Fifth Quarterly Report

A Project of
Fundamental Geoscience
Research and Development
BDM-Oklahoma
U.S. Department of Energy
National Oil and Related Programs

Prepared by:
William S. Dershowitz
Paul R. LaPointe
Golder Associates Inc.
Redmond, WA

Herbert H. Einstein
Violeta Ivanova
Massachusetts Institute of Technology
Cambridge, MA

This report describes progress on the project, "Fractured Reservoir Discrete Feature Network Technologies" during the period March 1, 1997 through May 31, 1997. The report presents summaries of technology development for three active research areas: (1) research related to development of the hierarchical fracture model, (2) discrete fracture analysis in support of the TAGS process, and (3) development and implementation of the Windows 95 data analysis system. In addition, the report provides information on project status, publications submitted, data collection activities, and technology transfer through the world wide web (WWW).

Hierarchical fracture model development made significant progress during the quarter, as the numerical model was implemented based on the geological database developed during the project. The hierarchical fracture model developed during the quarter is built from the depositional model of prograding and aggrading carbonate shoals, published data on the regional tectonic history of the Permian Basin, and the new geologic information, provided by Marathon Oil. Initial model parameters are based on estimates derived from the site database. Preliminary simulation results indicate that the proposed algorithms of the 3D hierarchical model will be well suited for the Yates field.

Research on derivation of spatial parameters for fractured reservoirs during the quarter focused on algorithms to convert fracture patterns in boreholes and outcrops to gridded data in formats which can be directly analyzed for geostatistical and fractal properties, and also directly entered to StrataModel. The procedures developed include a rule-based approach to derive spatial location model parameters.

To support the linkage of discrete fracture approaches to conventional reservoir simulators, we developed an approach for simulation of the thermally-assisted gravity segregation (TAGS) process within the discrete feature approach. Thermal measurements collected during the quarter confirm the usefulness of this approach, particularly when compared to single porosity continuum approaches.

This quarterly progress report describes activities during the period March 1, 1997 to May 31, 1997. Work was carried out on thirteen separate tasks. The major activities in the quarter were in research related to development of the hierarchical fracture model, implementation of a new discrete fracture network approach for simulation of TAGS reservoir stimulation at the Yates field, and development and implementation of the Windows 95 data analysis system. Major efforts were also made for preparation of the project annual report, and for updating of the WWW site.

During the quarter, Paul LaPointe, Thorsten Eiben, and Eugene Wadleigh attended the Fourth International Reservoir Characterization Technical Conference, Houston, Texas, to present the paper, "Compartmentalization Analysis using Discrete Fracture Network Models."

The following project deliverables were scheduled or submitted during this quarter.

This section describes progress during the quarter for each of the active tasks.

During the quarter, Marathon Oil Company collected fracture and production data from the project study site and provided this data to Golder Associates to provide the basis for the initial data warehouse. The following additional data was donated to the project during the quarter:

This data was assembled and is being incorporated into the project World-Wide-Web (WWW) site (Task 5.1.2). Figures 2-1 (2-2, 2-3 ) through 2-4 present examples of the data provided by Marathon during the quarter for the tract 49 steam testing carried out within the project scope.

During the quarter, MIT completed the interpretation of regional and local geologic mechanisms which may have caused fracturing in the Yates field reservoir rocks. A model for the historical evolution of the fracture network was developed and presented to Marathon Oil geologists. The model is based on depositional geology, geotechnical interpretation of principal stress directions and magnitudes, and new data (second derivative maps) provided by E. Wadleigh and E.S. Thompson from Marathon Oil. Based on the conceptual model for hierarchical fracture network evolution, and some new algorithms of the 3D hierarchical model, MIT initiated numerical modeling of the reservoir fracture network.

The Yates field reservoir produces from four formations of Middle Permian (Guadalupian) age. The oldest and most significant formation is the San Andres, which consists of more than 400 feet of dolomite. The best reservoir rocks in the Yates field are fractured, coarse-grained dolomites of the San Andres on the east side of the field, overlying low-quality deep marine dolomites. On the west side, the San Andres consists of clean fine-grained dolomite, interbedded with thin layers of shaley dolomite, grading downward into deeper quality shoals. The three oil-producing formations above the San Andres are the Grayburg silty dolomite, the Queen siltstone and dolomite, and the basal clastic portion of the Seven Rivers anhydrite (Craig 1990; Tinker and Mruk 1995).

The upper portion of the San Andres consists of a ramp, overlain by three major cycles of eastward prograding and aggrading carbonate shoals. On the east, rigid grainstones were deposited under high energy shallow subtidal conditions over deep marine carbonates with significant potential for dewatering and compaction. In contrast, on the west side, compactible carbonate and argillaceous mudstones were deposited in a lagoonal and intertidal low-energy environment. The distribution of lithofacies with different grain sizes and compactibilities has been observed in logs and cores throughout the field, as well as in other fields on the Central Basin Platform (Craig 1990), and in outcrops of the San Andres Formation and the Capitan Reef in southeast New Mexico (Sarg and Lehmann 1986). The presence of caves and other karst features, which is most intense on the highest portions of the major cycles of carbonate shoaling, suggests that high-standing parts of the San Andres were exposed as limestone islands several times during periods of fall of the Permian sea level (Craig 1988; Tinker et al. 1995).

The present-day structure in the Yates field Permian rocks is a broad asymmetrical dome with a northwest oriented anticlinal axis. The apex of the structure on the east side of the field is associated with the greatest accumulation of less compactible, grain-supported sediments. The structure is gently dipping to the west, in the area of fine-grained, compacted mudstones (Craig 1990). A thin layer of silty dolomite in the Seven Rivers formation about 200 feet above the top of San Andres, referred to as the "M horizon", is used as a datum for reconstruction of paleoelevations, existing before the formation of the field anticline. This layer, which can be mapped throughout the field and along the Central Basin Platform, is considered to have been essentially horizontal during deposition (Craig 1988; Tinker et al. 1995). Figure 2-5 and Figure 2-6 show the present surfaces of the Seven Rivers M horizon and the San Andres top in Tract 17 and Tract 49, respectively. The variation in elevations in Tract 17 is up to 500 ft, the steeper slopes being to the northeast towards the paleo basin. The relief in Tract 49, which is on the apex of the field structure, is up to 250 feet.

Figure 2-7 shows the present thickness of sediments between the San Andres top and the M horizon of the Seven Rivers in tracts 17 and 49. In the three-dimensional graphs this thickness is plotted as the depth of the San Andres top under the M horizon. High negative values indicate thick overlying sediments, i.e., topographic lows (sinkholes or compactional sags in the carbonate blocks) on the erosional surface which existed on the San Andres top before the deposition of the Grayburg sediments. Coupled closed highs and lows (steep gradients) may indicate early differential settlement of carbonate blocks. If the M silty layer was horizontal during deposition and there has not been any change in thickness since then, Figure 2-7 also illustrates the shape of the erosional surface (although the elevations were different). The karst surface has a maximum variation in elevations of about 80 ft, the steepest slopes being towards the sinkholes (closed highs).

