Mississippian limestone and chert reservoirs in northern Oklahoma have produced oil and gas since the early 1900s. Most fields were originally produced by vertical wells on closed structural highs and associated porosity pinch-outs. Given advances in horizontal drilling and completion techniques, wells can connect laterally heterogeneous reservoirs, thus increasing production as compared to vertical wells. As described herein, references to the Mississippian interval include the Mississippian-age deposits that are primarily limestone and chert and that exist above the Woodford Shale (the Mississippian-age portion of the upper Woodford Shale is not included). Mississippian limestone and chert reservoirs of the midcontinent have been referred to informally as the “Mississippi Lime” or “Mississippi Chat.” The chert-rich intervals were coined “chat” by drillers because of the chattering noise and bit-bounce during drilling (Rogers, 2001).

In south-central Kansas, Watney et al. (2001) examined core and well-log signatures to identify seven dominant lithofacies of the Mississippian. They analyzed the vertical stacking of the upward-shoaling lithofacies and interpreted four transgressive–regressive cycles within an overall upward-shoaling sequence. The cycles range in thickness from 20 to 55 ft (6–15 m) are characterized by cleaning-upward gamma-ray logs and are commonly capped by erosional or karst-related surfaces.

Duren (1960), Doveton (1973), and Peeler (1985) also examined well-log signatures to identify petrophysically distinct stratigraphic units. Their studies revealed characteristically low resistivity and high porosity in reservoir intervals. At Glick field in Kansas, Rogers et al. (1995) presented a model for chert development with the aid of 30 wells with full Mississippian penetrations and three cores, and proposed that sponge bioherms were responsible for the spatial distribution of the “chat” (spiculitic chert) reservoirs.

East of Tonkawa field in Osage and Kay counties, Oklahoma, using logs for 6600 wells and thin sections, Rogers (2001) presented models for tripolitic chert formation (also see explanation of tripoli by Khoury, 1986). The models involved two different depositional scenarios: (1) erosion of shelf-margin cherty limestone and deposition of the detrital material as conglomerates and breccias and (2) in situ vug and karst development of subaerial highs (e.g., sponge bioherms and cherty limestone). In both scenarios, deposition was followed by two main diagenetic stages: silica replacement of calcite and partial to complete dissolution of the remaining calcite to form secondary porosity (Khoury, 1986; see Rogers, 2001 for an illustration of the depositional model and tripolitic chert formation). Like at Glick field, the dissolution of soluble siliceous organisms, such as sponges (spicules), is a likely source of silica for the chert (Rogers et al., 1995; Rogers, 2001). Sponge spicules were also interpreted to be the source of silica in Osagean rocks of the western Sedgwick basin in Kansas (Thomas, 1982).

Dowdell et al. (2013a, b) used impedance, coherence, and curvature attributes to map tripolitic high-porosity “sweet spots” within a highly fractured Mississippian reservoir in Osage County, Oklahoma. Roy et al. (2013) also used seismic attributes and well-logs combined with unsupervised 3-D seismic-facies analysis to map Mississippian lithologies in Osage County. Costello et al. (2014) generated 3-D models of Mississippian lithology, porosity, and permeability in northeastern Woods and Alfalfa counties, Oklahoma using cores and well-logs. Lindzey (2015) expanded upon this work by integrating 3-D seismic data and attributes (e.g., acoustic impedance) with core, well-logs, and neural-network-derived lithology logs. Their work established that tripolitic chert, limey-dolomitic chert, and chert-rich limestone were the most productive lithologies, mapped their spatial distribution, and addressed the lithological and petrophysical controls on production.

For the Mississippian at Tonkawa field in Kay and Noble counties, Oklahoma (Figures 1, 2), this study uses 3-D seismic, core, well-logs, and production data to characterize the limestone and chert reservoirs in terms of their log responses and spatial distribution and explores correlations between lithology, hydrocarbon production, and other parameters. Tonkawa field was discovered on June 29, 1921, with the School Land 1 well. It initially produced from the Pennsylvanian Tonkawa sandstone and subsequently from the Pennsylvanian lower Hoover and Endicott sandstones; thus, the field was named Three Sands field (Clark and Aurin, 1924). With time, the deeper Mississippian strata and Simpson sandstones were also productive.

