this case, density contrast of 0.06 g∕cc is present throughout the entire vertical extent of our model, and the horizontal extent is identified in white. In contrast, the second simulation is illustrated in Figure 3c and it represents a density change from fluid movement limited to the lower 18 meters of the model. In this case, we have increased the horizontal extent of density change to the south, in white, such that the total volume of density change is approximately equal to the previous simulation in panel (b). The specific fluid flow pathways over time to reach these two density contrast models are not of interest. Rather, our goal is to utilize these two different models to determine if time-lapse gravity application can provide insight into unpredicted fluid movement based on recovery of bulk density distribution within the region.
4D SURFACE AND BOREHOLE GRAVITY DATA
Figure 2. Constructed model regions representative of the Jotun reservoir geometry for time-lapse gravity studies. The models successfully reproduce the 3D structure of the field. The models likewise provide the foundation for various 4D simulations based on the concept of partial vertical fluid penetration at the true Jotun site.
In the previous section, we discussed the need for geometrically complex site models for practical time-lapse applications, and demonstrated the ability to construct these reservoir models, even when limited prior information is available. We now focus our attention on numerically demonstrating that newer data, such as μGal-level measurements on the surface and in the horizontal wells, coupled with quantitative interpretation tools, such as a highly constrained inversion, can
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Time-lapse gravity contribute to an effective gravity-based monitoring tool for improved production efficiency. For this, we first generate two separate gravity data sets (gz ) for the various density models constructed for this demonstration. The first set is the surface data at 2000 meters above the field. The
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second is borehole data generated above the reservoir in two monitoring wells. We note that while the depth of the reservoir is representative of the Jotun field, the surface environment, such as terrestrial versus marine setting, and optimal survey design parameters incorporating these surface conditions are not a component of this paper. Our purpose is to illustrate that, provided a reasonable number of data are available, robust inversion algorithms can in fact extract subtle information from 4D gravity data during production of reservoirs that are geometrically complex, thin and relatively deep. We likewise seek to demonstrate that joint inversion of surface and borehole data will lead to improved recovery of fluid movement in the reservoir over surface data alone. Figure 4 illustrates the observation locations for all synthetic data relative to model location. In this example, there are 441 surface data (white dots) and 109 well-data (black dots) calculated above the full simulated density model. While the vertical separations between model, borehole, and surface have been adjusted for illustrative purposes, the horizontal positions are accurate. The data illustrated are the true response from the first simulation, full reservoir model, prior to the addition of noise for inversion.
Surface gravity data
Figure 3. Plan view of true models representing expansion of density change (swept zones) due to fluid movement over time. (a) Full sweep in vertical and horizontal directions of the reservoir model. (b) Full vertical sweep (30 meters) of the northern unit know as Elli to represent an early time during brine injection. (c) Partial vertical sweep (18 meters) of Elli over same interval of time nearly doubles horizontal movement of injected brine.
The generally accepted theory of potential field survey design (e.g., Elkins and Hammer, 1938; Reid, 1980; Murray and Tracey, 2001) identifies a station separation approximating the depth to target for many gravity applications. In practice, however, our data are always contaminated with noise, and one may prefer to consider this a maximum spacing and further tighten up station distances accordingly. For our simulations, the reservoir model is at a depth of 2000 meters, and we have opted to generate 441 surface data at a 1000 meter grid interval over a 20 × 20 km area. It is apparent by inspection of the noise-free data illustrated in Figure 4 that the outer 2 km (3 lines) could be safely removed from each end of our simulated grid, reducing the total number to 225 stations if desired. In practice, total data and station separation would be fine-tuned through further survey design analysis. We maintain the 20 × 20 km grid in our demonstration to present the complete gravity anomalies for each of our simulations. The final surface data for our three simulations are illustrated in Figure 5, and they are each contaminated with 5 μGal noise. In this figure, the inlaid models within the four data sets illustrate the density simulations from Figure 3 of which each data are calculated. The first panel, Figure 5a is the data assuming full vertical sweep of the entire reservoir as described in the previous section. This
Figure 4. Perspective view of data locations relative to the simulated reservoir models. In this example, there are 441 surface data (white dots) and 109 well-data (black dots) calculated above the full simulated density model from Figure 3a. The vertical separations between model, borehole and surface have been adjusted for illustrative purposes. The horizontal positions are accurate. The data illustrated are the true response from the first simulation, full reservoir model, prior to addition of noise for inversion.