Karstification of the San Andres formation occurred when the carbonate build-ups were exposed as limestone islands and subjected to subaerial erosion during lowering of the water level several times in the Middle Permian Guadalupe period (Tinker et al. 1995). Dramatic increase in effective loading with loss of buoyant support, caused by dewatering after deposition of the San Andres, must have led to collapse of caves and subsequent compaction of the carbonate muds under less than 200 feet of overburden prior to deposition of the M horizon (Wadleigh, pers. comm.).

Most of the Middle Permian limestone of the San Andres and Grayburg was dolomitized during the Late Permian. According to the seepage-reflux model (Adams & Rhodes 1960; Tucker & Wright 1990), hypersaline magnesium-rich brines seep downward from saline lakes (salina) and salt flats (sabkha), displacing the less dense water from the pores of permeable back-reef limestones, and converting them into dolomite. This model is commonly accepted today to explain the dolomitization of intertidal and subtidal facies, underlying sabkha and salina evaporites. During the deposition of the Seven Rivers evaporites in the Yates field, as well as throughout the Central Basin Platform, magnesium brines descended through the limestones of the San Andres and Grayburg and converted them into dolomites (Craig 1990).

Core description (Tinker & Mruk 1995) shows that the original fabric of the San Andres limestones was preserved during dolomitization. This indicates that dolomitization must have occurred at abundant nucleation sites, since this is an essential factor for retention of the crystal forms of the limestone (Tucker & Wright 1990). Abundance of dolomite nucleation sites is common in fine limestones, such as the mudstones on the west side of the Yates field. Dolomitization of the coarser-grained limestone on the east side probably occurred at fewer nucleation sites. Some of the large pores of the east side grainstone may have been produced later by leaching of limestone which was not dolomitized.

Dolomite is more brittle than limestone because the carbonate microcrystals "shrink" when calcite (limestone) is converted into dolomite via replacement of Ca by Mg (Tucker & Wright 1990). The process creates intercrystalline volumetric strains which may cause the rock to fracture more readily under imposed stresses. The different degree of dolomitization of lime mudstones and grainstones may also explain the different competency of the San Andres dolomite today. In the Yates field it has been observed that fractures, the result of brittle rock failure, are more abundant in the low porosity mudstones on the west side than in the porous grainstones to the east. More massive carbonate shoal build-ups are mechanically stronger which results in a smaller number of fractures with large aperture. Thin carbonates undergo intense fracturing with numerous short, low conductivity features (Tinker & Mruk 1995; Tinker, Wadleigh, pers. comm.).

Fractures comprise about four percent of the total porosity of the reservoir rocks. The immense network of interconnected pores in the San Andres formation, including the fractures, is a major factor for the high productivity of the Yates field reservoir (Craig 1990; Tinker & Mruk 1995). Fine intercrystal pores are predominant in the dolomitic mudstones on the west side of the field. Larger, intergrain pores are characteristic for the dolomitic grainstones to the east. During the periods of karst formation by island and subaerial erosion, many of the pores and fractures were enlarged (Craig 1988; Tinker et al. 1995).

Although comprising only a small portion of the Yates field storage capacity, the fracture network in the Permian reservoir rocks provides significant pathways for anisotropic permeability and secondary recovery of oil. The formation of the fracture network can be attributed to either the local or regional stress regime. At any moment in time and at any given location during the period of greatest interest (Middle to Late Permian) fracturing occurred if the combined action of local and regional stresses exceeded the strength of the rock.

The Permian, during which the reservoir rocks were deposited, was a tectonically quiet period, nor was there major tectonism in the area from the Permian up to the present day. The tectonic framework (Midland Basin - Central Basin Platform - Delaware Basin) which controlled the deposition of Permian rocks developed during the earlier, tectonically active, Pennsylvanian period (Craig 1963; Hills 1970; second quarterly report).

Based on regional fold and fault patterns in southeast New Mexico and West Texas, Hills (1970) derived the predominant stress directions on the Central Basin Platform during the period of tectonic activity from the Late Mississippian through the Pennsylvanian and to the Early Permian. Figure 2-8a illustrates the tectonic forces active from the Late Mississippian to the Middle Pennsylvanian, when the maximum compressive stress was rotated from east-west to about N65° E. The regional structures, created by the older east-west stress, consist of two conjugate sets: a major fault set, striking N50° W to N65° W, and another widely spaced set of faults striking N55° E to N80° E. The later NE/SW stress produced folds striking N35° W to N23° W in the earlier Paleozoic rocks, overlain by the Early Pennsylvanian sediments.

According to Hills (1970), relaxation of east-west stress and increase of the stress in a north-south direction created the regional stress system in Figure 2-8b during the last period of tectonic activity from the Late Pennsylvanian to Early Permian. Crustal extension in east-west direction, associated with the sinking of the Midland and the Delaware basins, left only the Central Basin platform emerged above the ancient seas. The maximum principal stress direction in Figure 2-8b, acting slightly west of north, was derived on the basis of reorientation of the regional stresses radially around the Marathon salient (in the southernmost part of the area). To the north of the Marathon salient a system of N10° W to N15° W strike-slip faults was created during that period, the most prominent being the West Platform fault. The strike of the faults, however, is more consistent with a regional maximum stress, acting slightly east of north (shown with a broken line in Figure 2-8b). According to rock mechanics principles, a fault develops in the plane of the intermediate principal stress (in this case, the vertical stress of gravity), and makes an acute angle with the maximum principal stress direction.

The relaxation of east-west stress and subsidence continued after the Early Permian. It was especially prominent during the Late Permian (Ochoa) when some downward movement may have occurred on the west side of the West Platform fault. However, there is no evidence anywhere on the Central Basin Platform that dip-slip movement along old Pennsylvanian faults was large enough for the deep faults to penetrate upward into Permian reservoir rocks. Throughout the platform, the orientations of fold axes are very consistent, but generally differs at least 30° from the predominant strikes of Pennsylvanian cross faults. This led Hills (1970) and Craig (1990) to conclude that the primary geologic process during the Permian was sedimentation, and that it is unlikely that faults in older strata controlled the structure in Late Permian reservoirs.

