Evaluating uncertainty in karst pore volume (KPV) is a current industry challenge that is critical for field development planning and optimizing recovery. Hydrocarbon pore volume in karst can be significant in large super-giant fields. Although a wide variety of karst features and the geologic processes that describe their morphology have previously been described in many studies, understanding exactly how to translate this knowledge of karst into practical guidelines for the assessment of pore volume in carbonate reservoirs remains an industry challenge. In this paper, we present a robust model-assisted characterization workflow that integrates well data, seismic data (when available), drilling data, geologic concepts from modern and ancient outcrop analogs, and the application of discrete fracture network (DFN) technology to explicitly model karst features. These DFN models of karst serve as powerful visualization and communication tools in addition to quantifying the KPV. The model-assisted characterization workflow presented is specifically designed for the rapid evaluation of multiple viable geologic scenarios in recognition of the inherent uncertainty in karst morphology, fill, and sampling bias. We present nomograms to facilitate fast practical estimates of karst abundance and porosity, as well as cave area estimates from volumes lost while drilling to help condition and validate the morphometric inputs used for modeling karst. A synthetic reservoir case study with varying degrees of karst that is interpreted to be coastal in origin is used to demonstrate the workflow.
Hydrocarbon pore volume in karst can be significant, commonly on the order of hundreds to thousands of millions of oil equivalent barrels in large super-giant fields, as for example Kashagan and Tengiz in Kazakhstan (Collins et al., 2006; Ronchi et al., 2010). Evaluating uncertainty in porosity related to karst is critical for assessing commercial field value, development planning, and optimizing recovery (Sun and Sloan, 2003). Classic karst reservoirs, such as the Ellenburger of West Texas, in which the presence of collapsed paleocaves in an otherwise tight matrix is the dominant control on reservoir quality (Loucks, 1999), are comparatively rare. In contrast, carbonate reservoirs modified by karst whereby dissolution creates a spectrum of voids (ranging in scale from vugs to caves) that can dynamically communicate with a variety of matrix types leads to good quality reservoirs (Tinker et al., 1995; Bourdon et al., 2004; Biver et al. 2012; Jones, 2015). Such distinction presents a fundamental reservoir characterization and modeling challenge pertinent to many carbonate fields.
A wide variety of karst features and the geologic processes that describe their morphology, from inception to evolution during burial, has previously been described (James and Choquette, 1988; Palmer, 1991; Mylroie and Carew, 1995; Loucks, 1999; Gabrovšek, 2002; Bosák, 2008; Worthington and Ford, 2009). However, exactly how to translate this knowledge of karst into practical guidelines for the assessment of pore volume in carbonate reservoirs remains an industry challenge. Tinker et al. (1995) presented one methodology for characterizing karst porosity (ΦK) within the Yates field. Using a log database from approximately 1800 wells and approximately 8500 m (∼23,000 ft) of core, they were able to develop a robust data set of cave distribution and porosity that was superimposed on a sequence stratigraphic framework to develop an accurate model for predicting the locations of cave porosity. Another approach at modeling the pore volume associated with karst processes was developed by Labourdette et al. (2007). Their workflow simulates the development of flank margin caves through object-based modeling with values of porosity and permeability coming from analog data sets. Kosters et al. (2008) provided a workflow for quantifying karst-related porosity by integrating three-dimensional (3-D) seismic attributes into dynamic model simulations that improved the history match. Although numerous workflows exist to address karst-related pore volume in carbonate reservoirs, these workflows are commonly optimized only for the field in which they were developed, and compilations of ΦK from commercially available reservoir databases rarely have sufficient information on the style and morphometrics of karst features for confident analog selection and quantitative geologic model inputs.
To help address this knowledge gap, we present a new systematic workflow for the quantitative assessment of karst pore volume (KPV). Our approach is similar to the method presented by Tinker et al. (1995) but expands on their workflow in several important ways. In addition to recognizing the various styles of karst that likely occur within the reservoir, our approach integrates available dynamic data, such as drilling information from lost circulation zones (LCZs), to help identify both the presence of karst and estimate the dimensions of karst features. We also use a novel application of commercially available discrete fracture network (DFN) technology to model the spatial distribution of individual caves that honor well control. These DFN models of karst serve as powerful visualization and communication tools in addition to quantifying the KPV. The hallmark of this workflow is driven by the model-assisted characterization that allows for the rapid evaluation of multiple, viable geologic scenarios in recognition of the inherent uncertainty in karst morphology, fill, and sampling bias.
In this paper, we generated a synthetic carbonate reservoir with karst pore volumes, field A, to illustrate the use of the workflow and demonstrate how to reduce pore volume uncertainty related to karst features. Karst present in field A is interpreted to be coastal in origin (Lace and Mylroie, 2013); however, the workflow presented is also applicable for alternative geologic concepts (e.g., burial karst). Application at field A is based on well data (i.e., subseismic karst), but we also discuss how seismic characterization of karst can be integrated with the workflow presented. Karst intensities used to demonstrate the workflow are similar to those observed in actual carbonate reservoirs with coastal karst. The workflow has been successfully used in several carbonate assets.