Tonkawa field is on the eastern margin of the Nemaha uplift and is divided into an upthrown western block and a downthrown eastern side, which are offset by as much as 500 ft (150 m) of vertical displacement. At the apex of the field, the entire Mississippian strata, Woodford Shale, and part of the Wilcox sandstone (Ordovician) are completely eroded at the Pennsylvanian unconformity. Pennsylvanian-aged shales are stratigraphically above the Wilcox Sandstone. Approximately 450 ft (135 m) of strata have been removed due to the uplift and erosion. On the eastern downthrown side of the field, greater than 400 ft (120 m) of the Mississippian section is present.

Data for this study include 290 vertical wells (260 with open-hole logs; 30 with raster logs), production data for 31 horizontal wells, and a 42 mi² (108 km²) 3-D seismic survey. The 3-D seismic data were acquired in 2001 and have an 82.5 ft (25.2 m) bin spacing. The 290 vertical wells are all complete Mississippian penetrations. Core from one well, the Range Resources 2 Jane, is located within the 3-D survey seismic area (Figure 2). Using these data, this study (1) identifies the key Mississippian lithologies, (2) classifies the lithologies in noncored wells, (3) establishes a stratigraphic and structural framework for the field, (4) generates well-constrained 3-D reservoir models of lithology and porosity, and (5) relates lithofacies and reservoir quality to Mississippian production behavior.

Tonkawa field is located on the boundary between the Cherokee platform and Nemaha uplift (Figure 1). Mississippian carbonate and silica-rich strata were deposited on an extensive distally steepened ramp that covered much of the central United States with scattered calcareous mud mounds, heterozoan assemblages, and abundant sponge bioherms (Figure 4; Rogers et al., 1995; Mazzullo et al., 2009). Rising eustatic sea level throughout much of the Mississippian facilitated progradational wedges of carbonate and spiculite sedimentation toward the south–southeast (Watney et al., 2001). As noted earlier, Watney et al. (2001) interpreted four transgressive–regressive cycles within an overall upward-shoaling sequence. Mazzullo et al. (2009) interpreted Osagean and Meramecian rocks in south-central Kansas as onlapping, upward-deepening strata overlain by upward-shoaling, progradational clinoforms. The deposits are interpreted to represent a transgressive systems tract followed by an off-lapping highstand systems tract. The direction of progradation was likely influenced by locally significant structural features (Figure 1; Gutschick and Sandberg, 1983).

During the Late Mississippian and Early Pennsylvanian, tectonic uplift of portions of the midcontinent (e.g., Central Kansas uplift, Nemaha uplift) related to the Ouachita orogeny coupled with eustatic sea-level fall, resulted in extensive subaerial exposure, erosion of Mississippian strata, and deposition of detrital clasts of reworked cherty limestones (Merriam, 1963; Parham and Northcutt, 1993; Rogers et al., 1995; Montgomery et al., 1998; Rogers, 2001; Watney et al., 2001; Mazzullo et al., 2009). The erosion resulted in the major, regionally extensive Mississippian–Pennsylvanian unconformity (Watney et al., 2001). As a result, the Mississippian deposits experienced a complex sequence of diagenetic events highlighted by several stages of silicification, dolomitization, and dissolution during deposition, meteoric diagenesis, burial diagenesis, and hydrothermal diagenesis (Ramaker et al., 2014).

The Mississippian interval is characterized by four distinct stages of deposition. From oldest to youngest these include Kinderhookian, Osagean, Meramecian, and Chesterian (Figure 3). The Kinderhookian interval is typically 50–225 ft (15–70 m) thick in the northwest portion of Oklahoma, but has been largely removed in central Oklahoma by post-Kinderhookian erosion (Northcutt et al., 2001). It is debatable if Kinderhookian strata are present in the study area or if Osagean rocks directly overlie the Woodford Shale (Figure 3). In the study area, it is interpreted that Meramecian and Chesterian rocks are not present.

The Mississippian reservoir rocks were analyzed using core and thin sections from the Range Resources 2 Jane well and open-hole logs for 260 of the 290 wells. The core description includes observations of lithology, grain size, texture/fabric, sedimentary structures, bounding surfaces, fractures, and fossils (Turnini, 2015). Thin sections and photomicrographs were acquired to document key aspects of each lithology. To estimate lithology in noncored wells for stratigraphic correlation and mapping, open-hole logs were compared to the core. Through this process, log-curve cut-offs (thresholds) were established, and these were used to generate lithology logs for noncored wells.