Because there have been no strong regional tectonic forces on the Central Basin platform after the Early Permian to present day (Hills 1970), it seems most likely that the maximum principal stress has been the vertical stress of gravity. An east-west regional crustal extension constitutes the minimum regional principal stress. The intermediate stress is probably oriented slightly east of north, the inferred direction of maximum stress during the period of tectonic activity which ended in the Early Permian. This orientation of the principal stress system is supported by the geometry of the fracture system in Cretaceous limestone in the Yates field. Figure 2-9 shows the strike orientations of outcrop fractures, compiled from five surface outcrops. Almost all of these fractures are nearly vertical joints, cutting across at least several beds of Cretaceous limestone (Figure 2-9b). The most prominent joint set strikes slightly east of north; another set is perpendicular to the first. Figure 2-9c shows the strikes of Cretaceous faults. Most of these faults are small, cutting across one to several beds.

Orthogonal joint patterns in sedimentary rocks in tectonically quiet regions are quite common (Stearns & Friedman 1972). Price (1966) and Price & Cosgrove (1990) explain the development of such patterns with rotation of tensile stresses associated with crustal extension and uplift. According to their theory, the major joint set develops perpendicular to the minimum principal stress. After strain relaxation due to this initial fracturing, the minimum and intermediate principal stresses temporarily exchange their directions. Then a second set, orthogonal to the first set, develops. Figure 2-10 illustrates the formation of the fracture system in Cretaceous limestone in the Yates field according to such a mechanism. The major set of nearly vertical joints, striking north to N10° E, developed parallel to the maximum vertical stress and perpendicular to the east-west "tension" (relaxation of compressive stress). After strain relaxation in the east-west direction, the minimum and intermediate principal stresses temporarily switched their orientations. This caused the formation of the second joint set, striking east-west, perpendicular to the new minimum principal stress. After release of elastic strains in the north-south direction, the minimum and intermediate principal stresses rotated again to their original orientations.

In the absence of significant regional tectonism during the Permian and later periods, Marathon Oil geologists generally consider two local mechanisms responsible for the formation of the structure in the Yates field Permian reservoir (Craig 1990; Tinker and Mruk 1995; also, Wadleigh, Curran, Tinker, pers. comm.). One is differential compaction between the highly compactible mudstones and the relatively rigid shoal grainstones. Another mechanism is dip-slip movement in the late Permian along faults in Pennsylvanian rocks about 5000 ft. below the reservoir. It has to be noted that the essential mechanism which formed the field anticline was drape folding (bending) of carbonate rocks, whether the underlying event was differential compaction, deep fault movement, or both. It is still important to know what geologic event formed the anticline, since this will provide information about stress directions and strain rates, and thus how the reservoir rocks fractured in relation to the field structure.

The anticlinal structures of oil fields throughout the Central Basin Platform are aligned along depositional strikes. This and the different compactibilities of the lithofacies led Craig (1990) to suggest that "differential compaction during and following deposition of shelf margin skeletal grainstone bars and associated lagoonal and intertidal mudstones was the dominant structure-forming process along the San Andres - Grayburg oil reservoirs."

There is field evidence which suggests that folding occurred at the end of the Late Permian (Ochoa), after deposition of Salado salt and before deposition of Rustler carbonates and clastics (Figure 2-11a). The formations between the reservoir rocks and the Salado salt (the middle and upper Seven Rivers, sandstone and siltstone of the Yates, and anhydrite and dolomite of the Tansill) are relatively constant in thickness and lithologies over the field. This indicates that they were deposited as horizontal layers, once the Grayburg, Queen and lower Seven Rivers sediments had reduced the relief by filling the topographic lows of the San Andres karsted failure surface. In the Permian Basin an angular unconformity separates the Salado salt and the Rustler formation. In the Yates field the Salado salt is almost completely missing. Where present, the Salado surrounds the field anticline, due to subaerial erosion from the apex of the anticline (Craig 1963).

The present configuration of the reservoir strata (Figures 2-5 and 2-6) also suggests that folding occurred at the end of the Late Permian. There is a remarkable similarity between the structure on the top of the San Andres and in the M horizon, which shows that they were most likely folded together after the deposition of the Seven Rivers anhydrite. The structures of the internal shoals are also very similar to that of the San Andres top and the Seven Rivers M horizon, especially in Tract 17 where they are actually mapped as tops of carbonate layers and bases of shale beds from log analysis. In Tract 49, where the shales are missing, the shoals are only projected as eastward prograding clinoforms.

From a mechanical point of view, differential compaction due to the overburden would occur gradually, with gradually increasing vertical stress and strain. This most likely happened during deposition and shallow burial, when the mudstones on the west side of the Yates field slowly compacted more than the grainstone shoals to the east. However, the slow compaction was probably punctuated by rapid effective stress loading and compaction during subaerial exposure of the limestone shoals during relative sea level fall. On the east side, skeletal carbonate shoals, cemented and less compressible, had prograded over highly compressible lime muds of the basin. This process was intensified by dewatering during relatively low paleo sea levels, when the increase of effective stress throughout the formation must have led to greater compaction (Wadleigh, pers. comm.).

By the end of the Late Permian, the Middle Permian sediments were already relatively compacted. Because limestone does not become ductile until depths of at least several thousand feet (Stearns & Friedman, 1972), the limestones were brittle under the relatively thin (700 ft.) overburden. Also, according to the seepage-reflux model, most of the limestone had already been dolomitized in the evaporitic environment of the Late Permian. If folding with high loading and strain rates occurred in the brittle dolomite and the strength of the rock was exceeded, a significant structure-related fracture network would develop.

Theoretically, a post-Salado movement along faults in strata underlying the Permian rocks could provide such a structure-forming mechanism. However, there is no field evidence on the Central Basin Platform that such movement occurred. Furthermore, most core fractures in the Yates field are tensile joints, while significant faulting would have produced numerous shear fractures in the Permian rocks. Therefore, one can accept the assumption that most of the field structure was formed by drape folding due to differential compaction of sediments. The following hypothesis about the combination of stresses which are likely to have acted on the Central Basin Platform at the end of the Late Permian can explain why most of this compaction occurred after the Salado salt deposition (Figure 2-11b).

One of the main reasons for the high production from the Yates reservoir is the presence of natural high fluid pressures in the reservoir rocks, controlled by a regional aquifer on the Central Basin Platform. Field data from oil fields on the platform indicate that paleo flow occurred from the northwest to the southeast (Craig 1990). Average fluid pressures in Yates reservoir rocks at a datum of 1050 feet above the sea level were 800 psi (5.5 MPa) when the field was discovered. Today, after large amounts of oil and water have been extracted from the reservoir, the average fluid pressures at the same datum are 500 psi (3.4 MPa) (Wadleigh, pers. comm.). During the Permian Guadalupe period, however, the aquifer in the San Andres limestone was still a phreatic aquifer. Today’s high pore fluid pressures most probably developed while the aquifer slowly changed from phreatic into confined during the deposition of the Seven Rivers anhydrite, which sealed the Yates reservoir.

