Third Quarterly Report
September 1, 1996 to November 30, 1996
A Project of:
Fundamental Geoscience
Research and Development
BDM-Oklahoma
U.S. Department of Energy
National Oil and Related Programs
Contract Number #G4S51728
Prepared by:
William S. Dershowitz
Paul R. LaPointe
Herbert H. Einstein
Violetta S. Ivanova
Golder Associates Inc.
Redmond, Washington
December 13, 1996
963-1357.521
This report describes progress on the project, "Fractured Reservoir Discrete Feature Network Technologies" during the period September 1, 1996 to November 30, 1996. The report presents summaries of technology development for four active research areas: (1) development of hierarchical fracture models, (2) derivation of hydraulic parameters for fractured reservoir systems using fractional dimension type curve approaches, (3) implementation of software for analysis of reservoir compartmentalization, and (4) linkage of discrete feature network and reservoir modeling approaches. In addition, the report provides information on project status, publications submitted, data collection activities, and technology transfer through the world wide web (WWW).
The development of hierarchical fracture models during the quarter combined geological, mathematical, and computer code development. The study of the regional geology of the Permian Basin initiated during the previous quarter was continued. Detailed information on the lithology, stratigraphy, and fracturing of Permian rocks in the project study area (Tracts 17 and 49 in the Yates field) was assembled and reduced for use in model development. Meetings were held with S. Tinker and M. Uland at the Marathon Oil Petroleum Technology Center (PTC) in Littleton, Colorado to advance the development of features of the hierarchical model consistent with observations at the Yates field. Based on the accumulated knowledge of regional and local geology, project team members at MIT started the interpretation of fracture genesis mechanisms and the conceptual modeling of the fracture system in the study area.
Research on derivation of hydraulic parameters for fractured reservoirs was initiated during the quarter. The report describes the development of a new procedure for deriving the hydraulic parameters for DFN approaches by combining fractional dimension type curve analysis with forward modeling of field tests. The procedure uses forward modeling to derive the conductive fracture intensity, transmissivity distribution, and a measure of the degree of channel flow within individual fractures.
Technology development for analysis of reservoir compartmentalization focused on development of a new, Windows-95 application, FraCluster, which implements the compartmentalization, tributary drainage volume, and reservoir matrix block size algorithms developed in the previous quarter. The application starts with stochastically generated discrete feature networks, and uses a combination of graph theory, stochastic geometry, and analytical geometry (convex hull) procedures to analyze reservoir compartmentalization.
Research on linkage of discrete fracture approaches to conventional reservoir simulators was initiated during the quarter, and will be further developed in the next quarter. The development described in this report focused on two alternative approaches: directly mapping discrete fractures onto reservoir model blocks, and deriving equivalent reservoir model block properties on the basis of discrete fracture networks.
This quarterly progress report describes activities during the period September 1, 1996 to November 12, 1996. Work was carried out on the following tasks:
The major activity in the quarter was development and implementation of hydraulic parameters and compartmentalization analyses and research related to development of the hierarchical fracture model. Major efforts were also made for preparation of the research report, "Fractured Reservoir Compartmentalization," and for updating of the WWW site.
The following project deliverables were scheduled or submitted during this quarter.
| Deliverable | Scheduled Date | Date Submitted |
| Research Report, Fractured Reservoir Compartmentalization | 96.11.30 | 96.12.27 (projected) |
| Second Quarter Progress Report | 96.06.15 | 96.06.26 |
| Prof. Meeting Papers (2) | by 96.12.30 | 96.12.05 |
The following issues were addressed during the quarter:
1. Contract modifications were completed to reflect changes in BDM technical and project officers
The following tasks were active during the 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 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:
During the quarter, Marathon Oil Company provided geological data requested by MIT, which will be the basis for the interpretation of the fracture system in the Yates Field. The following data were donated to the project by Marathon Oil:
This data was assembled and are being incorperated into the project World-Wide-Web (WWW) site (Task 5.1.2).Figures 2-2 through 2-17 present examples of the data provided by Marathon during the quarter. These figures are related to work carried out under task 1.2.1, and are therefore located near the appropriate citations in the following section.
2.2.2 Task 1.2.1: 3D Hierarchical Fracture Model
During the quarter, MIT focused its research on three main tasks. First, the preliminary study of the regional geology of the Permian Basin continued. Second, detailed information on the lithology, stratigraphy, and fracturing of Permian rocks in the Yates field study area (Tracts 17 and 49) was collected during meetings with S. Tinker and M. Uland at the Marathon Oil Petroleum Technology Center (PTC) in Littleton, Colorado. Third, based on the accumulated knowledge of regional and local geology, MIT started the interpretation of fracture genesis mechanisms and the conceptual modeling of the fracture system in the study area.
2.2.2.1 3D Reservoir Characterization of Permian Rocks in the Yates Field
In the three-dimensional hierarchical fracture model, fracture system generation is based on the material properties of the host rock and the geologic mechanisms that have acted in the area. Prior to fracture modeling, it is essential to develop a realistic representation of the geologic mechanisms, defined by the deposition sequence and the structural deformation. During the quarter, MIT researchers became familiar with the three-dimensional reservoir characterization of the Yates field by Marathon Oil geologists and engineers (Tinker 1996; Tinker et al. 1995; Tinker and Mruk 1995; also Tinker, Uland, pers. comm.).
The reservoir characterization of the Yates Field includes a 3D geologic model of the complete reservoir, based on a database that integrates geologic and engineering data from 1800 wells, 118 cores (total of 23,000 ft of quantified core description and analysis), and historical production data. The geologic model was built at PTC, Littleton, by Scott Tinker and other Marathon Oil geologists. The model, containing 6.8 million cells and 40 attributes per cell, was created using Stratamodel and other commercial software.