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with surface gravity permit more definite quantitative studies than could be made on the basis of the surface data alone.” (Smith, 1950). In addition to our long history of understanding the added benefits of jointly interpreting surface and borehole gravity data (Smith, 1950), it has also long been recognized that borehole gravimeters (BHGM) are a key factor for effectively characterizing reservoirs using gravity methods (Rasmussen, 1975; LaFehr, 1983; Herring, 1990; Popta et al., 1990). Perhaps the best-known early example is the detection of a gas reservoir near a dry hole in Michigan (Rasmussen, 1975). However, the practical application of the method to monitoring the dynamics of reservoirs has been severely limited by the large-diameter borehole gravimeters that can only operate in nearly vertical wells. Recent developments in this field are finally propelling borehole gravity monitoring into the realm of common practice. Nind et al. (2007) reported a slimhole gravimeter that is capable of operating in highly deviated wells. More recent, similar borehole gravimeters that can operate in horizontal wells have been deployed (C. Nind and T. Niebauer, personal communication, 2011). It is high time that we start understanding the information content and value of borehole gravity data from different well configurations in reservoir monitoring. With the advent of these new-generation gravimeters capable of collecting data in highly deviated to horizontal monitoring wells, one could design a monitoring array with a small number of wells, Borehole gravity data specifically emplaced to complement the geometry of the site. We limit the number of wells here to two and orient them such that “Supplement to Surface Gravity Data — It is obvious that borethey cross all three main reservoir structures as illustrated in hole gravity and borehole gradient would when used in conjunction Figures 4 and 6. Well heights are simulated 250 meters and 275 meters, respectively above the reservoir and sample data every 200 meters. Similar to surface data, the decision for gravity station separations comparable to target depth holds in the horizontal well setting above the source, and 200 meter spacing is a good approximation for our problem. The total number of borehole data from the two monitoring wells is 109. The data are contaminated with 10 μGal noise, because well environments are generally noisier than the surface. The data are presented in Figure 6 for the three model scenarios, and it is clear that they are successfully detecting, at the least, lateral density change from fluid movement. It is interesting to note in Figure 6 that we may be able to discern the extent of the fluid movement directly below the horizontal wells from the borehole gravity data because the wells are close to the reservoir. The surface data in Figure 5, however, lacks the high-frequency content as a result of the attenuation with the observation height and they may not be directly interpreted to define the 2D extent of fluid movement. Inversion is an effective way to combine the two data sets to obtain a more precise location of the flooded zone. Figure 5. 4D surface gravity data calculated 2000 m above the reservoir model for different recovery scenarios. Units are in μGal, and 5 μGal noise added to each data set. (a) Time-lapse data for full vertical sweep of entire reservoir. (b) Partial vertical sweep with INVERSION METHODOLOGY increased lateral fluid movement over Elli structure at early time. (c) Full vertical sweep within Elli structure at early injection time and slow fluid movement laterally. (d) Data Two inversion approaches are well suited for from panel (c) that contain correlated noise as might be expected for processed field data. time-lapse gravity problems. The first approach
represents the ideal end-scenario of 30 meters vertical fluid movement throughout the entire site. The peak gravity anomaly predicted for a full sweep is 29 μGal. The remaining panels, Figure 5b, 5c, and 5d, illustrate comparison of surface gravity responses for our later two density simulations at an early time, with different levels of vertical and horizontal sweep in the reservoir, and different noise characteristics in the data. Figure 5b illustrates the data for the scenario of poor vertical sweep and a larger horizontal extent for the water flood zone compared to panels (c and d). For this simulation, a less-defined surface gravity response is observed across the same area due to lateral spreading of the mass with decreased thickness. This level of response should be detectable, but interpretation of this surface data alone, as we will show, contains less detail about fluid boundaries and should be complemented with gravity data from wells. In contrast, Figure 5c and 5d show data calculated for the simulation first introduced in Figure 3b for complete oil displacement over a small portion of the reservoir. The peak gravity response on the surface is approximately 15 μGal and should likewise be detectable by surface gravity sensors. We demonstrate later the effects of inverting time-lapse gravity data for this simulation when the data are contaminated with uncorrelated noise (c) versus correlated noise (d) as one would expect for processed field data.