PARAMETER DEFINITIONS AND KARST CHARACTERIZATION WORKFLOW
The karst characterization workflow has six distinct steps that include key parameters used to classify the different components of the karst system (Table 1).
Step 1: Interpret Karst Intensity in Wells
Karst intensity (KI) is interpreted from the integration of multiple data sets including wire-line logs, in particular, caliper and image logs, core, and drilling data, including bit drops, LCZs, and intervals of poor core recovery. These data can demonstrate the presence of nonmatrix features (fractures and karst) and define their geometric characteristics and their frequency of occurrence along the borehole (Figure 1). Further integration of borehole-derived dynamic data (e.g., production logging tools, temperature logs, and drill-stem tests) is used to help interpret the pore volume and flow potential of different nonmatrix features penetrated (Fernández-Ibáñez et al., 2018).
Figure 1. Wireline response of karst in US Geological Survey monitoring well in Florida (Wacker, 2010). From left to right: depth (in feet), borehole televiewer image, caliper log, gamma ray, acoustic borehole image, near wellbore conceptual model, photoelectric factor (PEF), and density (RHOB). A cave is interpreted between 25 ft (7.6 m) and 32 ft (9.8 m) where the image logs show a cavity coinciding with an enlargement of the wellbore diameter. The RHOB log reads a low value because of wellbore conditions and the PEF log a relatively high value. GV = gross volume; KA = karst abundance; KT = karst thickness.
In this study, the criteria used to identify caves in wells build on the approach described for the Yates field by Tinker et al. (1995) but with the notable addition of image log interpretation (Figure 1). The presence of karst commonly results in characteristic, anomalous, geometric, image-log responses that can be conductive or resistive depending on whether the drilling fluid is water-based or oil-based, respectively. Image logs can significantly increase confidence in cave identification and cave fill. Furthermore, the sinusoidal shape of natural fractures in image logs can help partition nonmatrix features in reservoirs that exhibit both karst and fractures.
Recognizing and classifying pores as caves is a key interpretative decision in pore system partitioning and quantifying KI. Caves have a variety of definitions that span the multiple disciplines of earth science (e.g., Curl, 1964; White and Culver, 2005). As applied to this workflow, we define a cave as having a minimum void height of 0.2 m (0.7 ft) based on the detection limits of a karst feature determined from wire-line logs, including caliper and borehole imaging. Karst features smaller than 0.2 m (0.7 ft) are considered a component of the reservoir matrix pore system. For reference, a minimum void height of 0.3 m (1 ft) was specified for characterizing karst in the Yates field (Tinker et al., 1995). The interpreted KI for the seven wells available in field A ranges from 0.009 to 0.067 m−1 (0.03 to 0.22 ft−1) (Figure 2).
Figure 2. Conceptual model for island karst development. (A) An illustration showing the conceptual model of flank margin caves development along the edge of freshwater lenses. The freshwater lens here is vertically exaggerated for clarity; (B) simplified distribution of facies zones across field A; (C) karst intensity (KI) map built on the basis of well observations and guided by conceptual models (karst probability map) away from well control. R = recharge (i.e., rain).
Step 2: Interpret Karst Probability Maps
Karst probability (KPROB) maps are used to condition the prediction of karst features throughout the reservoir between well control. Outcrop analogs, cave maps, and process-based concepts provide a basis for reliable spatial predictions of KPROB (Labourdette et al., 2007; Jones, 2015). The karst observed in field A is interpreted as coastal in origin, being developed in a flank margin cave system (Mylroie and Carew, 1995; Labourdette et al., 2007). The specified probability of karst occurrence is map-based and captures trends in karst occurrence from the platform margin to interior, including differentiation between windward and leeward margins. For example, the probability of coastal karst will be greater at the platform margin than the interior (Roth, 2004; Labourdette et al., 2007; Wright et al., 2014), and on many isolated carbonate buildups, windward margins have a greater probability of early exposure and/or island development during sea-level drops that would lead to freshwater lens development and karstification (e.g., Minero, 1991; Mylroie and Carew, 1995; Prat et al., 2016). Vertical probabilities can also be specified to condition coastal karst to regions of the reservoir that experienced exposure, the duration of exposure, and the position of paleo-freshwater lenses (Tinker et al., 1995; Jones, 2015). Field A KPROB maps were based on well control, interpretation of platform geometry, depositional environments, and geologic concepts (Figure 2). If the distribution of karst geomorphology is seismically imaged (e.g., Kosters et al., 2008), it can help constrain the probability of karst occurrence between wells.