The lithologies include two forms of tripolitic chert, two types of dense chert, two varieties of limestone, and shale. More specifically, the seven lithologies include (A) chert conglomerate, (B) tripolitic chert, (C) massive-to-laminated dense chert, (D) dense chert breccia, (E) bioturbated limestone, (F) limestone breccia, and (G) nodular-to-bedded mudstone (shale; Figure 5).

The chert conglomerate occurs at the top of the Mississippian and has well-rounded to subangular clasts of tripolitic chert and limestone in a shale-rich matrix. It contains detrital chert that formed by weathering and erosion of Mississippian-age limestone, tripolitic chert, and shale and was deposited in structural lows (Rogers, 2001). Photomicrographs show that some clasts of tripolitic chert exhibit moldic and vuggy porosity (Figure 6A). Fracture porosity and remnant limestone are also present.

Across much of Tonkawa field, stratigraphically below the chert conglomerate, is an interval of tripolitic chert that formed in-place whereby the parent limestone is altered through successive periods of subaerial exposure, silica replacement of calcite, and partial to complete dissolution of the remaining calcite to form secondary porosity (Khoury, 1986; Rogers, 2001). In some cases, there is associated development of karst-related features. The in situ tripolitic chert is characterized by high porosity (core porosity = 16–28%) and a distinctive cream color; however, oil-staining is common. It is primarily composed of silica, and compared to the chert conglomerate, contains limited shale or remnant limestone. Photomicrographs illustrate partial to complete dissolution of limestone to form vuggy and moldic porosity and microporosity (Figure 6C).

Both the detrital chert conglomerate and in situ tripolitic chert exhibit similar open-hole log characteristics: very low resistivity (generally <5 ohm m) and high porosity (>10%). Because of this, it is not possible to distinguish the two types of tripolitic chert without core data. Therefore, the two types of tripolitic chert were combined as one tripolitic chert lithology for the log-based estimation of lithology in noncored wells.

Dense chert observed in core occurs in bands or layers (Figure 5C) or as a breccia (Figure 5D). The dense chert and chert breccia most likely formed by an incomplete process of tripolite formation in which silica replacement of calcite occurred; however, subsequent calcite dissolution to produce secondary porosity did not occur. The dense chert and chert breccia occur at the base of the tripolitic chert zone before grading stratigraphically downward into bioturbated limestone. Thin sections of dense chert show a variety of textures and an abundance of pyrite and fractures (Figure 6D). The dense chert texture suggests almost complete replacement by silica of a micritic parent limestone. Some remnant limestone exists with limited porosity (Figure 6E, F).

The most prevalent lithology is bioturbated limestone (Figure 5E), which has abundant horizontal burrows and is a dark gray in color. It contains multiple fractures that are both healed and open and contains stylolites and crinoids. It is low in porosity compared to the tripolitic chert (core porosity = 0–3%). Limestone breccia (Figure 5F) has similar characteristics to bioturbated limestone but has been weathered and exhibits core porosity ranging from 1% to 11%. It has large clasts of subangular to rounded limestone in a matrix of limestone and chert. Photomicrographs of the limestone confirm the dominant lithology is calcite but there is dolomite present (Figure 6G). Nodular to bedded mudstone (shale; Figure 5G) is dark gray to black in color and has abundant horizontal burrows and fractures. Core porosity ranges from 3% to 6%.

Through analysis of core descriptions and open-hole logs a lithology curve was generated for wells with gamma ray (GR), bulk density (RHOB), and deep resistivity (RILD) curves. Although the data set included neutron porosity and photoelectric logs, they are not common in most wells; thus, they were not used to generate lithology curves. To estimate lithology logs, it was observed that shale is generally present when the Vshale (generated from the GR) is greater than 0.7. Shales present within and above the Mississippian interval are generally very carbonaceous or siliceous and can exhibit a relatively clean GR signature. A high Vshale cutoff was necessary to ensure that the calculated lithology was shale and not a shaley carbonate or sandstone. Because GR responds to uranium, potassium, or thorium in the rock, the high GR values might not be associated with shale. In the upper portion of the Range Resources 2 Jane core, from 4464.5 to 4472 ft (1360.7–1363 m; Figure 3), there are high GR values associated with tripolitic chert; however, further studies are needed to determine the cause of the high GR values.