By the end of the Salado period sediments with total thickness of about 600 ft. were deposited above the San Andres limestones/dolomites. This number is calculated, using today’s average thicknesses of the formations above the San Andres, as follows:

Grayburg		Queen		Seven Rivers		Yates- Tansill		Salado		Total
50 ft.	+	50 ft.	+	400 ft.	+	50 ft.	+	50 ft.	=	600 ft.

In Tract 17 the San Andres formation has an average thickness of about 150 ft. above the datum 1050 ft. above sea level. Using a bulk density of 2,450 kg/m³ for the medium compacted carbonates, clastics, and evaporites, the specific weight of the overburden above the San Andres at the end of Salado can be calculated as:

where g is the acceleration of gravity. The vertical stresses at the datum at elevation 1,050 ft. is given by:

These calculations are approximate because the density of the material and the fluid pressures in the San Andres varied with depth and location. Nevertheless, the calculations show that at the end of Salado the lithostatic stress, and the pore fluid pressure became equal, although not simultaneously, at various points within the San Andres formation. Therefore conditions of zero effective stresses occurred at different locations throughout the San Andres, where:

and

at the datum used in the calculations. Due to the loss of effective stress at the mineral contacts, combined with increased overburden by younger sediments, maximum volume reduction must have occurred in the mud-supported sediments. The enhanced compaction transformed the mudstones on the shallow west side and the deep east side into the present matrix of very low porosity. Much less total volume change occurred in the cemented sediments on the upper east side, since there was less room for collapse into voids of grains, unsupported by other grains. The temporary conditions of zero vertical effective stresses can explain why, at the end of the Late Permian, substantial differential compaction occurred in the San Andres formation, and created the dome structure of the Yates field reservoir. The formations above the San Andres stretched to accommodate the convex upward shape of the dome, but retained their thickness.

Zero vertical effective stress does not exclude the possibility for faulting in deeper strata. Only additional field data from deep wells can indicate whether reactivation of Pennsylvanian faults also played a major role into the formation of the Yates field structure. Therefore, differential compaction of limestones and dolomites, due to a combination of overburden and high fluid pressure in the San Andres, created by the sealing of the reservoir at the end of the Late Permian, is accepted herewith to explain the formation of the Yates field structure. The drape folding occurred at strain rates high enough to produce a significant fracture system in the brittle carbonate rock of the San Andres. Some of the fractures probably propagated into the younger formations which were stretched and bent together with the San Andres. It is also possible that some, but not many, fractures propagated into the strata underlying the San Andres.

The present geometry of the fracture system in the Yates field Permian reservoir probably developed in the following order under the regional and local stresses, described in the previous section. First, individual cracks opened during deposition and shallow burial of limestones in the Middle Permian (Section 2.2.2.4.1). The regional stresses might have caused opening of field-scale systematic joints (Section 2.2.2.4.2). Next, dolomitization of the limestones in the Late Permian significantly increased the brittleness of the rock and the number of microcracks. Most of the present fracture system in the Permian reservoir developed during the folding at the end of the Late Permian, by coalescence of cracks along the planes of maximum shear and tension, defined by the anticline curvature (Section 2.2.2.4.3). Under the regional stresses some of the structure-related fractures were probably connected by secondary fractures in post-Permian time, and formed field-scale lineaments (Section 2.2.2.4.4).

Figure 2-12 illustrates the possible mechanism of fracture initiation in the San Andres limestone during deposition and shallow burial in the Middle Permian (Lower Guadalupe). Figure 2-12a schematically represents the differential deposition of carbonate lithofacies: compactible mudstones to the west, and rigid grainstones, prograded over marine muds, to the east. Under the increased overburden, the sediments were compacted and lithified into limestone. Due to different compactibilities, differential compaction caused some drape folding (Figure 2-12b). Cracks probably opened on the crest of the shoal on the east side due to stretching of the strata, and between the shale layers on the west side due to increased vertical shear strains. The same sequence of deposition, compaction and crack initiation continued in all subsequent shoal cycles. Stretching of the beds on the top of the carbonate shoals, associated with the drape folding, defined planes of weakness, perpendicular to the beds, for fracture propagation and coalescence (Figure 2-12c).

According to Craig (1988), caves and other karst developed in high-standing, exposed parts of the San Andres during low sea-level stands of the Permian. Analysis of 3D karst distribution in the San Andres by Tinker et al. (1995) showed that sea level fall and island erosion occurred several times during the Permian. Figure 2-13 illustrates the island hydrologic model, according to which karstification is caused by the hydrodynamic action of freshwater lenses under the limestone islands. Karstification was especially intense at the edges of the islands (zone A) where more pronounced water circulation leads to concentration of dynamic stresses and strains and probably local failure of the carbonates. Figure 2-13 also illustrates a mechanism which may have caused intense fracturing of the carbonate shoals during dewatering of the San Andres formation. When the sea level fell, the total vertical stress remained constant because the formation was still saturated, although part of it was above the water. In such cases, pore pressure decrease and effective stress increase led to gradual settlement and compaction. However, dewatering of the basinal lime muds, underlying the carbonate shoals,

probably occurred at slower rates (drainage is usually inhibited in a low porosity, clayey material). Due to the decreased overburden and the retention of high pore pressure, a condition of zero vertical effective stress (equation 2-4) may have occurred in the lime muds on the deep, east side of the field. Under the weight of the overlying shoals, rapid compaction of the muds occurred upon dewatering. This lead to the collapse and fracturing of the overlying sediments.

Lineaments of caves and associated high well production from the reservoir today can be related to intensified karstification along the fracture network, existing in the San Andres formation during the Permian. Solution and cave formation must have been especially intense along the open joints on the crests of the carbonate shoals, exposed as limestone islands. According to Craig (1988), paleo topographic depressions (sinkholes) developed on the San Andres unconformity due to maximum solution at the fracture intersections. If this fracture system had been created by the regional stresses (east-west relaxation of compressive stress) in unfolded sediments, it would have been very similar to the one which later developed in Cretaceous limestone (Figures 2-9 and 2-10). However, some differential compaction had already gently folded the Yates field Permian strata and pre-defined the preferential orientation of maximum tension to be on nearly vertical planes striking parallel to the anticlinal crest (i.e., to the alignment of limestone islands). A second derivative map of the present thickness of strata between the San Andres top and the Seven Rivers M horizon, shown in Figure 2-14, suggests that this alignment was in two orthogonal directions: to the northwest and to the northeast. Figure 2-15 illustrates a field-scale system of faults/drape folds which may exist in the Yates field. The system in Figure 2-15 has been derived on the basis of the map in Figure 2-14, combined with a dip variation of Permian strata flexure maps (Wadleigh, pers. comm.).