Step 3: Interpret Karst Intensity Away from Well Control
A KI property is generated that honors the KI observed in wells and is conditioned by KPROB maps that were based on the coastal karst concept described in step 2 (Figure 2). For field A, KI was modeled for the zone of interest using a 200 × 200 m (656 × 656 ft) grid. Coastal karst with a flank margin system is evident in the maps of KI (Figure 2). The KI is highest toward the margin and decreases both toward the platform interior and slope (Figure 2). The variability of KI around the platform margin is consistent with windward regions of longer-lived island development and exposure (Figure 3).
Figure 3. A karst probability map guided by conceptual models of costal karst developed in modern isolated carbonate platforms.
Step 4: Model Discrete Karst Features (Caves) with Discrete Fracture Network
To model karst in field A, we use DFN, a method commonly used to model fractures (Dershowitz et al., 1998). Although DFN methods have been used to model solution-enhanced fractures and karstic porosity along a fracture plane (e.g., Dershowitz et al., 2004), to the best of our knowledge, this is the first application of DFN to model coastal karst. The DFN functionality is available in commercial geologic modeling software to facilitate fast, practical modeling of fractures and karst (Parney et al., 2000; Vaughan, 2015).
Figure 4. (A) Modern flank margin cave (photography courtesy of John Mylroie); (B) the oblate ellipsoidal shape of this cave can be approached as two parallel plates where the distance between them is equivalent to the height of the cave (karst thickness [KT]); (C) example of a discrete fracture network realization modeling discrete cave elements (dark ellipses) in a single stack of cells. L1 = length of minor axis; L2 = length of major axis.
In field A, karst features are interpreted as flank margin caves, which, based on modern analogs, have oblate ellipsoidal geometries that may or may not be connected to other caves (Mylroie and Carew, 1995; Roth, 2004). The ellipsoidal shape is simplified as two subhorizontal parallel elliptical plates that are assigned a height based on statistics derived from karst thickness (KT; Figure 4). Cave orientation is specified as the dip and dip azimuth of an imaginary plane perpendicular to the minor cave axis. Field A caves are modeled as bodies with a horizontal major axial plane. This assumption is supported by modern analogs in which flank margin caves tend to develop concordant to stratigraphy and the position of the freshwater lens (Figures 2, 5). Cave height is defined as the distance from the roof to the base of the cave, and in the DFN method, it is the distance between the parallel plates (Figure 5). Cave height is specified from KT measured in image logs (e.g., Figure 1) and follows a log-normal distribution with an average height of 1.1 m (3.6 ft) with a minimum and maximum height of 0.2 m (0.7 ft) and 10.2 m (33.5 ft), respectively (Figure 5). This cave height distribution is consistent with field-based observations from analogs (e.g., San Salvador and Eleuthera island in the Bahamas [Roth, 2004]; northern Spain, [Wright et al., 2014]). Cave length and width refer to the lateral dimensions of the individual karst bodies and is implemented as DFN model inputs in terms of aspect ratio and equivalent radius. Surveys of numerous flank margin caves found throughout the Bahamas, Caribbean, and Pacific are used to estimate the aspect ratio of the ellipsoidal bodies modeled (Roth, 2004; Waterstraat et al., 2010). The average aspect ratio for these caves is 1:2, with a log-normal distribution that ranges from 1:1 to 1:10. The equivalent radius is defined by the radius of a circle with an area equal to the area of the polygon, which represents the flank margin cave. The equivalent radius follows a log-normal distribution with a mean value of 5.5 m (18 ft) and is consistent with data reported in Roth (2004). The equivalent average cave area is approximately 100 m2 (∼1076 ft2). The length of the long axis of these bodies is based on a 1:5 ratio between height and length, as constrained by data from modern coastal caves (Roth, 2004). A DFN model realization of field A caves using the method described is illustrated in Figure 4. Other styles of karst features, such as vertical karst shafts (Mylroie and Carew, 1995; Moore et al., 2004), can be modeled simultaneously in the DFN in a similar manner to different generations of fractures (Vaughan, 2015).
Figure 5. (A) Recent uplifted flank margin caves in the Marianas. Cave entrances range from 2 to 4 m (6.6 to 13.1 ft). Note how caves are aligned along a subhorizontal surface. Photography courtesy of John Mylroie. (B) Cumulative frequency distribution plot of cave heights interpreted from image logs in field A. Maximum observed cave height is 10.2 m (33.5 ft). Minimum interpreted height is truncated at 0.2 m (0.7 ft). This value represents the threshold between matrix and nonmatrix (blue dashed line). This is the basis for the cave height distribution used to model karst.
Step 5: Calculate Spatial Distribution of Karst Abundance
Karst abundance (KA) (the ratio of karst to matrix volume) is calculated using the distribution of karst intensity from step 3 (Figure 2) and the specified geometrical attributes of karst at the scale of a user-defined grid. The KA is a direct output of the DFN tool. For field A, the resulting average KA is 5.8% (Figure 6). The distribution of KA mimics the imposed KI trends for the flank margin cave concept, with high values along the platform margin and low values in the platform interior. Local maxima (>8%) occur along the platform margin, with an absolute maximum abundance of 21% in the vicinity of well A (Figure 6). Outboard of the platform margin, KA drops abruptly to zero because no meteoric karst is present in the middle to lower slope. The KA decreases progressively toward the north as the environment of deposition transitions from platform margin to platform interior. In the platform interior, KA ranges between 0.5% and 2.5% (Figure 6).