Tripolitic chert in the Mississippian interval characteristically exhibits low resistivity (<5 ohm m) on open-hole well-logs. The limestone and dense chert typically do not exhibit low values of resistivity. From 4488 to 4499 ft (1368–1371 m; Figure 3) in the core, there is a significant interval of limestone breccia with porosity, which is causing a lower resistivity than typically observed. Because of this lithology, it is difficult to estimate limestone in the interval from 4488 to 4499 ft (1368–1371 m). For the core, the lithology log incorrectly classifies the porous limestone breccia as tripolitic chert.

Dense chert, which generally occurs at the transition between the tripolitic chert interval and the lower unaltered bioturbated limestone, does not exhibit low resistivity, but can have relatively high-density porosity (low bulk density) due to the lower silica (quartz) grain density (2.65 g/cm³) in comparison to limestone (2.71 g/cm³). Taking this into account and the fact that there is porosity observed in photomicrographs, a bulk density cutoff of 2.54 g/cm³ was used to differentiate between limestone and dense chert. If the lithology does not meet any of the criteria for shale, tripolitic chert, or dense chert it is classified as limestone.

Of the 115 ft (35 m) of core, the calculated lithology log correctly matches 92 ft (28 m), which equates to an 80% accuracy (Figure 3). The cutoffs were applied to the remaining 259 wells in the data set with GR, RHOB, and RILD logs and the derived lithology logs were used with other logs for stratigraphic correlation and as a constraint for 3-D lithology modeling.

Within the study area, the Mississippian interval is structurally and stratigraphically complex and ranges in thickness from 0 to 500 ft (0–150 m; Figure 7). It is because of this geological complexity that production from the Mississippian interval is equally complex. To ultimately relate the variability in production to the geological complexity and heterogeneity, core from one well, open-hole and calculated lithology logs for 260 wells, and 3-D seismic data were analyzed and interpreted to (A) correlate the stratigraphy and map the Mississippian interval and Woodford Shale, (B) identify the main faults and structural features, and (C) develop a 3-D stratigraphic and structural framework for the area. Forty wells with density and sonic curves were used to generate synthetic seismograms for log-to-seismic correlation to tie wells to seismically defined horizons (Figure 2). Given their vertical resolution, the 3-D seismic data were used to interpret and map three key surfaces (horizons): the top of the Mississippian interval, Mississippian Limestone (within the Mississippian interval), and Woodford Shale (Figure 7). In addition, nine stratigraphic zones within the Mississippian interval (in ascending order stratigraphically: A through I) were interpreted and mapped based on a combination of well-log signatures from gamma ray (GR), spontaneous potential (SP), and deep resistivity (RILD) logs (Figure 3). Mississippian and Woodford Shale formation tops (interpreted structural elevations from well-logs) were used to generate average velocity maps to convert the Mississippian and Woodford Shale structure maps (horizons) from time to depth (Figure 7). Using the interpreted horizons (tops) from core, well, and seismic data, a 3-D stratigraphic and structural framework (3-D reservoir model grid) was constructed for the Mississippian interval that includes the stratigraphic zones and the fault that divides the field (Figure 8). The 3-D grid has individual cells that are 100 × 100 ft (30 × 30 m) aerially and 2 ft (0.61 m) vertically for a total of 61,180,704 3-D cells. The layering (stratal geometry) within each zone was created to follow (parallel) the basal surface of each zone with truncated layers at the top of each zone to reflect the erosional characteristic of the upper surface.

Results of the correlation and mapping illustrate that, for the lower part of the Mississippian interval, because there has been less diagenetic alteration, the stratigraphic zones are somewhat laterally continuous. In contrast, for the upper portion of the Mississippian interval, much of the limestone has been altered to tripolitic chert. The alteration at the top of the Mississippian has resulted in a much more heterogeneous and discontinuous character for the limestone and chert reservoirs. A major fault (zone) exists within the middle of Tonkawa field that coincides with the eastern margin of the Nemaha uplift. Displacement along a high-angle, arc-shaped normal fault (or series of faults) has formed an uplifted fault block (Tonkawa structure) that occupies the western portion of the study area and has as much as 500 ft (152 m) of vertical displacement (Figure 8). Seismic data suggest that faulting occurred through the end of the Mississippian but did not extend into the Pennsylvanian. Also, at the top of the western fault block, the Mississippian and Woodford Shale have been completely eroded placing Pennsylvanian Shale directly on top of Wilcox sandstone (Ordovician), whereas on the downthrown side of the fault and adjacent to it, there is greater than 400 ft (120 m) of the Mississippian interval preserved (Figure 7).