Figure 2-16 shows the Yates reservoir rocks at the end of the Late Permian. By that time, the San Andres formation had been completely dolomitized in the evaporitic environment of the Upper Guadalupe (Seven Rivers). Dolomitization increased the brittleness of the rock and possibly caused opening of a great number of microcracks. Some fractures probably propagated under the increased vertical stresses to form the system, shown in Figure 2-16a. However, most of the present day connectivity of the fracture network in the reservoir rocks most likely developed later, due to the intensive folding following the deposition of Salado salt.

According to the model above, post-Salado folding occurred due to the rapid compaction of argillaceous mudstone on the upper west side and on the lower east side of the field. Several factors intensified the fracturing at that time: the high fluid pressure, the high strain rates, the high extent of microcracking, and the relatively low confining pressure (600 ft. of overburden). The effect of fluid pressure, strain rate, and confining pressure on the brittle behavior of rocks is discussed by many authors (e.g., Singh, 1981).

Due to the high pore water pressures in the San Andres at the end of the Permian, the horizontal effective stress (s _h) most likely became tensile. The horizontal stress in normally consolidated deposits is normally less than the lithostatic stress. The horizontal effective stress (s _h'), which is equal to the total horizontal stress less the pore fluid pressure, can be calculated as:

Additional tensile stresses were induced during the formation of the dome structure due to the stretching of dolomite beds. Rocks have a very low tensile strength, often assumed to be zero. The tensile strength of the brittle dolomite of the San Andres was most likely very low (on the order of 4-6 MPa) at the end of the Late Permian, considering the negative effects of the fluid pressure, the strain rate, and the intense microcracking. Tensile stresses associated with the post-Salado folding of the San Andres formation probably exceeded the strength of the dolomite, and created predominantly tensile joints, related to the curvature of the newly-formed dome-like structure (Figure 2-16b). The folding of reservoir rocks significantly increased the fracturing of the dolomite matrix, and also intensified the fracture connectivity along the field-scale lineaments (Figure 2-15) in the zones of strain concentration.

Most of the fractures in the present day network are indeed tensile joints, which can be related to the reservoir structure. Figures 2-17 and 2-18 illustrate the orientations of fractures determined from log analysis of resistivity profiles from nine wells in the Tract 17 and 49 area. Rosette diagrams of fracture strikes are shown together with structure maps (elevations above sea level) of the San Andres top in Tract 17 and 49. In Figure 2-19 the predominant fracture strike orientations are superimposed on structure maps of the Seven Rivers M horizon in Tract 17 and 49, respectively. Since the M horizon was probably deposited as a horizontal layer, its structure today is a better indicator of the folding geometry.

Figure 2-20 shows four types of fractures which can be associated with the field asymmetric anticline. On the crest of the structure, most fractures are concentric tensile joints created by the radial stretching of the dome crest (type 1 in Figure 2-20). Most of the fractures in Tract 49, which is on the apex of the dome, are of this type; they strike approximately perpendicular to the slope of the structure.

The top of Tract 17 is in the zone of transition from rigid grainstones (including a local peak of the structure) on the east side to compactible mudstones to the west; downward the reservoir rock in Tract 17 grades into a better quality more rigid grainstone. The fractures in Tract 17 are of types 1, 2 and 3, shown in Figure 2-20 on the flank of the anticline and in the foreland. On the flank of the anticline, most fractures are extensional joints of type 1. Gravitational sliding can cause slope-parallel compression to develop in the foreland and locally on the flanks. This stress created the joints of type 2 in Figure 2-20. According to Price & Cosgrove (1990), who developed a model for jointing of mildly deformed sedimentary rocks, tension joints of type 1 and 2 constitute the predominant type of fracturing in rocks of low tensile strength. Also, according to their model, if some slight buckling occurs in the foreland due to the compression from higher parts, then an additional joint set (type 3 in Figure 2-20) may develop. Only in the strongest rocks, under high differential stress, will shear fractures (type 4) develop as well.

Figure 2-20 also shows the relation of fractures to the anticline in plan view in Tract 17 (crest axis is AA’ in Figures 2-17 and 2-19b). Because the anticline curves to the northwest, there is additional crest-parallel extension on the east flank of the fold. The asymmetrical shape of the field structure in Tract 17 suggest that the fractures observed at wells YU1711 and YU2511 represent flank to foreland type 2 fractures. The fractures in wells YU1755 and YU17D5 probably represent foreland, type 3 fractures. Which fracture type is predominant at a given location depends on the local maximum curvature of the structure.

Once the structure related fracture system developed and the folding-induced strains were accommodated, the regional stress system in the Yates field became predominant again. In the regional system, the lithostatic stress is the maximum principal stress, and an east-west relaxation of compressive stress constitutes the minimum principal stress. This stress regime favors vertical joints, striking predominantly north-south. It is possible that such joints developed after the Permian and connected the structure-related fractures to form field-scale lineaments. Figure 2-21a shows two major modes for fracture coalescence of two parallel inclined cracks under a vertical compressive stress (Bobet, current Ph.D. research, MIT). In the case when the cracks are collinear, a shear crack propagates between their edges to connect them. In the case when the two initial cracks are not collinear, they are connected by coalescence of two tensile wing cracks, which originate at their edges and propagate parallel to the maximum compressive stress. In the Yates field reservoir rocks, where a large number of fractures of various orientations existed after the Permian, fracture coalescence under the regional stresses would occur as shown in Figure 2-21b. Both types of coalescence, shown in Figure 2-21a, would occur, depending on the relative orientation of fracture pairs and their distance from one another. Most of the fractures, created in relation to the anticlinal structure (type 1, 2 and 3, in Figure 2-20), were parallel or perpendicular to the general trends of the asymmetric anticline (northwest and northeast). Therefore, field-scale lineaments, created by the fracture coalescence, would have the same predominant orientations.

Considering the hierarchical development, discussed above, the fracture network in the reservoir rocks can be divided into three distinct systems: the fractures which developed prior to the post-Salado folding (System 1); the fractures which were created in relation to the reservoir structure during the folding (System 2); and the fractures which opened in post-Permian time (System 3), and increased the connectivity of System 2.

System 1 consists of vertical fractures, created prior to the intense folding of the San Andres dolomite at the end of the Permian. Field-scale linear features (Figure 2-15) have been interpreted as faults and associated drape folds (Fitzsimmons et al. 1997; Wadleigh, pers. comm.). The strike of these linear features has been determined on the basis of two criteria: 1) lineaments of greatest thickness of sediments between the San Andres top and the Seven Rivers M horizon, possibly due to intense karsting along early field-scale joints; and 2) zones of greatest change of dip on the crest of the reservoir asymmetric anticline. The linear features shown in Figure 2-15 probably consist of multiple connected fractures, and represent zones of high fracture intensity. The dip of the fractures is near the vertical, since they were formed in conditions where the lithostatic stress was the maximum compressive stress.