Figure 6. Field-wide karst abundance (KA) in field A. (A) Histogram showing KA distribution results. (B) Field A KA map. Note that maximum values are found along the platform margin. Blue colors (zero values) in the outer domain of the platform margin represent absence of karst.
For a subsurface scenario in which the karst is interpreted as “open” (i.e., caves have no fill at all), the ΦK is equivalent to the KA (KA = ΦK). Therefore, for field A, assuming the caves are open, the mean ΦK for the coastal caves modeled is 5.8% (Figure 6). This ΦK is in addition to the matrix porosity. Karst features are also commonly observed to be partially or completely filled with collapse breccias and/or transported sediment (Tinker et al., 1995; Loucks, 1999). Accounting for karst fill and the corresponding discount in ΦK is described with case study examples in the discussion section of this paper.
To evaluate the uncertainty associated with karst variability from analog data, we ran several model sensitivities to quantify their impact on pore volume. Table 2 summarizes the variables evaluated and the corresponding low-side (10th percentile) and high-side (90th percentile) values. Results from this comparative sensitivity analysis are summarized in Figure 7. The hierarchy of parameters ranked by impact on KA, using the workflow presented, is as follows.
- average karst height (KT);
- a KT probability distribution curve;
- maximum KT (value at which the high side of karst height distribution is truncated);
- average aspect ratio (karst length-to-width ratio);
- equivalent radius; and
- maximum allowable aspect ratio.
Figure 7. Tornado diagram depicting the sensitivity of karst abundance (KA) (in percent) to selected modeling variables. The blue color represents a positive impact on KA (i.e., more than the reference case), and the red color represents a negative impact (i.e., less than the reference case). Height function refers to the type of probability distribution curve used to define karst thickness. Avg. = average; Eq. = equivalent; Max. = maximum.
The results demonstrate that KA is most sensitive to KI and average KT. Figure 8 shows multiple scenarios of the impact KI and average KT have on KA. By evaluating multiple scenarios with varying KI and average KT, a nomogram of KA as a function of KI and average KT was generated (Figure 8). Results show that for an average KI of 0.02, KA can range between 2% and 11% depending on the average karst height. This nomogram can be used as a quick reference to evaluate KA based on borehole image logs. The following two parameters are needed from the image logs: (1) a count of karst features interpreted from the logs (to calculate KI) and (2) the measurement of individual karst feature heights (KT).
Figure 8. Diagram showing the relationship between karst intensity (number of caves per meter) and karst abundance (in percent) for different average cave heights. The range of cave heights displayed is based on measurements from modern flank margin caves.
Step 6: Validate Karst Model for Geologic Consistency
Validating the karst model for geologic consistency is a critical step in the workflow. The first quality control check is “seeing the geology” (sensu Jones, 2015). The karst concept should be visually apparent in the distribution of KA and the spatial arrangement and geometry of modeled caves. Secondly, a KI check is conducted to ensure consistency with the observational data set. Model cells that intersect a well path are interrogated to obtain a count of karst features penetrated. This count is compared to the number of karst features interpreted in the image logs to confirm a reliable KI (Figure 9). Thirdly, a karst area check is performed to ensure consistency with modern analogs. The modeled cave area distribution at field A ranges from 3 to 938 m2 (32 to 10,096 ft2), which falls within 70% of cave areas reported by Roth (2004) for flank margin caves in the Bahamas, the Caribbean, and parts of the Pacific (Figure 9C). The model result is deemed a reasonable realization of a flank margin cave system. Finally, modeled caves are compared to size estimates derived from volumes of drilling fluid lost to the formation in LCZs, which are common in carbonate reservoirs with karst.
Figure 9. Generation and validation of a discrete karst element model. (A) Create a discrete karst distribution for each grid cell based on the target intensity using defined karst geometrical attributes; (B) at each well location, compare the number of caverns interpreted in the image logs (Nobs) with the number of karst intersections in the model (Nmod); (C) compute area of modeled karst and compare with modern analog data.
Drilling data provide valuable information on the magnitude and distribution of open caverns intersected by wellbores, including LCZs, bit drops, high rates of penetration, and large fluid pressure changes (e.g., Sweep et al., 2003; Narr and Flodin, 2012; Ibrayev et al., 2016). In this workflow, we primarily focus on the LCZ events because the total volume lost in each of these zones provides a minimum estimate for the connected KPV. We define and quantify each LCZ from drilling reports, including the top and base of the LCZ, maximum rate of losses, and cumulative lost volume for the zone. We then analyze wellbore images and caliper logs across each anomalous zone to determine the cause of the loss event (e.g., karst or fractures). When caves are identified, we use the total volume lost and the height of the cavern as seen in the image log to compute a minimum cave size. For the coastal karst at field A, we assume that most caves fit the flank margin cave model, and their size can be approximated using an oblate spheroid (e.g., Labourdette et al., 2007).