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Time-lapse gravity
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is interface inversions. These methods assume a known density contrast and a simple topology for the boundaries of the reservoir, and construct the interface of the water flooded zone. Examples of these approaches applied to salt body problems include Cheng (2003) and Jorgensen and Kisabeth (2000). The methods are equally applicable to the time-lapse problem we demonstrate here, and they have the advantage that they may directly input the known density change due to injection and provide direct information about the fluidcontact surface. Another advantage of these techniques is that the recovered surfaces, representing fluid-contact movement over time, can be seamlessly transferred between seismic and gravity interpreters. A second approach is to implement a highly constrained generalized inversion approach, such as the formulation of Silva Dias Fernando et al. (2008), the compact growing body technique of Camacho et al. (2000), or the binary formulation of Krahenbuhl and Li (2006). For the EOR problem we designed here, the methods would enable one to incorporate density contrast values appropriate to the time-lapse problem, similar to the surface-based inversion, while retaining the flexibility and linearity of cell-based density inversions. When implementing the binary formulation for the current problem, the swept regions take on values of 1, indicating change in density due to fluid replacement, while nonswept zones will take on values of 0. Both approaches utilize density information appropriate to the dynamic processes of the problem, and they seek to resolve shape information or distribution of the anomalous regions — in our demonstration, these are the swept zones. To demonstrate one of the current approaches for time-lapse gravity interpretation, we naturally recover information on fluid-contact movement by inverting the surface and borehole gravity data using the binary approach.
Binary inversion Krahenbuhl and Li (2006) have formulated binary inversion by using explicitly the Tikhonov regularization approach (Tikhonov and Arsenin, 1977). The formulation was developed for the case of salt imaging at the presence of density reversal, but it is generally applicable and was subsequently demonstrated for the timelapse problem of aquifer storage and recovery (ASR) monitoring (Krahenbuhl and Li, 2009). The binary inverse problem is one of minimizing an objective function subject to restricting model parameters, ρ, to attain only one of two values at each location. The total objective function consists of the weighted sum of a model objective function, ϕm , and data misfit, ϕd . The minimization problem is then formulated as
minimize
ϕ ¼ ϕd ðρÞ þ βϕm ðτÞ;
subject to
ρ ∈ f0; ΔρðrÞg;
(1)
where ϕd is formulated as the χ 2 measure of our data misfit (Pearson, 1900; Fisher, 1924; Parker, 1977), and ϕm limits the solution of admissible models to those that are structurally simple (Li and Oldenburg, 1996). Although discrete physical property values can take on difference values in different cases, a general representation is to work with a binary model, τ, and scale it by expected density contrast at location x, y, z
τðrÞ ∈ f0; 1g;
Figure 6. Borehole gravity data generated for horizontal monitoring wells above the various reservoir models in Figure 3. Well 1 is 250 m above the field, and Well 2 is 275 m above. Data are sampled every 200 m and are contaminated with 10 μGal noise. The borehole data are clearly detecting changes in density related to fluid movement here.