Three key surfaces (interpreted as high-frequency sequence boundaries) observed in the cored well were tied to well-logs for correlation and also to compare the well-log characteristics to the core. A sequence boundary at the top of zone H, within the tripolitic chert interval, correlates to remnants of an algal–laminite bed (possibly associated with a tidal-flat setting). Another sequence boundary observed at the top of zone C correlates to a boundary between a highly bioturbated limestone that overlies a nodular-to-bedded siltstone. The surface is associated with a change in well-log values that is characterized by the GR being higher in the siltstone while being lower in the above bioturbated limestone. In the siltstone, porosity ranges from 3.5% to 6.4% on the open-hole logs and core plugs whereas the bioturbated limestone has much lower porosity (0–3.6%). In core from a nearby offset well in which the entire Mississippian was cored, sequence boundaries are characterized as either lithology bounding surfaces, disconformable shale boundaries, or altered surfaces in the tripolitic chert interval. In some cases, sequence boundaries observed in the offset cored well were not identifiable on the open-hole logs; therefore, not all sequence boundaries are likely to be identified on well-logs. The upper part of each stratigraphic zone is generally characterized by cleaning-upward intervals on the GR (decreasing GR values upward), increasing RILD values upward, and is capped by thin shales that exhibit relatively high GR and low RILD values (Figure 3).

Because of alteration and subsequent erosion, the character of the seismic reflector at the top of the Mississippian is variable. In general, when an interval of tripolitic chert is present at the top of the Mississippian, three seismically defined horizons are resolved and mappable: (1) a trough that represents the boundary between the overlying Pennsylvanian Shale and the Mississippian chert (top of the Mississippian); (2) a peak that represents the boundary between the tripolitic chert and the lower limestone (top of the Mississippian limestone); and (3) a trough that represents the top of the Woodford Shale (base of the Mississippian limestone; Figure 8). The top of the Mississippian is generally represented by a trough for areas in which tripolitic chert is present and resolvable by seismic (tuning thickness > ~ 10 ft [3 m]). However, at the top of the Tonkawa structure, where tripolitic chert is absent, the top of the Mississippian is the boundary between overlying Pennsylvanian Shale and the underlying Mississippian Limestone (Figure 8) and is represented by a peak amplitude. In general, the top of the Mississippian on the Tonkawa structure is represented by a peak (tripolite is absent), and on the downthrown block, it is represented by a trough (tripolite is present; Figure 8). This observation was followed for seismic interpretation of the top Mississippian in areas with limited well control.

The uppermost and thickest stratigraphic interval, I, is present across the southeastern portion of the field, but absent across the rest of the field. Many of the lower zones thin to the southeast (basinward). The stratigraphic intervals range from zero to over 100 ft (30 m) thick depending on their basinward location and position relative to the Pennsylvanian unconformity.

The lower zones, A to G, which comprise most of the Mississippian interval on top of the Tonkawa structure, are less than half of the entire Mississippian in the southeastern portion of the field. This is likely the result of syndepositional tectonics during deposition of the Mississippian along with the regional uplift observed along the Nemaha uplift. Due to faulting and erosion associated with the Pennsylvanian unconformity, the intervals also subcrop at the top of the Tonkawa feature (Figure 8A).

The main lithologies within the Mississippian interval in the study area are chert conglomerate, tripolitic chert, massive-to-laminated dense chert, dense chert breccia, bioturbated limestone, limestone breccia, and nodular-to-bedded mudstone (shale). For reservoir modeling, petrophysically similar lithologies were combined resulting in (A) tripolitic chert, (B) dense chert, (C) limestone, and (D) shale.