Figure 2-1 shows the location of the Yates Field on the southeastern tip of the Central Basin Platform. This location represents the highest present position of the structure of the Permian strata (San Andres, Grayburg, Queen, and Seven Rivers) on the platform.
The maximum dips of the structure on top of the San Andres are 3 to 5° to the east and south into the Midland Basin and the Sheffield Channel, respectively, and 0.5° to the west towards the Central Basin Platform axis (Craig 1990; Tinker et al. 1995). The Yates Field anticlinal structure was formed primarily by Late Permian (post-Salado and pre-Rustler) drape folding over buried pre-Permian anticlines and fault scarps (Hills 1970). The main cause for the drape folding is interpreted to be the differential compaction between relatively rigid shoal facies and highly compactible lagoonal and intertidal facies (Craig 1990; Tinker and Mruk 1995).
2.2.2.1.2 Depositional Model, Stratigraphy, and Lithology
Figure 2-2a represents a west-to-east stratigraphic section from the 3D geologic model of the Yates Field. The stratigraphic framework of the upper San Andres formation is composed of two major depositional sequences (Figure 2-2b): (1) Sequence 1: a ramp complex, prograding from west to east, overlain by (2) Sequence 2: a group of four major cycles, aggrading and prograding to the east (Tinker 1996; Tinker and Mruk 1995). Paleoelevations of the surface boundaries between major cycles were reconstructed according to depths from a datum in the Seven Rivers RMS horizon which was deposited as a horizontal layer (Craig 1988). In Figure 2-2a, Cycles 3 and 4 are collectively referred to as Cycle 3, since Cycle 4 was almost entirely removed by subaerial erosion following the deposition of San Andres and defining its top as a major unconformity.
Figure 2-2b illustrates the west-to-east distribution of the three dominant San Andres lithofacies, superimposed on the major sequence stratigraphy. Each major cycle in the San Andres represents a high-frequency sequence (HFS), composed of three to five minor sequences. On the west side of the Yates field, HFSs consist of vertically stacking shale-carbonate layers, deposited as low-energy mudstones and wackestones (classification by Dunham 1962). Shales (shown in green in Figure 2-2b) are thickest and most extensive at the base of each HFS, and become thinner and laterally discontinuous near the HFS top. Figure 2-3 shows a typical log profile from the west side of the field. The HFS boundaries in the geologic model were correlated between the wells in the west side of the field. The vertical distribution of shale is explained by the deposition of clays (90% illite and 10% chlorite) in lagoons behind the shoal islands during sea level fall, and their later upward grading during subsequent sea level rise into shallow subtidal mudstone/wackestone, and shallow shelf packstone/grainstone.
In the deep west side and on the upper east side of the Yates Field, the HFSs of the San Andres consist of hundreds of vertical feet of clean carbonates (white in Figure 2-2b) with higher porosity and low gamma ray response. These carbonates were deposited as higher-energy, shallow, subtidal shoals of fusulinid packstones and grainstones which were subsequently dolomitized. A third lithofacies, present on the lower east side of the field, was the low porosity, low gamma ray, wackestone of the eastern slope and deep ramp (blue in Figure 2-2b). The major cycles cannot be correlated from log and core data on the east side of the field since the shale layers are completely missing. The major cycles, correlated in the west, are projected into the clinoformal geometries of the shoals in the east according to the depositional model of eastward carbonate shoal progradation and aggradation.
The Grayburg sediments (Figure 2-2a) onlapped the karst paleosurface of the San Andres during marine transgression, filling topographic lows and thinning over topographic highs. The Grayburg and Queen sediments were deposited as clastic and carbonate mudstones and wackestones in shallow subtidal to intertidal/supratidal environments. The Seven Rivers predominantly evaporite facies were deposited in hypersaline environments. On the east side of the Yates Field, sandstone facies of the Seven Rivers were deposited in the subaerial environment of a low-relief beach and dune complex over the buried San Andres topographic high.
2.2.2.1.3 Porosity Distribution Defined by Rock Lithology and Texture
Table 2-1 summarizes the distribution of dominant lithofacies, rock textures, and porosity types within the San Andres formation in the Yates Field (Tinker and Mruk 1995). On the west side of the field (Tract 17), two major lithofacies are present in the San Andres formation: (1) argillaceous dolomites ("shales"), and (2) clean dolomites (95% dolomite per rock volume). On the east side of the field (Tract 49) dolomite is the predominant mineral (96% of the rock volume). Limestone, principally as calcite cement, is the only other significant lithologic/mineralogic component, present both on the west and east side of the field. Rock matrix pores in both areas, the low porosity west side and the higher porosity east side, are dominated by moldic, fusumoldic, and vuggy types (classification by Choquette and Pray 1970), in addition to the crystalline porosity typical for dolomite.
Grayburg sediments (10 to 115 ft thick) consist of approximately equal amounts of clastics (mostly silt) and carbonates (90% dolomite). The Queen formation (about 45 ft thick) also consists of clastics (sand and silt) and carbonates (mostly dolomite). The predominant porosity in both Grayburg and Queen is of micro-intercrystalline type, some vuggy and fenestral pores also being present. The Seven Rivers anhydrite (300 to 400 ft thick) forms the seal of the reservoir. The clastic portion of the Seven Rivers (an up to 100 ft thick arc of sandstone, siltstone, and dolomite cement) has predominantly micro-crystalline and intercrystalline porosity.