Prior to post-Salado folding, System 1 possibly contained many fractures striking approximately north and east, according to the model illustrated in Figure 2-10. Figure 2-22 shows fracture sets identification based on dip for well YU1711. The fracture set dipping more steeply than 75 degrees, is indicated as S (for "steep"). Many of the S-fractures probably belong to System 1. The predominant strike of S-fractures at this location is sub-parallel to the nearest linear fracture zone (line marked axis of anticline in Figure 2-17). During later folding, the width and the transmissivity of the linear zones in Figure 2-15 most likely increased due to high fracture intensity caused by tensile strain concentration in the zones of maximum curvature on the crest of the asymmetric anticline. The predominant orientations of the younger fractures in the zones are most likely sub-parallel to the greatest local curvature of the asymmetric anticline.

The persistence of System 1 needs to be modeled stochastically, since the fracture extent at depth is not obvious. However, two factors can significantly reduce the uncertainty. First, System 1 initiated predominantly on the crests of the major shoaling cycles and propagated downward. Second, the fractures of System 1 were affected by the karstification of the San Andres during the Permian. Therefore, to find the extent of System 1 at depth, one needs to do best fitting via trial-and-error to the cave distribution in the San Andres formation. The fractures formed in limestone prior to dolomitization and probably not all of them survived the diagenesis. Also, many of the fractures are at least partially filled with precipitated calcite. Therefore, even if the System 1 fractures extend across the entire depth of the reservoir, in terms of transmissivity, because of their filling, they may not be persistent.

The fractures of System 2 are by far the most numerous of all fracture sets in the reservoir. This is due to the combination of factors which acted during the formation of System 2 at the end of the Late Permian: high strain rate, high fluid pressures, very brittle material, etc. Most of the fractures, determined from log analysis, belong to System 2. Hence any rosette diagrams of all fracture strikes from log analysis actually show the predominant orientation of the structure-related fractures. In Figure 2-22 fracture sets dipping 47°-74° are indicated as D (for "dome"). The fracture set identification in Figure 2-22 is only approximate; some of the steep S-fracture may actually belong to System 2, since a structure-related system also includes vertical fractures.

System 2 fractures will be generated with the three-dimensional hierarchical model. The parameters, describing the system, are as follows:

The number of fractures observed in cores is lower than that determined from log analysis, although cores were taken close to the logged wells (Figure 2-17 and 2-18). Figure 2-23 shows some statistics of the fractures observed in the cored well YU1776. Several characteristics of core fractures are important:

The fact that fracture intensity from log analysis is higher than that from core description may be due to one of two reasons:

Core description is the only sampling procedure where fractures are actually observed and not assumed based on other data. Therefore, the intensity of fracturing in cores (also confirmed from the horizontal logged well) can be assumed as the best initial value in the numerical simulations. An initial estimate of the mean fracture size is assumed based on core description as follows. Core description has been done by counting the number of fractures in every foot of core, and indicating whether the fractures penetrate or not across the entire cored foot. Therefore, if for a number of continuous core feet there is a strictly vertical fracture, it can be assumed that this is one large feature, cut by the coring device. By counting the number of continuous fractured core feet, the size of that large feature can be found. For example, in cored well YU1776 (Figure 2-23) such a vertical fracture extends approximately from elevation 1050 to 1075, i.e., for 25 continuous feet. A more rigorous analysis of all core data can give a number to be used as a good first approximation of mean fracture size to start the trial-and-error simulations with the hierarchical model. At the interpretation of the size of fractures, non-parallel to the coring device, a correction has to be assumed to account for the fact that only a portion of the fracture has been intersected.

In the polygon marking process of the 3D hierarchical model, polygons can be marked as fractured, based on their orientations and locations, and the average porosity of the rock. The first marking process is accomplished as follows:

is the normal vector to the second order surface, defined above (Equation 2-7). In the second marking process, a higher fracture intensity is assumed near the linear fracture zones, shown in Figure 2-15. The third marking process is performed as follows:

where N is the number of geocells from the reservoir StrataModel intersected by the polygon, and f i is the porosity of the i-th cell.

For simplicity, the fractures of System 2 can be generated within the entire modeling volumes of Tract 17 and 49. For Tract 49, which consists of massive dolomite, this is a good approximation. In Tract 17, where propagation of fractures may be inhibited by the shale layers, a certain termination percentage is assumed.

The predominant orientation of such a system is defined by the regional stresses. Therefore, System 3 is best modeled striking northwest to northeast, and dipping near vertical. Once the fracture planes are generated, their intersections with fractures of System 2 will define the extent of the connecting fractures of System 3. The overall predominant fracture connectivity and transmissivity of System 2 and 3 fractures will be oriented NW/SE and NE/SW.

The difficult work of creating a conceptual model of the geology of the Yates field (Sections 2.2.2.1 through 2.2.2.4) and translating that model into a DFN model (Section 2.2.2.5) is now complete. This quarter, MIT began numerical modeling of the reservoir using the DFN model described above. Results will be described in a future report.

Significant progress on implementation of spatial analysis of fracture patterns was made during the quarter. Current efforts are focusing on implementation of a generalized gridding algorithm and data structure within Fractal 1.0, to support the rule-based spatial structural analysis described in Dershowitz et al. (1997). A user interface has also been developed for Fractal 1.0.

The Fractal 1.0 data gridding program converts fracture trace and borehole data (Figure 2-24) to an (X), (X,Y), or (X,Y,Z) grid, including consideration for missing data as "empty" cells (Figure 2-25). To support fracture spatial location analysis, grid values can be assigned as

This gridding algorithm is useful both for spatial data analysis and for the interface to StrataModel (see Section 2.2.5 below).

During the quarter, significant progress was made on extending technologies for derivation of hydraulic parameters for fractured reservoirs exhibiting "fractional dimension" flow behavior. The goal of this research is to develop an integrated approach to analysis of hydraulic tests in fractured rocks exhibiting "fractional dimension" (Barker, 1988) and heterogeneously-connected behavior.

The flow chart for the derivation of hydraulic parameters from well test data is illustrated in Figure 2-26. The analysis is described in Dershowitz et al. (1997).

These analyses are implemented in a Windows 95 code, "Flare" which was developed this quarter and is currently being tested. This code is available online at:

These features make it possible for reservoir engineers to determine whether the flow dimensions which might be observed in a fracture network would be consistent with those observed in situ. The algorithms implemented are described in Dershowitz et al (1997).

To execute Flare, select the Flare icon, and double click with the mouse. The general procedure for analysis is summarized in Table 2-1. The operation of the individual Flare menu items (top window in Figure 2-27) are described in the next section. Navigation through Flare is done using Microsoft Windows mouse conventions. In general, the left hand mouse button is used for making selections.