(2)
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ρðrÞ ¼ τΔρðrÞ:
(3)
The density contrast model in equation 3 can be generalized to a constant value representative of the reservoir site as a whole, as we implement in the demonstrations to follow (0.06 g∕cc), or it can vary spatially (Krahenbuhl and Li, 2006) provided that adequate knowledge of 3D reservoir parameter distributions are available. When applied to the 4D gravity problem, a value of zero in the recovered model τ would represent regions of zero density change, such as background geology or unaltered reservoir volume, while a value of one corresponds to change in density over time associated with dynamic processes. As a result, inversion solutions using this formulation are often presented in black and white (zeros and ones) representing these respective regions. The minimization problem is then expressed in τðrÞ, where r is the location within the model, and we can work with 0 and 1 for the minimization problem. The actual density contrast values associated with dynamic processes are incorporated into the forward modeling of predicted data during the inversion.
RESULTS In the previous sections, we demonstrated that dynamic systems as thin and relatively deep as Jotun may generate a surface response in 4D gravity data well above the current noise thresholds of modern sensor and survey technologies. Likewise, we are moving into the realm of gravity data acquisition in the horizontal well environment for improved collection of time-lapse data. In this section, we illustrate that, given current sensors, inversion technologies, and the inclusion of realistic reservoir geometries, the previous dogma of appropriate sites for time-lapse gravity monitoring may be largely unfounded. We first illustrate that a robust inversion algorithm can reliably recover fluid movement in relatively thin and deep reservoirs, such as our Jotun representation. We likewise show that results are equally reliable for data contaminated with Gaussian noise — common to many geophysical studies — and for data containing correlated noise as would be expected if one were to process their field data. In our final simulation, we show that the joint inversion of surface and borehole gravity data significantly improves our ability to recover fluid movement over surface data alone, particularly when the dynamic regions of the reservoir continue to thin beyond the full thickness of our reservoir model at the given depth.
Simulation 1: Full reservoir model Inversion results produced by the binary technique are presented here for three scenarios of relevance to this demonstration. We first show inversion results for scenario one of full vertical and lateral sweep. The true model is presented in Figure 3a, the associated surface data with noise in Figure 5a, and the borehole data with noise in Figure 6a. Results are illustrated in Figure 7a in which a majority of the volume of the simulated reservoir is successfully recovered from the noisy gravity data simulated on the surface and in the borehole environment. The result illustrated in Figure 7a shows a plan view of the upper surface of the recovered model, and it is the same at each depth within the 30 meter thick reservoir volume. The percentage of volumetric recovery between the true and recovered models is provided in Table 1. Approximately 87% of the true model is recovered in this instance. The 13% difference is primarily the collection of unrecovered volumes concentrated along the outer edge of the reservoir. The inversion result is a good representation of our model field and confirms successful sweep of the entire reservoir. The value of this simulation is that it can justify moving forward with additional injection scenarios where smaller responses would naturally exist.
Simulation 2: Early time with full vertical sweep (Gaussian noise)
Figure 7. Inversion results illustrating horizontal swept regions predicted by joint surface and borehole gravity data. (a) Full sweep of the entire reservoir model at the end of production. (b) Full vertical sweep at early time with gravity data contaminated with uncorrelated noise. (c) Full vertical sweep at early time with data containing red noise, for comparison with panel (b).
The second scenario illustrates application of 4D gravity as a potential interseismic monitoring tool by identifying density change consistent with predicted reservoir simulations. Figure 7b shows that a full vertical sweep at early time, and therefore predicted horizontal movement of the fluid-contact, may be successfully recovered by jointly inverting the surface and borehole gravity data. The true model, surface gravity data and borehole data with Gaussian noise are presented in Figures 3b, 5c, and 6b, respectively. The recovered model is a good representation of the true model with a 93% volumetric recovery (Table 1). As with the previous example,
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Time-lapse gravity the concentration of unrecovered volumes occurs primarily along the outer edge of the reservoir model, and along the southern boundary of the water flooded zone, as expected.