Table 2-1 Lithology, Texture, and Porosity of the San Andres in the Yates Field
| Formation | San Andres west Tract 17 | San Andres east Tract 49 |
| Lithology | "shales": argillaceous dolomites silt and shale 40% of rock volume); clean dolomite; limestone (calcite cement) | 96% clean dolomite; limestone (calcite cement) |
| Texture | mostly mudstone and wackestone; some packstone | packstone and grainstone |
| Porosity type | intercrystalline and micro-intecrystalline; moldic, fusomoldic, vuggy | intercrystalline and micro-intecrystalline; moldic, fusomoldic, vuggy |
| Comment | low porosity; high gamma ray | higher porosity; low gamma ray (corrected for uranium) best quality reservoir rock |
Calcite in the San Andres formation is present primarily as secondary cement, filling the pores of the rock matrix and decreasing its permeability (Tinker and Mruk 1995). Percent of calcite present in cores and estimated percent of calcite calculated from log analysis are integrated in the Strata model. The 3D geologic model of the reservoir includes spatial distribution of pore-filling calcite and a model for the calcite origin. The origin of secondary calcite is explained by biodegradation of oils at the paleo oil-water contacts. Under this process, a flat layer of calcite would be deposited at the oil-water contact elevation during a relatively long period of constant sea level.
2.2.2.1.5 Cave System and Other Karst in the San Andres
Paleokarst in the San Andres formation is recognized by lithologic features in cores, extremely high flow rates from early wells, bit drops and other log anomalies. Karst in the San Andres was formed by solution, including dissolution along joints, of porous limestone which later was subjected to dolomitization. Indicators of caves are observed in more than 15% of the wells across the Yates field. 1050 caves, ranging in height from 1 to 21 ft, or a total of 4477 cave feet (i.e. vertical feet of cave) are recorded throughout the field (Tinker et al. 1995).
Figure 2-4a shows the position of caves in the San Andres formation, superimposed on the sequence-stratigraphic framework from Figure 2-2. Figure 2-4b summarizes the distribution of normalized cave feet (cave feet per 1000 logged feet) and average cave height in Cycles 1 and 2 (green) and Cycle 3 (blue) as a function of depth below the Seven Rivers M datum. The spatial distribution of caves in the San Andres is best explained by the island hydrologic model, illustrated in Figure 2-4c for Cycle 3. According to this model, karst was formed by the action of dynamic freshwater lenses beneath low-relief limestone islands during relative fall of the level of Permian seas (Craig 1988). Such meteoric processes under subaerially exposed islands occurred several times during the Permian, leading to the present distribution of caves and other karst features within the San Andres: shifting to the east from Cycle 1 to 3, and progressively decreasing in number and size under the paleo sea levels (Tinker et al. 1995).
2.2.2.2 3D Geologic Characterization of Permian Rocks in Tracts 17 and 49
During the quarter, MIT obtained core descriptions from locations in the vicinity of the study area. These data are not available for presentation to the public, being from locations outside of Tract 17 and 49 (there are no cored wells in the study area). However, core data, although very sparse, present the most reliable information on the lithology and the type of fracturing in Permian rocks in the Yates field. Core data will be input in the interpretation and modeling of the fracture system in the study area.
In addition, MIT obtained data from the mini-Stratamodels of Tract 17 and Tract 49, extracted from the field model and further enhanced by Marathon Oil engineers (John Whitney for Tract 17 and Mike Uland for Tract 49). Table 2-2 summarizes information on the Stratamodels of the study area.
Table 2-2 Stratamodels of Tracts 17 and 49 Area
| Location | Number of Geocells | Number of Attributes |
| Tract 17 | 1.12 million | 28 |
| Tract 49 | 0.78 million | 65 |
From the mini-Stratamodels, MIT obtained structure maps of the contact surfaces between major and minor formation sequences, and complete spatial distribution of the following attributes within the study area: gamma ray response (corrected for uranium in Tract 49), porosity, calcite content, and cave locations. In addition, values of structure curvature and slope were obtained for Tract 49 (not available for Tract 17). These attributes were selected for input into the 3D hierarchical fracture model of the study area for the following reasons: (1) they significantly affect fracture intensity, orientation, and permeability in the Yates field; (2) their spatial distribution is extrapolated from data available from all 1800 logged wells and 118 cores in the field. Many other Stratamodel attributes, although closely related to fracturing, are extrapolated throughout the reservoir volume from very sparse data in the geologic model.
2.2.2.2.1 Structure and Stratigraphy
Table 2-3 summarizes how the stratigraphic framework in Tracts 17 and 49 is built. Sequence 1 is the deep ramp. Sequence 18 is the erosional surface of the unconformity, truncating the underlying top San Andres carbonates. Proportionally layered sequences (odd numbers) are carbonate shoals, and onlap sequences (even numbers) are shales.
Figures 2-5 and 2-6 are structural slices along two layers in the San Andres formation in Tract 49: layer 168 is in the top carbonate facies of the San Andres, and layer 15 is within the first carbonate shoal above the ramp, respectively. Color scale in these figures indicates elevation, hot and cold colors representing relative topographic highs and lows, respectively. The holes in layers in Figure 2-5 represent locations where this layer is missing, i.e. where Grayburg sediments penetrate deep into the San Andres, filling the topographic karst depressions. The wells which penetrate the two layers are indicated in Figure 2-5. Most wells in the Yates field are drilled only to relatively shallow depths and do not penetrate the entire San Andres. Therefore properties of the reservoir, extrapolated between wells in the geologic model, are more reliable for the upper San Andres. Only two deep wells penetrate the entire thickness of the San Andres in this version of the full-field Stratamodel. Scott Tinker has recently updated the full-field model with data from eight deep wells. Since mini-Stratamodels of the study area are not available yet, and because of the time constraints, MIT has started its fracture modeling based on the previous full-field Stratamodel.