	Command	Action
1.		Run FracMan/FracWorks to produce the fracture pattern to be analyzed. Save the file in .FDT binary or .BAB ASCII format.
2.	File/Open .BAB or .FDT	Load the .FDT .BAB format fracture data file
3.	File/Open*.SAB	Load a .SAB object containing geometries for boreholes and analysis regions
4.	Edit/Exploration	Modify the geometry of the wells to be tested
5.	Edit/Analysis	Define and modify the analysis parameters as necessary. Select the wells to be included in the current analysis, and the test interval(s) in each well
6.	Analysis/Dimension	Calculate the conductance as a function of radial distance from each of the wells
7.	File/Print	Print selected analysis statistics
8.	File/Exit	Leave Flare

New: Begin a new analysis, without closing the current analysis. Opens a window for the new analysis.

Open: Open fracture geometry (.FDT or .BAB) and borehole object (.SAB) files. The standard Microsoft Windows File Open menu syntax and assumptions are used.

Close: Close the current active analysis and all windows related to that analysis.

Exit: Exit Flare. Warns the user if statistical reports have not been saved.

Exploration: Edit the currently active exploration program containing borehole and analysis region specifications. The Edit/Exploration menu uses an object approach with a tree structure to describe tunnels. Only linear boreholes are currently supported. Analysis regions can be specified as boxes, slabs, or cylinders. The Exploration Menu provides the following options;

Add: Add an additional exploration object. A submenu provides the option to select the type of tunnel object.

When editing or adding an object, three property tabs are available. The General tab always provides the object name. The Geometry tab requires different input for each object type. The Boundary Conditions tab is not active for Flare.

Dimension: Simulate well tests from selected boreholes, and report the resulting distance vs. conductance, and distance vs. flow area in tabular and graphical form. The middle window in Figure 2-27 shows the user interface in the Dimension Analysis menu.

After launching Flare, the user is confronted with the information and licensing screen. Upon accepting the license agreement by clicking on "OK", the user comes to the main window (top window in Figure 2-27). Under the Files menu, the user should use the mouse to highlight the discrete fracture network (DFN) files to be processed.

Returning to the main menu, the user next selects Edit, to define or modify the exploration objects and set the analysis parameters for the analyses to be carried out. Once these have been set, the user can continue to Analysis, to run the simulated well tests.

After completing analyses, the user can use the View menu to obtain graphical displays desired (e.g., graphs at bottom of Figure 2-27), and File/Save to save statistical summary (.STS) files.

During the quarter, software development was initiated for linkage between StrataModel and the FracMan discrete feature simulator. Table 2-2 provides the format for StrataModel geological models. This is a grid-cell-based system, which contrasts to the discrete fracture approach, which is a fracture-coordinate-based system. Therefore, a significant level of effort is required to map between the two systems.

X Coor	Y Coor	elev	Depth	GR	POR	PERM	CAL %	FRAC	NFRAC	P21
2640	39600	-1961	5144	39.10	0.05	150.2	15.0	0	0	0
2640	39600	-1962	5145	40.19	0.15	160.8	23.0	1	2	0.14
2640	39600	-1963	5146	41.16	0.16	175.6	53.0	1	7	1.28
...	...	...	...	...	...	...	...	...	...	...

The algorithm currently being implemented for converting between DFN models and StrataModels is as follows (Figure 2-28):

Figure 2-29 shows a heterogeneous, 2000’ x 2000’ x 2000’ discrete fracture network (DFN) model. The parameters used to generate this DFN model are provided in Table 2-3 (see FracMan manual). Figures 2-30 and 2-31 provide views of vertical and horizontal cross-sections through the StrataModel interpretation of this DFN, using algorithms (a) through (c).

Set #	Initial Point of Feature	Strike, Dip of feature	Region Size	Mean Orient.	Orient. Model	Mean size	St. dev	P₂₁
1 slab	(0,-1000, 800)	0,15 E	2000 x 2000 x 200	270,75	Biv. Bing. k₁=k₂=20	40	10	0.03
2 slab	(0,-1000,100)	0,15 E	2000 x 2000 x 300	0,0	Fisher k=1	100	25	0.01
3 slab	(0,-200,800)	0,15 E	2000 x 2000 x 500	270,85	Fisher k=10	20	5	0.02
4 cylinder	(100, 500, 500)		r=2000 l=1000	45,75	Fisher k=10	75	25	0.02

Flare and Fractal are still under development. The other components of the MS Windows 95 analysis system are complete, operational, and are now available on the World Wide Web. All five programs will undergo further improvements and should be considered Beta 1.0 versions.

Software	Application	Status during Q5
NeurIsis b 1.0	Orientation Analysis	Available through Web Site
FlowDim b 1.0	Flow Dimension from Well Tests	Available through Web Site
Flare b 1.0:	Flow Dimension from Discrete Fracture Networks	Implementation of user interface and refinement of algorithms
Fractal b 1.0:	Spatial Data Analysis	Implementation of data structure, user interface, and gridding algorithm
FraCluster b 1.0	Compartmentalization and Block Size Analysis	Available through Web Site

During the quarter, Golder Associates initiated development of the discrete fracture analyses in support of thermally assisted gravity segregation (TAGS). TAGS is the key to development of the Yates field project study site. The TAGS process being simulated by the DFN approach is illustrated in Figure 2-32.

The TAGS process uses the vertical fracture connectivity to provide a preferential pathway for steam and to serve as a kind of heat-exchanger to the oil in the rock matrix (Figure 2-33). The steam flow direction is parallel to the primary fracture set orientation, forming an elongated zone around each fracture. The light components of the oil (e.g., propane, butane, pentane) will become volatile when heated. Obviously in the gas phase it is much easier for those components to leave the matrix. The remaining heavy components will have a decreased viscosity when they are heated. This will increase the ability of the oil to flow within the rock matrix.

The TAGS process is directly dependent on the fracture network geometry and connectivity as follows:

The DFN model for support of TAGS must simulate the discrete fracture control of the TAGS process in ways which continuum models cannot. The spatial distribution of heated matrix volume depends mainly on the spatial distribution of the fractures and hence cannot be modeled using averaging continuum model assumptions.

During the quarter, the DFN approach was extended to model thermal effects. The algorithm is based on a particle tracking approach, except that each particle does not carry a quantum of mass but a quantum of heat (Figures 2-35 and 2-36). The temperature is a function of the number of particles per volume. The particles are released from a source defined by the user (e.g., an injection well). The implemented approach for heat transfer includes two mechanism:

The temperature profile in a DFN model depends on the velocity, locations, and paths of the hot particles. The physics of heat transfer from hot particles to the rock and the heat dissipation from the hot rock to the global environment must also be modeled. The equation of energy around the hot particle is

where, r _h = density of the flowing fluid hot particle, [kg/m³]
C_h= heat capacity of hot fluid, [kcal/kg° C]
T = temperature of hot fluid or hot particle, [° C]
T_m = temperature of rock, [° C]
T_h = initial temperature of hot fluid, [° C]
h = heat transfer coefficient between hot fluid and rock block,
[kcal/m²s° C ], and
a = fracture aperture, [m].