Figure 10. Plot of total volume lost and cave area. The total volume lost is for an individual cave and includes the total volume of drilling fluids lost into a single feature plus any additional lost circulation material added to control the losses. The cave area is calculated approximating the cave geometry with an oblate ellipsoid where the minimum axis of the ellipsoids equals the cave height as observed in wire-line logs (image logs and/or caliper). The accompanying box plots represent the range (minimum and maximum values) and the interquartile range of modern cave areas (Roth, 2004) and volumes lost into caverns in isolated carbonate platform reservoirs. The latter includes more than 50 data points from different age reservoirs for which a cave was the likely case for the losses. LCZ = lost circulation zone.
We calculate the geometry of an oblate spheroid for each LCZ by combining observations from the wellbore image log with information collected from daily drilling reports and ranges of the horizontal aspect ratios of flank margin caves, which in most cases range between 1:1 and 1:2 (Roth, 2004; Waterstraat et al., 2010). The total volume of fluid lost provides a minimum volume for the cave. A minimum cave area is calculated by dividing the volume of fluid lost during an LCZ event by the cave height determined from the image log. Figure 10 shows the relationship between the total volume lost and minimum cave area for different cave heights. The box plot in Figure 10 shows the range and the interquartile range distribution of more than 50 LCZ events interpreted to be caves from carbonate reservoirs. Assuming that the height of most flank margin caves ranges between 1 and 5 m (3.3 and 16.4 ft), the calculated cave area for the most common volume of drilling fluids lost to cavernous porosity in carbonate reservoirs is consistent with the low side of the observed range of cave areas in modern analogs (Figure 10). Rare, large caves with potentially greater mud volume losses than those recorded in the LCZ data presented (if they are not controlled fast enough) are predicted based on Figure 10. Based on our experience, drilling losses provide valuable data for helping quantify ΦK but have generally been underused in carbonate reservoir characterization. For calibration, the inset box plot shows the range of areas calculated from surveyed flank margin caves from Roth (2004). The two horizontal axes of the oblate spheroid are estimated using Figure 11, which calculates the length of the short horizontal axis for different cave heights and aspect ratios 1:1 (Figure 11A) and 1:2 (Figure 11B).
Figure 11. A plot of total volume lost and length of the minimum horizontal cave axis for (A) 1:1 and (B) 1:2 aspect ratios. The axis length is calculated approximating the cave geometry with an oblate ellipsoid where the minimum axis of the ellipsoids is the cave height as observed in wire-line logs (image logs and/or caliper). The accompanying box plots represent the range (minimum and maximum values) and the interquartile range volumes lost into caverns in isolated carbonate platform reservoirs. LCZ = lost circulation zone.
Controls on Karst Porosity: Karst Fill and Cave Collapse
The workflow presented is designed to estimate porosity related to karst in a carbonate reservoir (ΦK). Karst is initially modeled as open without any fill. This provides the maximum value of ΦK for the karst system modeled. Any impact on ΦK from burial processes and porosity occlusion from fill are subsequently accounted for to discount ΦK.
Modeling the volume of pore space related to caves requires an understanding of the processes and evolution of karst development from initial formation to burial. Before burial, caves are mostly open with a variable range of detrital fill. The variability in fill can be attributed to cave type. For example, epigenic caves that form by acids and recharge from the overlying surface are more prone to detrital fill because of their connection to sediment transport (Palmer, 1991). In contrast, hypogenic caves, including coastal, flank margin caves (Mylroie and Mylroie, 2017), are formed by acids and recharge in a way that is decoupled from the overlying surface; therefore, inputs of detrital sediments are rare unless surface water invades the cave after development (Palmer, 1991). Qualitative estimates of detrital sediment in epigenic caves range from approximately 20% to 100% of the cave volume (A. N. Palmer, 2017, personal communication). Conversely, hypogenic and coastal caves are much lower, with values ranging from approximately 1% to 5%, although some breached coastal caves can have significant amounts of sediment infill (Florea et al., 2004). Based on these characteristics of sediment fill, we plotted modern cave data to demonstrate the relationship between ΦK and KA based on the classification of cave type and assumptions of karst feature porosity (ΦKF) before burial (Figure 12).
