2. TASK PROGRESS

2.1 Active Tasks
2.2 Task Progress
2.2.1 Task 1.1.2: Data Updates
2.2.2 Task 4.1.2: Well Testing Data Acquisition
2.2.3 Task 4.2.1: Reservoir Model Implementation
2.2.4 Task 4.2.2: Reservoir Simulation
2.2.5 Task 5.1.2: WWW Site Updates
2.2.6 Task 5.2.1: Progress Reports
2.2.7 Task 5.2.2: Research Reports
2.2.8 Task 5.2.3: Presentations
2.2.9 Task 5.3.1: Workshop Preparation
2.2.10 Task 6: Management

2. TASK PROGRESS

2.1 Active Tasks

The following tasks were active during the quarter:

• Task 1.1.2 Data Updates
• Task 4.1.2 Well Testing Data Acquisition
• Task 4.2.1 Reservoir Model Implementation
• Task 4.2.2 Reservoir Simulation
• Task 5.1.2 WWW Site Updates
• Task 5.2.1 Progress Reports
• Task 5.2.3 Presentations
• Task 5.3.1 Workshop Preparation
• Task 6 Management

2.2 Task Progress

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

2.2.1 Task 1.1.2: Data Updates

During the quarter, Marathon Oil Company collected production and field testing data from the project study site and provided this data to Golder Associates. Data provided by Marathon included:

The data provided by Marathon during the quarter was assembled and is being incorporated into the project World-Wide-Web (WWW) site (Task 5.1.2). (Figure 2-1, Figure 2-2, Figure 2-3, Figure 2-4, Figure 2-5, Figure 2-6, Figure 2-7, Figure 2-8, Figure 2-9, Figure 2-10, Figure 2-11, Figure 2-12, Figure 2-13)

2.2.2 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. Well responses, steam injection, and production data provided by Marathon during the quarter are illustrated in Figures 2-14, 2-15, and 2-16.

2.2.3 Task 4.2.1: Reservoir Model Implementation

During this quarter, a conditioned DFN model of the Yates field Tract 17 was implemented as an extension to the stochastic DFN models developed during the previous quarters. The preliminary DFN model described in Dershowitz et al. (1998a) and used for tracer test modeling in Tract 17 was enhanced to better account for the effects of curvature, shale content and porosity.

2.2.3.1 Fracture Orientations

Geological analysis of fracturing in the Yates Field suggests that a major component of the fractures were formed by differential compaction and folding in the Middle and Late Permian. As a result, the orientations of these fractures relate to bedding curvature. The present-day curvature of the San Andres reservoir relates only in part to the drape folding, having been affected by later karsting. The present-day curvature of the overlying Seven Rivers "M" horizon is thought to be a better representation of the bending-induced stresses that may have produced fractures in the San Andres, since it was less affected by karsting and other sedimentological processes.

Figure 2-17 shows the structural contour maps for the Seven Rivers "M" horizon for the Tract 17 area. This map was produced by contouring picks from wells shown in the respective figures using an algorithm developed by Swain (1976). Orientations of fractures formed due to folding would be systematically related to local bedding orientation. The two most common orientations for joints would be perpendicular to bedding and parallel to bedding strike, and perpendicular to bedding and parallel to bedding dip. Faults should form in conjugate pairs relative to these two orientations of extension joints. They should make a solid angle with the extension joints that depends upon the mechanical properties of the rock, but typically might be from 20 to 40 degrees (Figure 2-18).

Analysis of fractures from the three vertical wells YU1711, YU1755 and YU2511 in the Tract 17 vicinity (Figure 2-19) shows that fractures occur in many different strike orientations. The poles to these fractures define bands that represent fractures that dip about 70 degrees. The least common fractures are those that dip to the northwest.

Interpretation of the FMI and FMS data suggests that most fractures are joints, not faults. Bending-related extension fractures should form perpendicular to bedding, and so those that strike parallel to bedding strike should dip approximately 90 degrees from bedding dip. Histograms of FMS and FMI data for Tracts 17 (Figure 2-20) show that bedding dip is typically in the 5 to 15 degree range, which in turn would suggest that joints should dip between 75 and 85 degrees. Table 2-1 shows the statistics for different types of features detected in the four wells.

Table 2-1 Dip statistics for three vertical and one horizontal well in the Tract 17 test area

Analysis of the structural contour maps for both the San Andres and the Seven Rivers "M" show much shallower slopes than the bedding plane dips determined from FMI and FMS logs. Even in the most steeply dipping portions of the tracts (for example, in the northeast corner of Tract 17), regional dips are only on the order a few degrees at most. Thus, the structural contour maps of these horizons may be useful indicators of bedding strike, but do not accurately reflect dip. In the conditioned DFN models for Tract 17, strike was assigned on the basis of the structural contour map strikes, and dip was assigned as a Fisher distribution with mean dip _ of 70 degrees with Fisher dispersion _ of 8 (Figure 2-19). The resulting orientations of fractures generated according to this procedure are shown in Figure 2-21. They show a good correspondence with the fracture orientations inferred from well data.

2.2.3.2 Influence of Shale Content and Porosity on Fracture Intensity

Tinker and Mruk (1995) discussed the relation between shale content and porosity in the San Andres, and fracture intensity. They showed that fracture intensity begins to decrease as matrix porosity approaches 20%, reducing to roughly half of its peak value for the dolomitic reservoir lithologies.