Table 2-3 Yates Field Stratigraphic Framework (Tracts 17 And 49)
Figures 2-7 and 2-8 illustrate the stratigraphy in tracts 17 and 49, respectively. The color scale from 1 (dark blue) to 18 (red) represents the depositional sequences from elevation 800 ft above sea level to the San Andres top (the elevation boundaries of the study area). In Figure 2-7 (wells YU1755, left, and YU1701, right) one can see to what extent erosion and compaction have changed the top surface of the San Andres carbonates. The top carbonate shoal facies is almost completely eroded at YU1701, which is the structural peak of the San Andres top in Tract 17. In Figure 2-8 (well YU4063) the formation sequences with even numbers (onlap shale facies) are completely missing. This figure illustrates the fact that in Tract 49 the San Andres lithology is almost entirely composed of dolomite (odd number carbonate shoal sequences in Stratamodel).
2.2.2.2.2 Shale, Secondary Calcite, and Porosity
In the shale layers on the western side of the field 40 API gamma ray (GR) corresponds to 10% argillaceous content (Tinker and Mruk 1995). In Figure 2-9, illustrating the 3D distribution of GR response in Tract 17, red color indicates locations where GR>20 API. Figure 2-10 illustrates the GR response in Tract 49 (corrected for high values due to uranium). On the same color scale, the red color is almost completely absent, once again indicating the clean dolomite in the Tract 49 area.
Figure 2-11 shows the distribution of secondary pore-filling calcite in Tract 49. In the color scale, light blue to red colors indicate the presence of higher percent calcite. Since calcite was precipitated in the pores of horizontal layers at paleo oil-water contacts, the flexure of the top calcite elevation indicates the structural deformation of the San Andres formation after the calcite deposition (Tinker and Mruk 1995).
Figure 2-12 illustrates the porosity distribution in Tract 49. Red color marks porosity higher than 22% of the rock volume. One can see the high porosity of the best reservoir rocks: dolomite packstones and grainstones on the upper east site of the Yates Field. In the deep northeastern end of Tract 49, cold color (blue) indicates the low porosity mudstones of the deep ramp and eastern slope. Figure 2-12 includes porosity due to fractures, accounting for nearly 4% in the San Andres formation in the Yates field (Tinker and Mruk 1995).
2.2.2.3 Fracture Interpretation and Modeling
During the quarter, MIT started its interpretation of fracture genesis mechanisms that have acted regionally in the Permian Basin and locally in the Yates field. A complete conceptual model of the fracture genesis will be presented to Marathon geologists for discussion during the next quarter. Major points in the current fracture interpretation and conceptual modeling are summarized below.
2.2.2.3.1 Geologic Mechanisms of Fracturing in the Yates Field
Tinker and Mruk (1995) recognize three major mechanisms for fracture development in the Late Permian rocks of Yates field: (1) a regional mechanism due to activation along pre-existing planes of weakness, defined by a pre-Permian system of folds and faults; (2) a field-scale mechanism associated with the formation of the field anticline; and (3) a local mechanism on the west side of the field caused by differential compaction of shales and carbonate mudstones. Other authors (for example, Stearns and Friedman 1972) also describe regional orthogonal systems of nearly vertical fractures in reservoir sedimentary rocks.
Tinker and Mruk (1995) relate regional fracture patterns to the folds and faults developed during pre-Permian times of tectonic activity (Hills 1970). During the Late Mississippian to Early Pennsylvanian it is thought that compressive stress was approximately east-west. During this time, folds were created striking N23-35°W, and fault systems were created striking N55-80°E, and N50-65°W. In the late Pennsylvanian to Early Permian, it is thought that the regional stress reoriented from east-west to north-south. North-south strike-slip faults were created during this period, including the significant West Platform fault along the west edge of the Central Basin Platform. According to Hills (1970), the asymmetric Late Permian structures developed in relation to the older tectonic structures. Downward movement along the west side of the West Platform fault in the Late Permian (Ochoa) caused relaxation of regional stress. NW/SE striking joints and minor normal faults opened due to several post-Permian events, including Tertiary tilting of the Delaware Basin and Holocene movement along the West Platform fault.
The dominant orientations of the orthogonal regional system are N50°W (along the axis of the Central Basin Platform) and N40°E (Tinker and Mruk, 1995; Curran, Tinker, pers. comm.). Figure 2-13 shows the regional fracture trends superimposed on data of depositional trends, karst and well-production lineaments, and log analysis. The NW/SE fracture strike is generally considered the dominant regional fracture orientation. However, in the only FMS/FMI interpretation from a horizontal well (YU17D5 in Tract 17) the predominant strike of both open and calcite field fractures is N40°E (Merkel, 1992).
According to Tinker and Mruk(1995), the local fracture system in the Yates Field strikes parallel or perpendicular to the San Andres anticlinal structure. Since the anticlinal structure is related to pre-Permian structures, fracture strikes in the anticline-related fracture system may also have predominantly NE/SW and NW/SE directions. Fracture dips, however, probably differ from the vertical and are related to the structure curvature. The third fracture system, associated with shale compaction in the San Andres on the upper west side of the field, does not have an obvious orientation. Fractures of this system are developed in the brittle dolomites and often terminate at the more ductile shales (Tinker, pers. comm.).