Dowdell et al. (2013b) show a correlation between P-Impedance (Z_p) from inversion and tripolitic chert abundance in the Mississippian interval. This relationship was also observed through this study, and Z_p maps were used as a constraint to aid in modeling the spatial distribution of the tripolitic chert through 3-D lithology modeling. The same 40 wells used to develop the structural and stratigraphic framework were also used to calibrate the Z_p model and determine Z_p cutoffs (Figure 9). Tripolitic chert is present when Z_p ranges from 16,000 to 50,000 ft/s × g/cm³ but is most distinct from the other lithologies below 30,000 ft/s × g/cm³. From 30,000 to 42,000 ft/s × g/cm³, there is a transition between the lithologies and predominately limestone above 42,000 ft/s × g/cm³. With these cutoffs determined from log data, a Z_p model was generated for the interval from the Oswego horizon (above the Mississippian) down to the Woodford Shale. A statistical wavelet extracted from the interval was used for tying to the wells and building the model. The Z_p curves generated from the seismic were compared to the corresponding log-calculated Z_p curves for the 40 wells used previously for the stratigraphic and structural framework. The majority of the wells show an error of approximately 0.3. Visually, the weakest correlation to the seismic-derived impedance was in the upper portion of the interval, just below the Oswego and outside of the interval of interest. The Mississippian interval showed greater correlation between the two curves. Average impedance for the tripolitic chert interval and average impedance for the limestone section of the Mississippian were mapped across the field. For the seismically defined intervals, the tripolitic chert interval has a much lower Z_p than the Mississippian Limestone interval. Given the relationship between Z_p and lithology (Figure 9), the average tripolitic chert Z_p map (Figure 10) was normalized for use as probability map to constrain the spatial distribution of tripolitic chert for the 3-D lithology model. Based on the log-scale cutoffs, the map was rescaled to be 1 when less than 30,000 ft/s × g/cm³ and 0 when greater than 42,000 ft/s × g/cm³ reflecting the higher probability of tripolitic chert occurrence when Z_p is below 30,000 ft/s × cm³ and little to no tripolitic chert when P-Impedance is above 42,000 ft/s × g/cm³.

The 3-D stratigraphic and structural framework (3-D model grid of Mississippian stratigraphic zones) was used as a first-order constraint to map the spatial distribution of lithology and porosity in the study area. Sequential-indicator simulation (SIS) was used to generate a well-constrained lithology model using (1) upscaled well-logs (Figure 3), (2) histogram of lithology percentages by zone (Table 1), (3) vertical and horizontal variograms for each lithology (Table 2), (4) a vertical lithology proportion curve, and (5) the Z_p map for the seismically defined tripolitic chert interval (Figure 10A). The upscaled logs adequately represent the original lithology logs given the layering scheme that was used. Based on the upscaled wells, the percentages of each lithology that are honored in the 3-D lithology model are 14.1% tripolitic chert, 6.4% dense chert, 77% limestone, and 2.5% shale. Zones I and H have the most significant amount of tripolitic chert. This is because the tripolitic chert is generally developed at the top of the Mississippian, and the top of the Mississippian is primarily the I interval on the hanging wall and the H interval on the footwall (up-thrown) block. Because there is a positive relationship between the low Z_p and the presence of tripolitic chert, the normalized average Z_p map from the tripolitic chert interval was used as a probability map for the horizontal trend of tripolitic chert, specifically in the two upper zones (zones H and I), which exhibit the most tripolitic chert. The resulting 3-D lithology model is illustrated as Figure 10B, and isopach maps of each lithology based on the 3-D model are depicted in Figure 11.

In general, the thickest and most laterally continuous tripolitic chert deposits exist in the southeastern part of the field. In this area, tripolitic chert average thickness is approximately 80 ft (25 m) and can be up to 120 ft (35 m; Figure 11). Although there might have been this much present at one time on top of the western fault block, it has been eroded due to uplift. Tripolitic chert is also estimated to be thicker near the main fault zone. It is possible that postdepositional faults provided conduits for meteoric water, thus creating relatively thicker in situ tripolitic chert intervals. In addition, chert conglomerate might also exits above the in situ tripolitic chert. The Range Resources 2 Jane core is located within the fault zone and contains both chert conglomerate and in situ tripolitic chert (Figure 3). The presence of both chert conglomerate and tripolitic chert is also more likely where the Mississippian thickness is greater than 425 ft (> 130 m). Well control in the northern part of the field shows the Mississippian to be approximately 425–450 ft (130–140 m) thick, and it is suggested that the greater thickness near the fault coincides with the presence of both chert conglomerate and in situ tripolitic chert. Although somewhat uniformly distributed, dense chert (Figure 11B) is thicker to the east, and this correlates with the total thickness of the Mississippian interval. Limestone thickness (Figure 11C) also correlates with Mississippian thickness (Figure 7) and becomes thicker to the east. Shale is a minor component of the reservoir and is irregularly distributed (Figure 11D).