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constructed from surface gravity data alone and the joint inversion of surface and well data. Simulation 4: Surface data inversion
Simulation 3: Early time with full vertical sweep (correlated noise) Effect of noise characteristics It is common to formulate synthetic studies with data that are contaminated with uncorrelated noise. One reason for such an approach is the lack of specific knowledge regarding the spectral content of the noise that might arise in practical applications. For this reason, we have used Gaussian white noise in all our simulations to avoid unrealistic assumptions. However, while the choice of noise does not necessarily alter the flow of well structured feasibility studies, the noise spectrum could have a profound impact on the performance of inversion algorithms in postacquisition interpretation. A robust algorithm should perform well regardless of noise characteristics. We therefore digress slightly to demonstrate that current time-lapse gravity interpretation techniques are equally reliable when data contain red noise (Gilman et al., 1963) as a natural consequence of data processing and filtering. Toward this end, we treat the data shown in Figure 5c as raw time-lapse data and apply a Wiener filter to attenuate the noise. The Wiener filter uses parameters estimated from the radially averaged power spectrum of the data without any prior information. The resulting processed data are shown in Figure 5d, which has a much cleaner appearance. The main anomaly shape, however, has been altered and the peak amplitude is reduced. We then invert these data using the same binary algorithm used thus far. The recovered model of density change is shown in Figure 7c. Comparison with the result in Figure 7b for the unprocessed data with white noise shows that the inversion algorithm has performed almost equally well on both data sets. There is a 4% difference in volumetric recovery between the two (Table 1). Therefore, for the purpose of our current study, it suffices to add white noise to the data. We will use this approach henceforth.
Simulations 4 and 5: Early time partial vertical sweep In the final simulations, we show that 4D gravity can distinguish between the previous model expected for full vertical sweep with slow horizontal movement, and the third scenario with partial vertical sweep and increased lateral fluid flow. With these simulations, we simultaneously show a comparison between inversion results
We first demonstrate interpretation results for the final 4D simulation when surface data are inverted alone. The results are illustrated in Figure 8a. The gray region outlines the horizontal boundary of the true simulated model, and the white region is the recovered zones of fluid movement. When only surface data are inverted for this problem, our ability to resolve this simulated density model is significantly reduced. With the current geometry, depth, physical properties, and an 18 meter thick sweep from base of the reservoir, the percentage of volumetric recovery here is 57% (Table 1). As with the previous simulations, the unrecovered volumes along the outer edge of the model account for nearly 10% of the differences, while the remaining unrecovered volumes inaccurately bisect the water flooded zone. The source of this poor result is that we are inverting data from a small portion of the reservoir in lateral and vertical directions, that there are no well-data close to the reservoir, and that the surface data no longer contain enough resolving power to properly recover the water flooded zone. The true model is only 18 meters thick on average and spans a small area of the total Jotun simulation. Additional information from well data is required to improve upon this result. Simulation 5: Joint inversion of surface and borehole data Figure 8b illustrates inversion results for the final time-lapse simulation when surface and borehole data are simultaneously inverted. In comparison to Figure 8a without well data, the recovered model shows a significant improvement. It is clear that the combination of thickness, depth, and density contrast for this scenario is straddling the detection limit of surface data alone, and that supplementary well data are necessary here. The borehole gravity data in our final example clearly supplement the surface observations with significant information and lead to a more meaningful understanding of fluid movement within our Jotun simulation. The percentage of volumetric recovery for this scenario is now 75% (Table 1), and it is an 18% improvement over the inversion with surface data alone. We note that the results are still less resolved than for the previous thicker simulations. However, the true value of the gravity inversion here is that it would instantly indicate that the bulk distribution of time-varying density change from fluid movement is not consistent with the projected water flood zone from reservoir simulations. It is progressing laterally far too fast,
Table 1. Percentage of volumetric recovery from the number of binary cells.