Figure 12. Nomogram showing the relationship between karst porosity (ΦK), karst feature porosity (ΦKF), and karst abundance (KA). Squares and circles represent karst reservoirs and modern caves, respectively (Table 3). Triangles represent scenarios that explain how to read the nomogram (see text). The red diamond represents initial conditions of karst at field A with the gray shaded area reflecting the region of possible outcomes of ΦK, ΦKF, and KA for uncertainty analysis. Dotted arrows represent scenarios 1 and 2 as discussed in the text. Scenario 1 assumes the cave is partially filled with detrital sediments and that the cave remains largely intact during burial. Scenario 2 assumes the cave system undergoes partial collapse. Є-O = Cambrian–Ordovician; K = Cretaceous; N = Neogene; P = Permian; pЄ = pre-Cambrian.
Figure 12 illustrates the relationship between ΦK, ΦKF, and KA with trajectories that represent how karst systems can evolve over time to impact pore volume. During burial, caves can be modified in response to mechanical compaction, resulting infill from overlying sediments and the development of breccias (Loucks, 1999). Partial to complete cave collapse and/or additional sediment infill reduces ΦK by altering both the porosity in the cave (ΦKF) and the volume of rock impacted by karst (KA). For example, if we assume that a modern karst system has caves that are 100% open (ΦKF = 100%) and these caves account for 7.5% of the total porosity of the surrounding rock volume (i.e., ΦK = 7.5%), the abundance of karst in the host rock (KA) will be 7.5% (red triangle in Figure 12). During burial, this cave system can evolve in one of two end member scenarios. In scenario 1, the cave is assumed to be partially filled with detrital sediments, and ΦKF is reduced by 50% (trajectory from red to green triangle in Figure 12). In this scenario, we assume the cave remains largely intact during burial (i.e., no collapse), and thus changes to KA are minor (i.e., KA remains at 7.5%). Conversely, scenario 2 assumes the cave system undergoes partial collapse that results in a 50% decrease in ΦKF (trajectory from red to blue triangle in Figure 12). Assuming no detrital sediment occluded ΦKF, ΦK remains unchanged, but the redistribution of ΦKF increases KA to 15% thus expanding the cave “footprint” (blue triangle in Figure 12). Real cave trajectories in Figure 12 are likely a combination of these processes that experience varying degrees of sediment fill and brecciation caused by collapse (e.g., Loucks, 1999).
Understanding the distinction between ΦK, ΦKF, and KA facilitates building reliable geologic models for uncertainty analysis. An excellent example showing where the integration of these components enhances reservoir characterization is from Tinker et al. (1995). In their study of the Yates field, a ΦKF of 40.8% was determined from wire-line logs, and this value in combination with measurements of matrix porosity, linear cave feet, and total logged feet in boreholes was used to calculate a ΦK of 0.7% (Tinker et al., 1995). A KA of 1.75% for Yates field can be calculated based on ΦK and ΦKF (orange square in Figure 12). These parameters guide how to implement karst features in a geologic model that can be conditioned to sequence stratigraphy and areas prone to diagenesis responsible for karst development such as exposed islands and their associated freshwater lenses (Mylroie and Carew; 1995; Tinker et al., 1995).
The magnitude and distribution of karst fill and its impact on ΦKF and ΦK is typically a key subsurface uncertainty in carbonate reservoirs with karst. Figure 12 provides a practical tool to estimate the key components of the karst system (ΦKF, ΦK, KA) if only one of the variables is quantified and reasonable geologic assumptions are applied. If ΦK is approximated, which is commonly the case, we can estimate the size of the karst container that would need to be implemented into the model (i.e., KA) by estimating the amount of porosity that remains open in the karst system (i.e., ΦKF). For example, the Renqiu field in eastern China has a reported field-wide average ΦK of approximately 3% (Qi and Xie-Pei, 1984). While insightful this information fails to capture the extent of the karst system that exists in the reservoir. However, if we assume that 70% of the karst system has been occluded by some combination of detrital sediment fill and collapse (i.e., ΦKF = 30%), a value of 3% ΦK requires a KA of 10% (purple square in Figure 12). Consequently, any attempt to reduce KA necessitates that ΦKF must increase, assuming the value of ΦK remains fixed at 3%. In addition to Renqiu field, additional reservoirs with karst have been plotted in Figure 12 to illustrate the range of likely values for ΦK, ΦKF, and KA (Bouvier et al., 1990; Wang et al., 1999; Kosters et al., 2008) (Table 3). Although these numbers are interpretative, given that for each case study only one value was reported (i.e., ΦK or ΦKF), they suggest a clustering of values expected for karst reservoirs and provide a range of values on the uncertainty associated with these systems.
We can apply our understanding of the relationship between ΦK, ΦKF, and KA to field A to generate multiple, geologically viable karst scenarios for subsurface uncertainty analysis. If the karst in field A is initially considered open (ΦKF = 100%), then KA and ΦK are 5.8% (red diamond in Figure 12). Most caves at reservoir conditions, however, have some fill that results in a reduction in ΦKF; consequently, KA > ΦK. If field A karst features have an average ΦKF of 50%, which is supported by limited data on karst reservoirs that describe a ΦKF of 30% to 60% (e.g., Tinker et al., 1995; Kosters et al., 2008), then a range of possible outcomes exists for ΦK and KA (gray shaded area in Figure 12).