The 3-D lithology model was used as a constraint with sequential-Gaussian simulation (SGS) to generate a total porosity model (Figure 10C). The porosity model was also constrained to upscaled porosity logs, the range of total porosity values (porosity histogram), and vertical and horizontal porosity variograms by lithology (Table 2). In general, porosity of tripolitic chert (10–50%) is much greater than for limestone (<7%; Figure 12A, B).

For comparison to the SGS-derived porosity model, the Z_p model was combined with other seismic attributes using EMERGE software (Hampson-Russell) to create a neural network to predict total porosity. The same 40 wells that were used in the inversion were used to calibrate the total porosity model. Based on the observed error, a combination of six attributes, with the Z_p model providing the highest correlation, most accurately predicted porosity. For the 40 wells, the average error in porosity between open-hole logs to the seismic-derived porosity was approximately 4 porosity units. Wells that contained higher porosity tripolitic chert generally exhibited greater error in predicting porosity than wells in limestone most likely because of seismic tuning effects. Average porosity maps based on the neural-network-derived porosity model were generated for the seismically defined limestone and chert reservoir intervals (Figure 12C, D).

When comparing average porosity maps, the SGS-derived model exhibits higher porosity values versus the neural-network porosity model (Figure 12). The SGS-derived porosity model is constrained to upscaled well-logs that have higher vertical resolution (2 ft [0.61 m]) as compared to the resolution of the seismic data. Thin tripolitic chert intervals are commonly below seismic resolution, and some very thin tripolitic chert intervals at the top of the Mississippian exhibit very high porosity (>30%) but are not captured in the neural-network-derived porosity model. The neural-network porosity model has the greatest error in the high-porosity tripolitic chert intervals. Both porosity models show similar values in the limestone intervals. Z_p stratal slices (following the top Mississippian) through the Mississippian interval show the gradual loss of porosity with depth.

One thickness and porosity anomaly is associated with the Range Resources 1-12 Austin well (Figures 2, 12, 13). A cross section between the Range Resources 1-12 Rock and 1-12 Austin wells (Figure 13) illustrates the anomalous change in tripolitic chert thickness over a short distance between the wells (2155 ft [655 m]). The Range Resources 1-12 Austin has a relatively thick (>175 ft [>53 m]) tripolitic chert interval that is apparent on the isopach and porosity maps (Figures 11, 12). A second porosity anomaly (Figure 12; south of the first anomaly) was not drilled but exhibits similar seismic characteristics. Most-positive-curvature and energy-ratio-similarity attributes generated using AASPI software (Attribute Assisted Processing & Interpretation Consortium, the University of Oklahoma) were computed to further characterize the reservoir (Figure 14A, B). The attributes are especially useful to identify karst (areas of relatively thick tripolitic chert), collapse features, faults and to estimate fracture density. The Austin 1-12 well is drilled in an area with greater tripolitic chert thickness, higher porosity, and distinct edges observed with a concave-up signature and low similarity based on most-positive-curvature and energy-ratio-similarity attributes, respectively (Figure 14A, B). This anomaly is a possible karst feature due to solution collapse at the top of the Mississippian. The adjacent Rock 1-12 well is just outside of this anomaly where tripolitic chert is relatively thin (Figure 13). Like the karst feature observed around the Austin 1-12 well, there is a feature on the north side of the study area where the Range Resources 1 Leona well is located that shows greater tripolitic chert thickness at the top of the Mississippian (Figures 14, 15). The tripolitic chert thick and possible karst-related feature has a distinct edge with a decrease in similarity and a concave-up signature.

In the study area, of the 30 horizontal Mississippian wells, 28 are producers, 1 had complete mechanical failure and never produced, and 1 had significant mechanical issues and does not accurately represent well potential; therefore, it was not considered. Cumulative oil, gas, and water production for the 28 wells includes data for 7-, 30-, 60-, 90-, and 180-day periods. Data for the time until peak-oil production were also available; that is, amount of time before oil IP took place. All of the horizontal wells were drilled and completed in the tripolitic chert interval at the top of the Mississippian interval. If there was little to no tripolitic chert present, the well path landed at the top of the Mississippian. Because of the variable lateral lengths, production was adjusted to be on a 3000 ft (915 m) equivalent lateral length. All of the wells were completed similarly, including hydraulic-fracture-stimulation stage, length, and size, and all were initially produced through a submersible pump.