Simulation True (# cells) Recovered True (m3 ) Recovered (m3 ) % Recovered
1 Full reservoir
2 Gaussian noise
3 Correlated noise
4 Surface data only
5 Joint surface and well data
13,880 12,004 233 E6 201 E6 87%
3295 3070 55.4 E6 51.6 E6 93%
3295 2928 55.4 E6 49.2 E6 89%
3708 2113 62.3 E6 35.5 E6 57%
3708 2793 62.3 E6 46.9 E6 75%
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Krahenbuhl and Li
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Figure 8. Comparison of inversion results from (a) surface data alone, and (b) joint surface and borehole data. The gray region outlines the horizontal boundary of the true simulated model, and the white region is the recovered zones of fluid movement. The model represents the concept of an early production time, where approximately half the vertical extent of the field experiences density change from brine injection (lower 18 meters), and a resulting increase in lateral change. It is apparent that surface data alone do not contain enough information about fluid movement when the lower 18 meters of the reservoir alone are being produced. Joint interpretation of surface and borehole data is essential for a meaningful inversion of 4D gravity data in this instance. hinting that there might be a problem with the extent of vertical sweep. This is valuable information that can raise legitimate concern during production, and thus warrant further investigation, possibly with a more timely seismic survey.
CONCLUSION There are different approaches to applying time-lapse gravity for monitoring efforts and no one approach fits them all. The geometry, physical properties, surface conditions, availability of borehole data, and prior information, such as seismic surfaces, are site dependent. There are many successful developments and applications, and each has contributed to the advancement of time-lapse gravity. We have implemented one monitoring scenario in this demonstration and one inversion technique adapted to time-lapse problems for recovering density change. In our study, we have aimed to provide researchers in the reservoir monitoring community with a glimpse into a few of the ongoing developments in the 4D gravity method and their potential value. In particular, there are four relevant components that we have addressed. First, we have demonstrated that the 4D gravity method may contribute to improved production efficiency and reservoir management in-between the more traditional, but much more expensive, 4D seismic surveys. While resolution of 4D gravity may never achieve the level of 4D seismic at particular sites, the bulk distribution of time-varying density due to fluid replacement
can be successfully recovered, at the least, for comparison with projected fluid-contact movement from reservoir simulations. Second, we have demonstrated how reservoir modeling for dynamic systems is moving beyond the simplistic 2D and 3D geometric representations of actual reservoirs. For pre- and postdata acquisition stages of a project, such as initial feasibility studies and later field data interpretation, respectively, it is now feasible to use detailed density models whose complexity is comparable to that of the engineering model used in reservoir simulations so that the structural complexities and physical property distributions of a site are incorporated. This ability to take full advantage of available reservoir information is imperative. These detailed models are the foundation for understanding the true application and limitations of the 4D gravity method at a production site. Thirdly, we have shown that the joint inversion of surface and borehole gravity data significantly improves our ability to recover fluid movement compared to using surface data alone. This is particularly clear for reservoirs that are extremely thin and at large depths. In our time-lapse simulations we have shown that an 18 meter thick section at 2000 meter depth will likely require the addition of borehole gravity data in conjunction with surface measurements. Finally, we have illustrated that the application of 4D gravity for reservoir monitoring may be greatly undervalued. When using robust inversion algorithms that incorporate available reservoir parameters, we can use modern 4D gravity data collected at the surface and in boreholes to effectively monitor fluid movement in reservoirs that are much thinner and deeper than previously perceived.
ACKNOWLEDGMENTS We gratefully acknowledge the advice and clarification for our constructed reservoir model by Martin Terrell of ExxonMobil. The concept of this study, based on the Jotun field, arose from his invited presentation to the gravity exploration community at the Workshop on 4D Gravity Monitoring of Reservoirs and Aquifers at the 2007 SEG Annual International Meeting. We would like to thank the reviewers of this manuscript for their constructive and necessary recommendations that ultimately led to this document. We thank Kristofer Davis and Misac Nabighian for helpful discussions. This work was supported in part by the industry consortium Gravity and Magnetics Research Consortium at the Colorado School of Mines. The current sponsoring companies are Anadarko, Bell Geospace, BG Group, BGP, BP, ConocoPhillips, Fugro, Gedex, Lockheed Martin, Marathon, Petrobras, Shell, and Vale.
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