2.2.2.3.2 Relation of Fracture Intensity to Rock Properties in the Yates Field
Figure 2-14 illustrates the distribution of fracture intensity (fracture counts) for four major lithology classes (Tinker and Mruk 1995). The fracture intensity in this figure is represented using histogram porosity distributions, which include the porosity due to fractures. Fracture log counts are generally lower and less reliable than fracture core counts. Fracture intensity in the Yates Field is closely related to the lithology and porosity of the Permian rocks. The greatest fracture counts are observed in dolomite mudstone and wackestone, typical for the upper west side of Yates (Tract 17). Fracture counts in dolomite increase up to 8 to 10% porosity, and then decrease with increased porosity. The higher porosity, ductile dolomite packstone and grainstone in the Yates east site (Tract 49) are less fractured than the brittle, low porosity mudstones on the east side. Fracture intensity is much lower in the San Andres shales on the west side, and in the ductile sandy dolomites of the Grayburg.
2.2.2.3.3 Parameters of the 3D Hierarchical Model for Tracts 17 and 49: Orientation and Intensity
Figure 2-15 shows an upper hemisphere pole stereoplot of 265 fractures and bedding planes picked from the log image profile at well YU1711. No Terzaghi correction has been applied. Since this well is in Tract 17, fractures may belong to any of the three fracture systems, discussed above. Open and calcite filled fractures at this well have very similar orientation distributions, demonstrated by their rosette plots in Figure 2-16a and 2-16b, respectively. The predominant strike direction is consistent with the major regional NW/SE trend, and is also perpendicular to the San Andres structure at this location. The steeply dipping fractures are perpendicular to the flat sedimentary beds. Fracture orientations in other wells, however, vary much more, indicating that the fracture genesis mechanisms are still require a more reliable interpretation.
The approximate horizontal lineaments of the regional orthogonal features in the Yates Field have been defined by B. Curran from Marathon. The orientations of these structures will be refined during the upcoming quarter, using a probabilistic algorithm to synthesize data such as 3D cave lineaments, and 3D porosity and lithology distributions in the vicinity of the approximate locations. According to Tinker and Mruk (1995), on the west side of the field, regional fractures are confined to discrete linear zones, whereas on the east side they broaden and coalesce due to later enhancement, associated with shale compaction.
The orientations of local fractures can be reproduced stochastically in relation to the field structure. Figure 2-17a shows the top surface of the San Andres formation in Tracts 17 and 49. Second and third order quadratic surfaces are fitted with correlation coefficients higher than 0.92 to the San Andres tops in Tracts 17 and 49 (Figure 2-17b). These plots illustrate two major points:
Local fracture intensity (ratio of fractured and intact areas on potential fracture planes) will be modeled stochastically as a function of rock matrix porosity and lithology. For compaction-related fracture sets in the dolomite on the upper west side of the field, a certain fracture termination percent will be defined at the shale contacts.
The earlier 3D Hierarchical Fracture Model (Ivanova 1995, and Ivanova et al. 1995) has been enhanced with procedures which allow great flexibility for defining input parameters. For example, during fracture modeling in the Yates Field San Andres formation, fracture intensity will be defined for the first time as a function of rock matrix porosity. Other geometric procedures are currently developed. The most important new concept is the definition of a varying mean fracture orientation. In existing stochastic models, including the old version of the 3D hierarchical model, mean orientation is usually fixed and deviations from the mean are described by an often complex mathematical expression. Orientations related to curved structures (folds) can be better modeled by a mean orientation, defined simply as a normal vector to the structure surface at any point, and a simple variation, for example uniform in a cone around the mean, of possible fracture deviations from the mean. The new enhancements of the 3D Hierarchical model add to its capability to realistically represent complex fracture networks in natural rocks.
2.2.3 Task 2.1.3 Hydraulic Parameter Analysis
Hydraulic pathways through fractured rock are frequently formed by a combination of matrix permeability, flow in planar features such as fractures and fracture zones, and flow through one-dimensional channels such as those formed by selective mineralization, disolution, and fracture intersection processes (Figure 2-18). This combination of flowing features of different dimensionality is referred to as "fractional dimension response" (Barker, 1988; Doe and Chakrybarty, 1996), as illustrated in Figure 2-19. At the project study site, for example, there are indications that one- and two-dimensional solution features play a significant role in fluid transport to production boreholes.
During the quarter, significant progress was made on development of technologies for derivation of hydraulic parameters for fractured reservoirs exhibiting this "fractional dimension" flow behavior. The goal of this research is to develop an integrated approach to analysis of hydraulic tests in fractured rocks exhibiting this type of "fractional dimension" (Barker, 1988) and heterogeneously connected behavior.
The approach developed combines fractional dimension type curve analysis (Doe and Chakrybarty, 1996) with discrete fracture network simulation (Dershowitz et al, 1996) and the "OxFilet" approach for derivation of fracture properties by deconvolution of hydraulic test results. This section describes the progress of research during the quarter in development of the fractional dimensional analysis approach, and integration of the approach into the existing "OxFilet" analysis.
2.2.3.1 Fractional Dimension Analysis
Differently dimensioned flow systems have significantly different behavior. In addition, since the systems are fractured, they can be both scale dependent and heterogeneously connected. Research was carried out toward development of procedures for analysis of fractional dimension type curve responses, using Laplace transform solutions for the equation of fractional dimensional flow.