Karst Sampling Bias, the Importance of Data Integration, and Geologic Concept
Several previous studies have documented the issue of sampling bias in penetrating epigenic karst in a vertical wellbore (e.g., Worthington, 1999). Such bias presents a fundamental challenge in carbonate reservoir characterization and reinforces the important influence of integrating geologic concepts to debias well-derived measurements of karst. A minor amount of karst in a vertical setting likely indicates that a significant amount of ΦK may be present in the reservoir. Conversely, if a well penetrates a high proportion of karst (e.g., well A [Figure 6]), it is important to recognize how representative the KI observed in that well is for the entire reservoir. The discriminating factor is the interpreted geologic concept. For example, in field A, the interpretation of karst as coastal in origin implies a distribution and style of karst that would differ from a reservoir with epigenic karst. Coastal karst will condition the distribution of the highest KA to occur around paleo-shorelines, such as the platform margin (Figure 6). Epigenic karst, however, would imply that dendritic patterns likely occur across the entire platform (e.g., Kosters et al., 2008). Understanding the style of karst that likely occurs within a reservoir will guide geologic modeling concepts and potentially impact field development strategies, including widespread extrapolation of areas with high KI, such as those observed in well A.
To explore the extent of KPV that could be present within a reservoir, we ran a Monte Carlo simulation (40 iterations) in a 256 × 256 × 400 m (840 × 840 × 1312 ft) volume (∼16-ac well spacing), using input parameters described in this paper for field A. Simulation results demonstrate that a vertical well has a 95% probability of intersecting only a single cave (karst feature) out of a possible 670–768 caves present in the volume (Figure 13). This result demonstrates that tens of thousands of probable caverns may be distributed in reservoirs in which karst is rarely penetrated. For the same model and assuming KA = ΦK (i.e., all caves are 100% open), intersecting one karst feature implies a significant uplift in pore volume of up to 14%. This result depends on the assumed matrix porosity and the average height of the karst. In low matrix porosity rocks, the presence of karst features has a greater impact on the uplift in pore volume. For example, a 5% porosity matrix intersecting a single cave can result in a 7%–14% increase in KPV (assuming an average karst height of 1 m [3.3 ft] and 3 m [9.8 ft], respectively). In reservoirs with a higher matrix porosity of 25%, the effect of karst sampling bias on pore volume is reduced, and the total pore volume would increase by 1%–2%. Intersecting multiple karst features in a well can exponentially increase the estimate of KPV in the reservoir.
Figure 13. An example of a Monte Carlo iteration in which caves were randomly distributed in a 256 × 256 × 400 m (840 × 840 × 1312 ft) volume. We run 40 iterations where the number of cavers generated ranges from 670 to 768. For each iteration, only one cave was intersected by the well. This demonstrates that even in the case in which a well intersects one cave, the number of caves statistically possible for a given volume can be noticeably larger. On the left (A), one iteration with 705 caves is shown. The figure in the center (B) shows the one cave (out of 705) that is intersected by the well. The histogram on the right (C) shows the number of caves on each of the 40 Monte Carlo iterations in which the well only intersected one cave.
Well placement can be a decisive factor in the number of karst features that are intersected. Results from Monte Carlo simulations return realizations in which a cave is not penetrated by a well, despite as many as 500 caves being present in the modeled volume. This observation reinforces the importance of the interpreted geologic concept and integrating all data types, including those that sample the reservoir beyond the borehole wall to debias the data. Specifically, the character of well test derivative curves, which commonly exhibit a distinct signature for larger karst features, provide key insights into the presence of karst hundreds of meters to several kilometers from the wellbore (Horne, 1995; Neillo et al., 2014). Reservoir simulation history matching studies, although nonunique in their nature, also provide important insights about the presence and magnitude of large pore volumes, likely related to karst, not observed in wells (e.g., Kosters et al., 2008). Indeed, porosity multipliers that are commonly required to match production history are a common manifestation when not explicitly including sufficient ΦK in reservoir models because of the sampling bias (Jones, 2015).