Equation 2-10 represents the loss of energy from a hot particle that is completely absorbed by an adjacent rock block. The solution of Equation 2-10 is

As time passes, the temperature of a hot particle cools to the temperature of the adjacent rock. This cooling is described by a decay rate which is proportional to K.

To apply Equation 2-11 to the discretized fracture elements, the rock volume must be relatively large compared to the fracture medium so that T_m in Equation 2-11 can be treated as constant during heat transfer.

Because T_m varies from fracture element to element, Equation 2-11 is applied to every fracture element that particle travels through where T_h,i equals the temperature of particle at the entrance of the element i, T_m,i equals the temperature of rock surrounding the fracture element i, and t is the time that a particle takes to traverse the fracture element.

The energy released by a particle to the surrounding rock during the trip across an element is

where t_i is the residence time of a particle in element i and K_i is the K value defined by Equation 2-11b with a replaced by a_i, the aperture of element i.

The energy, q_i, in Equation 2-12 has units of kcal/m³. The energy retained by the hot fluid and particle is

where, PE = potential energy (relative to T_o) of a particle [kcal];
T_o= initial temperature of the system (fracture + rock media);
D V = volume of hot fluid.

Because PE and T_o are provided by the user, D V is the only unknown in Equation 2-13.

The total energy released from the hot fluid to a fracture element i is Q_i, which is the volumetric energy, q_i, multiplied by the volume of the hot field:

Equation 2-14 is true if the temperature of rock, T_m,i, varies little while D V passes through element i. The temperature of the hot fluid is assumed uniform.

The energy transferred to rock increases the temperature of rock. Assuming that we are not interested in the heat conduction, and temperature of the rock is uniform ( heat conductivity of rock is infinitely large), the temperature of rock can be calculated from:

	EXECUTIVE SUMMARY
1.	QUARTERLY PROGRESS OVERVIEW
1.1	Overview of Progress
1.2	Project Deliverables
1.3	Issues and Resolutions
2.	TASK PROGRESS
2.1	Active Tasks
2.2	Task Progress
2.2.1	Task 1.1.2: Data Updates
2.2.2	Task 1.2.1: 3D Hierarchical Fracture Model
2.2.3	Task 2.1.2 Spatial Location Analysis
2.2.4	Task 2.1.3 Hydraulic Parameter Analysis
2.2.5	Task 3.1.1: Linkage to Reservoir Models (Software Development)
2.2.6	Task 3.2.1: MS Windows 95 Analysis System
2.2.7	Tasks 3.2.2 Discrete Fracture Analysis for TAGS Processes
2.2.8	Task 3.2.3: Software Linking
2.2.9	Task 4.1.1 Fracture Image Data Acquisition
2.2.10	Task 4.1.2: Well Testing Data Acquisition
2.2.11	Task 5.1.2: WWW Site Updates
2.2.12	Task 5.2.1 Progress Reports
2.2.13	Task 5.2.2: Research Reports
2.2.14	Task 5.2.3: Presentations
2.2.15	Task 6: Management
3.	SCHEDULE, DELIVERABLES, AND MILESTONES
3.1	Schedule
3.2	Milestones and Deliverables

Table 2-1	Flare Analysis Sequence
Table 2-2	StrataModel *.rw File Format Example
Table 2-3	DFN Model Parameters
Table 2-4	MS Windows 95 Analysis System
Table 2-5	Simulation Parameters for Heat Transfer
Table 3-1	Milestones and Deliverables

Figure 2-1	Yates Field Tract 49 Steam Test Area
Figure 2-2	Steam Injection Schematic
Figure 2-3	Steam Miverret in Tract 49
Figure 2-4	Radius of Steam Influence
Figure 2-5	Reservoir Structure in Tract 17
Figure 2-6	Reservoir Structure in Tract 49
Figure 2-7	Thickness of Sediments Between San Andres and Seven Rivers M: 3D Surface
Figure 2-8	Stress Directions During The Last Period of Regional Tectonism
Figure 2-9	Rose Diagrams of Fracture Strikes in Cretaceous Limestone
Figure 2-10	Mechanism For Development of Two Orthogonal Joint Sets
Figure 2-11	Possible Mechanism For Late Permian Folding in the Yates Field
Figure 2-12	Fracture Initiation in the San Andres Formation: Middle Permian
Figure 2-13	Mechanisms of Karstification During Island Exposure: Middle to Late Permian
Figure 2-14	Thickness of Sediments Between San Andres Top and Seven Rivers M
Figure 2-15	Possible Drape Folds or Faults in the Yates Field
Figure 2-16	Types of Fracturing Caused By Late Permian Folding
Figure 2-17	Fracture Strikes in Tract 17
Figure 2-18	Fracture Strikes in Tract 49
Figure 2-19	Fracture Strikes in Tracts 17 and 49: Relation to the Field Anticline
Figure 2-20	Types of Fractures Associated With the Field Anticline
Figure 2-21	Fracture Coalescence
Figure 2-22	Fracture Set Identification in Logged Well YU1711
Figure 2-23	Fracture Observations in Cored Well YU1776
Figure 2-24	Examples of Scan Line, Borehole, and Trace Map Data
Figure 2-25	Gridding Algorithms
Figure 2-26	Flare 1.0 Flow Chart
Figure 2-27	Flare 1.0 User Interface
Figure 2-28	DFN to StrataModel Steps
Figure 2-29	DFN to StrataModel Demonstration Case
Figure 2-30	StrataModel Vertical Cross-Section for DFN Demonstration Case
Figure 2-31	StrataModel Horizontal Cross-Section for DFN Demonstration Case
Figure 2-32	TAGS Process Schematic
Figure 2-33	Heat Exchange in Fracture Network
Figure 2-34	Role of Fracture Geometry in TAGS
Figure 2-35	Heat and Particle Tracking in MAFIC
Figure 2-36	Particle Tracking Algorithm Flowchart
Figure 2-37	Test Case of Heat Migration on Single Fracture Meshes
Figure 2-38	Results of Heat Transport Simulations
Figure 2-39	Steam Injection Data
Figure 2-40	Production History Data

Deliverable	Scheduled Date	Date Submitted
Research Report, Fracture Data Analysis Technology	97.03.15	97.09.30 (projected)
Annual Report	97.03.15	97.04.19