Although dense chert, limestone, and shale do exhibit some porosity, tripolitic chert is the main reservoir rock for the Mississippian interval. Bubble maps comparing the early time (7-day) and late time (180-day) cumulative production for oil and total fluid (oil + water) in conjunction with tripolitic chert thickness were created to evaluate the relative impact and contribution of lithology to production (Figure 16).

Both early- and late-time cumulative fluid production of wells on the Tonkawa structure is less as compared to wells on the downthrown block (e.g., eastern side of field); tripolitic chert is thin on the Tonkawa structure as compared to the downthrown block (Figure 16A, B). This suggests that storage capacity and estimated ultimate recovery vary directly with tripolitic chert thickness. In contrast, early-time cumulative oil production shows that wells on the Tonkawa structure have higher initial cumulative oil production (Figure 16C) in comparison to wells on the downthrown block. The map of 180-day cumulative oil production shows the opposite relationship (Figure 16D). At 180 days, oil production on the Tonkawa structure has declined, and wells on the downthrown block have surpassed them. Where tripolitic chert is relatively thin, storage capacity is low, and the wells quickly reach peak production because the reservoir is easier to draw down. Where tripolitic chert is relatively thick, storage capacity is high, and wells maintain oil production for longer time periods (higher estimated recovery). However, cumulative oil production is still highly variable on the downthrown block where tripolitic chert is relatively thick; therefore, factors other than tripolitic chert thickness must impact oil production (e.g., nonmatrix features such as karst and fractures, structural compartmentalization, or stratigraphic baffles and barriers, water saturation).

The Mississippian limestone and chert reservoirs at Tonkawa field in Kay and Noble counties, Oklahoma consist of seven key lithologies: (1) chert conglomerate, (2) tripolitic chert, (3) massive-to-laminated dense chert, (4) dense chert breccia, (5) bioturbated limestone, (6) limestone breccia, and (7) nodular-to-bedded mudstone (shale). Of the seven lithologies, four are identifiable on open-hole logs: tripolitic chert, dense chert, limestone, and shale. The lithologies stack to form a stratigraphic and structural framework with nine reservoir zones. The field is divided into an upthrown western block and a downthrown eastern side, which are offset by as much as 500 ft (152 m) of vertical displacement. Erosion of the western block has removed over 450 ft (137 m) of the Mississippian and Woodford Shale such that, locally, Pennsylvanian shales lie directly on the Ordovician Wilcox sandstone. On the eastern side of the field, greater than 400 ft (120 m) of Mississippian strata are present.

Tripolitic chert is most common at the top of the Mississippian, but deeper cycles within the Mississippian are also capped by high-porosity, low-resistivity chert. Open-hole logs and seismic data show that the top of the Tonkawa structure is primarily devoid of tripolitic chert whereas on the downthrown fault block there is a thick tripolitic chert interval between 20 and 120 ft (6–36 m) at the top of the Mississippian. Tripolitic chert porosity ranges from 10% to 50% on open-hole logs. Although cherty limestone is abundant, average porosity is <3%. Volumetric attributes including energy-ratio-similarity and most-positive-curvature could reveal karst-related features where a decrease in similarity and a concave-up signature exists. Wells drilled into such features show thick tripolitic chert zones whereas adjacent wells do not.

Well-constrained 3-D lithology and porosity models that are conditioned to core, well-log, and P-Impedance data illustrate the variable distribution of the Mississippian reservoirs. When compared to production data, there appears to be a direct relationship between fluid (oil + water) production and tripolitic chert thickness. Areas with thick tripolitic chert have higher cumulative fluid production than areas that have thin to no tripolitic chert development. There is not a direct relationship between tripolitic chert thickness and oil production, indicating there must be other factors that play key roles in hydrocarbon production (e.g., karst and fractures).

We thank Range Resources for providing 3-D seismic, core, well-log, and production data. Funding was provided through the sponsors of the Reservoir Characterization and Modeling Laboratory at the University of Oklahoma and the “Mississippi Lime” Consortium: Chesapeake Energy, Devon Energy, QEP Resources, and Sinopec (Tiptop Oil and Gas). We thank CGG and Schlumberger for Hampson-Russell and Petrel software, respectively. The authors appreciate the constructive reviews of Mark Longman and an anonymous reviewer.