Integration of Karst Characterization from Seismic Data
The quantitative assessment of pore volume is significantly more reliable when karst is seismically imaged and calibrated to well and/or production history (Bourdon et al., 2004; Vahrenkamp et al., 2004; Mohammad et al., 2016). Seismic interpretations of karst features and even dendritic karst networks can be imported directly as 3-D “geobodies” into reservoir models or used as training images in multiple-point statistics for quantitative assessment studies (Bourdon et al., 2004; Jones, 2015; Mohammad et al., 2016). However, reservoir drilling experience, as observed in outcrop analogs, demonstrates that karst features that are subseismic in scale coexist with seismically resolvable features. These subseismic karst features can have a material impact on field resource size and production performance (Bourdon et al., 2004; Mohammad et al., 2016). The workflow presented in this paper provides a robust method for modeling the subseismic KPV that can be integrated with karst features resolvable in seismic scale. Perhaps an underappreciated aspect of seismic karst characterization is the identification of viable geologic concepts of karst, such as coastal karst or structurally controlled burial karst (Ibrayev et al., 2016; Mohammad et al., 2016). The spatial distribution of KI probability (step 2 of the workflow presented) that is predicated by the geologic concept of karst interpreted is the most sensitive parameter in quantifying KPV uncertainty (Figure 7). Finally, seismically imaged karst can be used to condition the abundance and distribution of subseismic karst in a reservoir model. This enhances the “seeing the geology” validation criteria and increases confidence in the karst interpretation and corresponding pore volume (workflow step 6).
Static versus Dynamic Assessment of Karst Pore Volume
In addition to uncertainty in resource size, karst is a significant control on hydrocarbon recovery (Sun and Sloan, 2003; Kosters et al., 2008). However, estimating the permeability of a reservoir modified by karst that reliably predicts flow through both matrix and nonmatrix features that commonly include fractures in addition to karst remains a fundamental business challenge.
For certain types of karst pore systems, depending on the scale of features and nature of their fill, it may be appropriate to adopt an effective porous media approach, in which the karst is modeled as an integral part of the reservoir matrix (Jones, 2015). In contrast, when flow behavior in a karst network is dramatically different from the matrix, a dual porosity–dual permeability model may provide a more reliable flow prediction (Medekenova and Jones, 2014). From a model-assisted characterization perspective, because the workflow in this paper leverages DFN technology to model discrete caves (step 4; Figure 4), it is possible to calculate the permeability of this nonmatrix pore system at the scale of interest for reservoir simulation (Vaughan, 2015). A distinct advantage of the DFN method, when used this way, is that it can calculate a single nonmatrix permeability tensor that encompasses both the fracture and karst components of the pore system. Nonetheless, a recognized current limitation of this approach is the potential for rapid flow, in open connected karst pores, that can become turbulent (e.g., White and White, 2005). The emergence of turbulent flow lowers the effective hydraulic gradient and reduces the effective permeability relative to laminar flow (e.g., Halihan et al., 1999), which is assumed in commercially available DFN tools. Accounting for turbulent flow in carbonate reservoirs modified by karst is the subject of future research that will realize the benefits of the workflow presented to help address karst permeability uncertainty in addition to pore volume.
Evaluating uncertainty in KPV is a fundamental challenge that is critical for field development planning and optimizing hydrocarbon recovery. Most oil and gas reservoirs in isolated carbonate platforms exhibit strong evidence of coastal karst; therefore, the potential volumes associated with coastal caves can have a large impact on the in-place resource. In this paper, we present a robust model-assisted characterization workflow that integrates well data, seismic data (when available), drilling data, dynamic data, geologic concepts from modern and ancient outcrop analogs, and the application of DFN technology to explicitly model karst features (caves). We estimate KPV through a systematic method of evaluating the geologic validity of the modeled cave (e.g., cave type and platform location) and by testing alternative karst-fill and collapse scenarios.
A synthetic reservoir case study with seven wells and varying degrees of karstification interpreted to be coastal in origin is used to demonstrate the workflow. The contribution of karst to the reservoir pore volume results in an average field-wide porosity increase of 5.8% (if the caves are assumed to be open). The ΦK modification by cave collapse and sediment fill are an integral part of the workflow necessary to investigate alternative karst scenarios and evaluate resource size uncertainty.
The KA is critically sensitive to KI as interpreted between subsurface well control. This result reinforces the importance of modeling to a defined geologic concept (e.g., coastal karst). In this respect, an interpolation of KI from wells alone, especially if well control is poor, will yield unreliable estimates of ΦK.
The volume of mud losses from LCZs as a direct result of a karst feature, in combination with the height of the feature derived from log analysis, can provide a reasonable estimate of the cave area. We present nomograms in this paper to facilitate fast practical estimates of cave area to help condition and validate the morphometric inputs used for modeling karst.
Penetrating karst features with a vertical wellbore is subject to considerable sampling bias. Monte Carlo simulations demonstrate that the penetration of a single karst feature likely indicates that a significant amount of ΦK can be present. Conversely, the absence of a karst penetration, in data-poor carbonate reservoirs, should not rule out the potential for a scenario in which karst can significantly impact resource size. The integration of karst geologic concepts is critical to debias well data.
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We thank Rod Myers for his guidance using the discrete fracture network tool. We also thank Paul Hinton, Brodie Thompson, Lyndon Yose, and Jon Kauffman for their comments and guidance throughout different stages of this work that greatly improved the manuscript. We thank John Mylroie, Imelda Johnson, and AAPG Editor Barry Katz for their thorough review of an early version of this manuscript. ExxonMobil Upstream Research Company is acknowledged for permission to publish this work.