The main assumptions made in the course of developing the models for transient rate and pressure behavior in a two-zone composite system are as follows:
1. Transient Darcian flow takes place in the system, the near flow direction is radial
2. The ith zone is characterized by flow dimension ni (i = 1 for the inner zone and i = 2 for the outer zone), where ni is not necessarily an integer; the source well is an n1-dimensional "sphere" projected through three-dimensional space
3. The ith zone is characterized by hydraulic conductivity and specific storage Ki and Ssi, respectively (i = 1 for the inner zone and i = 2 for the outer zone)
4. The system is infinite, and either a constant-rate or a constant-pressure condition is imposed at the source well
5. Wellbore/source storage capacity is non-negligible
The radial flow behavior of water in a two-zone composite system is governed by the following equations (the form of the equations is the same as in Barker, 1988):
(2-1a)
and
(2-1b)
respectively, where
(2-1c)
In terms of the dimensionless variables, the initial and boundary conditions become
(2-2a)
(2-2b)
(2-2c)
(2-2d)
and
(2-2e)
where
(2-2f)
(2-2g)
and
(2-2h)
Laplace transforms can be used to solve the system of partial differential equations. The subsidiary equations are
(2-3a)
and
(2-3b)
After transforming the boundary conditions, Equations (2-3a) and (2-3b) are solved simultaneously. The solutions in Laplace space are
(2-4a)
and
(2-4b)
where
(2-5a)
(2-5b)
(2-5c)
(2-5d)
(2-5e)
Using equations 2-1 through 2-5 and the related type curves of Figures 2-20, 2-21 and 2-22, it is possible to derive both transmissivity, storativity, and flow dimension as a function of distance from the well bore from well tests. Of these, the flow dimension as a function of distance may prove to be the most important for reservoir design, since lower flow dimensions indicate that only a small portion of the reservoir is being accessed (Figure 2-18).
The next stage in the current task is the develop technologies for derivation of fractional dimension hydraulic parameters from well test results. This is done by applying the fractional dimensional type curves of Figures 2-20, 2-21, and 2-22, or by directly solving the Laplace equations 2-1 through 2-5 to fit the data. These codes and procedures are currently under development.
2.2.3.2 "OxFilet" Analysis for Fractional Dimension Flow
The flow chart for the "OxFilet" analysis approach is illustrated in Figure 2-23. The analysis starts with a file containing the results of transient packer test or drill-stem hydraulic test results, expressed as interval transmissivity and flow dimension.
The user then assumes the discrete conductive feature geometry, expressed as distributions of orientation, size, intensity, and spatial process, and the discrete conductive feature hydraulic properties, expressed as a fracture transmissivity distribution and a "channeling factor" for each fracture. The "channeling" factor represents the degree of flow channeling within the fracture (Figure 2-24). OxFilet then simulates the process of hydraulic testing in fracture networks with these properties to obtain simulated distributions of packer interval or DST transmissivity and flow dimension. The flow dimension is derived from the variation of effective flow area with distance into the fracture network away from the borehole, as shown in Figure 2-25. The simulated transmissivity and flow dimension results can then be compared to the measured responses.
Based on this comparison, the assumed fracture geometric and hydraulic properties can be adjusted until parameters are derived which match the observed behavior (Figure 2-26). This approach will be designed to honor probabilistic disciplines of geologic features.
The software to carry out this analysis is currently under development.
2.2.4 Task 2.1.4 Compartmentalization Analysis
During the quarter, software was implemented corresponding to the compartmentalization analysis, tributary volume analysis, and reservoir block volume described in our second quarterly progress report (Dershowitz et al, 1996). These analyses are implemented in a Windows 95 code, "FraCluster". This code is available online at:
The program incorporates calls to QHULL (Barber et al., 1995).
FraCluster includes the following features:
These features make it possible for reservoir engineers to rapidly define key reservoir engineering parameters for fractured reservoirs from discrete fracture network models.
The algorithms implemented are described in LaPointe et al (1996).
2.2.4.2 FraCluster User Interface
Figures 2-27 through 2-33 provide an annotated guide to the features of FraCluster.
To execute FraCluster, select the FraCluster icon, and double click with the mouse. The operation of the individual FraCluster menu items are described in Section 2.2.4.3 below. The general procedure for analysis is summarized in Table 2-4.
Navigation through FraCluster is done using Microsoft windows mouse conventions. In general, the left hand mouse button is used for making selections.
Table 2-4 FraCluster Analysis Sequence
|
|
Command | Action |
| 1. |
|
Run FracMan/FracWorks to produce the fracture pattern to be analyzed. Save the file in .FDT binary format. |
| 2. | File/Open *.BAB | Load the *.BAB format fracture data file |
| 3. | File/Open*.SOB | Load a .SOB object containing geometries for boreholes and analysis regions |
| 4. | Edit/Exploration | Modify the geometry of the boreholes and analysis regions as necessary |
| 5. | Edit/Analysis | Define and modify the analysis parameters as necessary |
| 6. | Analysis/Intersections | Calculate fracture intersections and build adjacency lists |
| 7. | Analysis/Compartmentalization | Carry out compartmentalization analysis, and report statistics |
| 8. | Analysis/Tributary Volumes | Carry out tributary drainage volume analysis, and report statistics |
| 9 | Analysis/ReservoirBlock Size | Carry out reservoir block size analyses, and report statistics |
| 10. | File/Print | Print selected analysis statistics |
| 11. | File/Exit | Leave FraCluster |
New: Begin a new analysis, without closing the current analysis. Opens a window for the new analysis.
Open: Open fracture geometry (.BAB) and borehole object (.SOB) files. Uses the standard Microsoft Windows File Open menu syntax and assumptions.
Close: Close the current active analysis and all windows related to that analysis.
Save As: Saves statistical analysis .STS file for current analysis.
Exit: Exit FraCluster. Warns the user if statistical reports have not been saved.
Undo: Not currently implemented
Cut: Not currently implemented
Copy: Not currently implemented
Paste: Not currently implemented
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.
Remove: Remove the selected object
+ : Expand the current selection to display specific objects
- : Collapse the display to show only object types
Edit: Double click on a selected object to edit its properties.
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 FraCluster.
Analysis Options: Define the analysis parameters for the compartmentalization, tributary drainage volume, and reservoir block size analyses.
Toolbar: Display or hide the toolbar display
Statusbar: Display or hide the line providing status information.
Fractures: Display or hide fractures.
Boreholes: Display or hide boreholes
Clusters: Select clusters to display
Compartments: Select compartments to display
Histogram: Select histograms to display
Stats: Select statistics to display
Intersections: Calculate fracture intersections. This feature is only available once the fractures have been loaded.
Adjacency Lists. Calculate adjacency lists corresponding to the fracture connectivity map. This feature is only available once the fracture intersections have been calculated.
Cluster Analysis: Define fracture network clusters (interconnected groups of fractures which are not connected to other interconnected groups of fractures). This feature is only available once the adjacency list have been built.
Compartment Analysis: Define the volume and area statistics of fracture compartments. This feature is only available once the clusters have been identified.
Tributary Volume Analysis: Define the tributary drainage volume corresponding to user specified boreholes, using ;one of two alternative algorithms. This feature is only available once the clusters have been identified and the boreholes have been selected.
Reservoir Block Analysis: Determine the block size distribution for matrix blocks defined by fractures. This feature is only available once the adjacency list has been built.
New Window: Open a new window for the current analysis
Cascade: Cascade currently open windows
Tile: Tile currently open windows
Arrange Icons: Neatly arrange icons for minimized windows
Close: Close the current window
Close All: Close all the windows in the current analysis.
Help Index: Not currently implemented
Using Help: Not currently implemented
About FraCluster: FraCluster QA, copyright, and license information.
2.2.4.4 FraCluster Walk-through
This section describes an example user session with FraCluster.
FraCluster is run by clicking on the "FraCluster" icon. From this icon, the user is first confronted with the information and licensing screen (Figure 2-34). Upon accepting the license agreement by clicking on "OK", the user comes to the main window (Figure 2-27). Under the FILES menu, the user should use the mouse to highlight the discrete fracture network (DFN) files to be processed. For the tributary volume analysis, the user must also specify and exploration object file in .SOB format. The formats for the .BAB and .SOB files are described in Table 2-5 and Table 2-6.
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. This menu contains options to execute the reservoir compartmentalization analyses. These items generally need to be executed in sequence. A check mark appears once an analysis has been carried out to help the user keep track. First, the user should choose intersection calculations, and then generation of adjacency lists (Figure 2-35).
Once the fracture intersections have been computed and the adjacency lists have been built, the user can choose the type of analysis to be carried out. Under the Analysis menu are the choices Compartment, Tributary Volume and Matrix Block.
Selecting Compartment invokes a series of linked processes. First, the adjacency list is used in conjunction with the DFN files to create an intermediate file of points that corresponds to the (x,y,z) coordinates of fracture vertices. Next, QHULL is called to compute the volume and surface area of the convex hull that encloses these points. In order to compute the horizontal cross-sectional area of the hull, the (x,y,z) coordinates are projected onto a horizontal plane. This file is then processed by QHULL to compute the 2D cross-sectional area. This process is repeated until all compartments for all selected files have been analyzed. Upon completion, the user is returned to the Analysis menu. The user should then use the View menu to select the statistics and histograms to display.
Before selecting Tributary Volume from the Analysis, the user must provide a thickness through the Edit menu. This thickness corresponds to the distance into the matrix in which oil is mobilized through the pressure differential existing between the matrix and the fracture system menu. Upon selecting Tributary Volume from the Analysis menu, the user must first select boreholes to be analyzed from the loaded or defined exploration object file. Then, the user will chose either the Slab or the Convex Hull algorithm, as described in LaPointe et al. (1996). FraCluster processes the adjacency list and retains only those fractures connected to the specified boreholes. Next, the tributary volume associated with these retained fractures is calculated using the selected algorithm. This process can be time-consuming, so the program maintains a counter to indicate how many fractures out of the total have been processed. Upon completion, the user is returned to the Analysis menu. The user should then use the View menu to select the statistics and histograms to display.
For the Matrix Block analysis, the user is prompted to selected either the MDS or the Convex Hull algorithm, as described in LaPointe et al (1996). If the MDS option is selected, then the user will need to specify boreholes and borehole fields through the Edit menu. If the Convex Hull option is selected, the user will need to specify the number of points to be used in specifying the block through the Edit menu. The matrix block volume, area, etc. can then be calculated by FraCluster. Upon completion, the user is returned to the Analysis menu. The user should then use the View menu to select the statistics and histograms to display.
After completing analyses, the user can use the View menu to obtain graphical displays desired, and File/Save to save statistical summary (.STS) files.
To view results, the user should select View from the main menu. From this menu, the user can select the results. Options are available for displaying fractures, clusters, compartments, and statistics. For the compartmentalization analysis, the plots correspond to the volume and surface area of the 3D convex hull, and the area for the horizontal projection.
If the tributary volume analyses are selected, then graphs showing the histogram frequency (pdf) for the tributary volume of accessible matrix are displayed.
Likewise, if the matrix block sizes have been calculated, then the user can display histogram frequency (pdf) graphs of block volume, surface area and block dimensions corresponding to the user specified boreholes.
Table 2-5 BAB Discrete Fracture Network File Format
| Record Type | Variables | Interpretation |
| 1 | SCALE, NPROPS |
SCALE is the scale factor (in meters). NPROPS is the number of properties
assigned to each fracture (3 to 20). The values are specified in Babylonian
(base 60) notation, with no space between values. For example, a scale factor
of 1000 with 5 fracture properties would be specified as:
1E00O5 |
| 2 |
IVECTOR (I),
JVECTOR(I), KVECTOR(I) |
IVECTOR, JVECTOR, and KVECTOR are the X, Y, and Z components of unit vector normal to corresponding fracture. Values are given in Babylonian notation with no space between values. See note for further explanation. |
| 3 | X(I),Y(I),Z(I) | X(I),Y(I), and Z(I) are the coordinates. Values are given in Babylonian notation with no space between values. See note for further explanation. |
| 4 | fracture header |
Header record after last node specification and before beginning of fracture
specifications. Format for this record is:
*** FRACS *** |
| 5 |
NNODE(I),NSET(I),
VALUE(I,NPROPS) |
NNODE is the number of corner nodes defining this fracture, NSET is the set to which this fracture belongs, and VALUE provides the NPROPS values of transmissivity, storativity, transport aperture etc. Assigned to this fracture according to PROP.COD. There is one record of this kind for each fracture, and fractures are numbered in the order of the records. Values are given in Babylonian notation with no space between values. |
| Babylonian notation: In this file, all number are expressed in base 60 ("Babylonian notation), using ASCII characters 1 through 0, A through Z, and lower case a through lower case x. In this file, integers are expressed as one digit base 60 numbers. Real values are expressed as five digit numbers, with the fifth digit containing the sign and the exponent. Values which can be represented in Babylonian notation range from approximately 10-28 to 1016. However, babylonian numbers do not carry as many significant digits as are expressed in the REAL*4 binary representation. | ||
| Note: Record types 2 and 3 provide node and orientation information for fractures. For each fracture, there are NNODE(1)+1 records of type 2, where NNODE(1) is the number of corners specified for fracture 1. The first record of type 2 provides the orientation of the first fracture. The next NNODE(1) records are of type 3, and provide the coordinates for each of the nodes defining fracture 1. This is followed by a record of type 2 for the second fracture, then a series of records of type 3 for the nodes at the corners of the second fracture. This series is repeated until orientations and nodal coordinates are provided for all fractures. | ||
Table 2-6 Exploration Object Format (*.SOB)
|
# Any record beginning with a # is a comment #Borehole BEGIN borehole name = "Borehole NE-1X" survey_id = 1 origin = 80 -80 0 scan_trend = 0 scan_plunge = 0 scan_length = 160 radius = 0.12 END #Traceplane BEGIN traceplane name = "Tracemap XJX-43-2K" survey_id = 2 origin = 80 80 0 scan_trend = 0 scan_plunge = 0 scan_length = 160 tran_trend = 0 tran_plunge = 90 tran_width = 160 END |
2.2.5 Task 3.1.1 Linkage to Reservoir Models (Software Development)
During the quarter, initial discussions were carried out between Golder Associates and Marathon Oil to define the linkage to be made between three discrete fracture network (DFN) models and the Stratamodel stratigraphic analysis package. Initial development focused on definition of DFN and Stratamodel file formats and underlying concepts. Two fundamental concepts are being considered:
Further development will be initiated during the next quarter.
2.2.6 Task 4.1.1 Fracture Image Data Acquisition
During the quarter, Marathon collected and processed fracture image data, and provided the data for posting on the WWW server.
2.2.7 Task 4.1.2 Well Testing Data Acquisition
During the quarter, Marathon collected and processed well test and hydraulic response data, and provided the data for posting on the WWW server. The well test and hydraulic responses provided by Marathon during the quarter are summarized in Figures 2-36, 2-37, and 2-38.
2.2.8 Task 5.1.2 WWW Site Updates
During the quarter, Golder Associates updated the World Wide Web (WWW) Server for the project. The update included the following postings::
2.2.9 Task 5.2.1 Progress Reports
The quarterly progress report for the period June 7, 1996 to August 31, 1996 was prepared during the quarter, and was posted to the WWW.
2.2.10 Task 5.2.2 Research Reports
The research report, "Compartmentalization Analysis for Fractured Reservoirs" was completed during the quarter.
2.2.11 Task 5.2.3 Presentations
A paper describing project work was submitted for the "Fourth International Reservoir Characterization Technical Conference", sponsored by DOE-BDM/NIPER.
The following significant management activities were carried out during the quarter:
No project deliverables were prepared or delivered during the quarter.
No schedule revisions are contemplated at this time.
3.2 Milestones and Deliverables
The following project milestones during the quarter are described in Table 3-1. All milestones and deliverables during the quarter were met.
Table 3-1 Milestones and Deliverables
| Milestone or Deliverable | Scheduled Date | Delivery Date |
| Second Quarter Progress Report | 96.06.15 | 96.06.26 |
| Research Report, Fractured Reservoir Compartmentalization | 96.11.30 | 96.12.27 (est.) |
b extent of flow region, L
Dr ratio of inner-zone to outer-zone diffusivities
h hydraulic head, L
hD dimensionless head
hw constant head at source, L
H head in source, L
HD dimensionless head in source
Iv (z) Modified Bessel function
K hydraulic conductivity, LT-1
Kv (z) modified Bessel function
n flow dimension
p Laplace transform variable
q transient flux rate for constant-head conditions, L3T-1
qD dimensionless flux rate for constant-head condition
Q constant injection (or withdrawal) rate for constant-rate condition, L3T-1
QD dimensionless cumulative injection (or withdrawal) for constant-head condition
r radial distance from source, L
rD dimensionless radial distance from source
rD1 dimensionless radius of the inner region
r1 radius of the inner region, L
rw radius of the source, L
Ss specific storage, L-1
Sw storage capacity of the source, L2
SwD dimensionless storage capacity of the source
t time, T
tD dimensionless time
v parameter defined in (A20)
an area of a unit sphere in n dimensions
D1 dimensionless group defined by (A16)
D2 dimensionless group defined by (A17)
l1 dimensionless group defined by (A18)
l2 dimensionless group defined by (A19)
s dimensionless parameter defined by (A10)
Subscripts
D dimensionless
i = 1 (for inner region), or 2 (for outer region)
w source
1 inner region
2 outer region