Shale content also influences fracture intensity. As the percentage of shale increases, the rock tends to behave more ductility, reducing the amount of brittle strain, or fractures propagating in the dolomites terminate prematurely against the shales, likewise reducing fracture intensity. Tinker and Mruk (1995) showed that the fracture intensity in the more argillaceous units was about half that in the cleaner dolomitic units. Their data suggested that rocks with shale content greater than 10% (corresponding to a gamma ray response of greater than 40 API) should have fracture intensities approximately half that of the less argillaceous units.

The gamma ray profiles for wells in Tract 17 and Tract 49 (Dershowitz et al., 1997) show that the reservoir in Tract 17 have shale-prone areas, while the reservoir in Tract 49 has little shale or argillaceous material.

A total fracture intensity of 0.07 m^-1 was reported in Dershowitz et al. (1998). In the conditioned Tract 17 model, fracture intensities in areas where matrix porosity is greater than 20% or shale content is greater than 10% were reduced by 50% to P₃₂ = 0.035 m^-1. As a result, the average intensity P₃₂ in the model is 3.85x10^-2 m^-1 .

A typical realization of the conditioned Tract 17 DFN model is shown in Figure 2-22a. Figure 2-22b illustrates trace patterns of one extension joint set on horizontal cross-sections through the DFN model.

Table 2-2 Conditioned DFN Model for TAGS Support Simulations (Tract 17)

2.2.4 Task 4.2.2: Reservoir Simulation

During this quarter, the conditioned Tract 17 DFN model was used to derive effective properties for heat transport /reservoir simulation of TAGS. The heat transport /reservoir simulations will be completed during the tenth quarter.

The Tract 17 reservoir parameters derived during the quarter are summarized in Table 2-3. All analyses were carried out using the preliminary 11,250 cell THERM/DK and ECLIPSE grid of 30 cells of 71 m (E-W) by 25 cells of 71 m (N-S) by 15 cells of 18.5 m (Z).

Table 2-3 Reservoir Parameter Simulations

*At a fracture transmissivity cutoff of 10^-4 m²/s

2.2.4.1 MAFIC Numeric Permeameter Simulations

Block permeability simulations were carried out by dividing the DFN model into 11,250 cells according to a preliminary THERM/DK - ECLIPSE model. A unit gradient was applied in each direction in turn. The boundary conditions for these simulations are provided in Figure 2-23. Effective conductivity was calculated from the block flux as,

K_x = Q_x / A_x i_x (Equation 2-1)

K_y = Q_y / A_y i_y

K_z = Q_z / A_z i_z

where the subscripts x, y, and z indicate the direction, K is the conductivity (m/s), A is the flow area, and i is the gradient. A gradient i of 1 was used in all simulations. The flow area for x and y directions was 71 m x 18.3 m = 1300 m² , and the flow area A for the z direction is 71 m x 71 m = 5041 m² . The conversion between units of m/s and milliDarcy [mD] units is,

K [mD] = K[m/s] _[Pa^.s] / (__oil[kg/m³] * g[m/s²])/(9.869233*10^-16)

__oil[kg/m³] = __water[kg/m³] 141.5/(131.5+API)
(Equation 2-2)

where _ is the viscosity, _ is the density, API is the API density in degrees, and g is the gravitational constant. For Yates, the reference density was taken as 30° API, corresponding to 876 kg/m³ , the gravitational constant g was assumed at 9.807 m/s², and the viscosity was taken as 7.5 centipoise, corresponding to 0.0075 [Pa^.s]. As a result, 10^-5 m/s corresponds to 8841.479 mD.

The results of MAFIC grid block simulations are provided in Tables 2-4 and 2-5. MAFIC grid block conductivities are illustrated in Figures 2-24 and 2-25.

Table 2-4 Grid Block Conductivity Statistics

Table 2-5 Grid Block Anisotropy Statistics

2.2.4.2 StrataFrac Analysis

StrataFrac was designed to (a) adapt statagraphic (cellular) data for use in DFN model conditioning, and (b) derive cellular values from DFN models. For the present analysis, StrataFrac was used to convert the conditioned DFN model (Figure 2-22a) into a geocellular model using the reference 71 m x 18.3 m grid.

The first StrataFrac analysis addressed the issue of active/inactive cells and flow barrier cells. Inactive cells are cells with no fracture permeability in x, y, or z directions. Of the 10,530 cells, 8941 or 84.9% have permeability greater than 10^-7 m/s in at least one direction. Thus, 15.1% of the cells can be considered inactive.

Flow barriers are cells in which there is no permeability at least one direction. Based on StrataFrac analysis of the DFN model, flow barrier percentages are as follows:

• X direction: 73% of cells have no connectivity for flow in the X direction
• Y direction: 70% of cells have no connectivity for flow in the Y direction
• Z direction: 10% of cells have no connectivity for flow in the Z direction

This is consistent with the relationship between fracture size and cell size. In the DFN model, the fracture size is generally on the range of 36m to 75 m in diameter, and every grid cell has on the order of 1 to 3 fractures. As a result, few cells do not have sufficient fracturing to percolate through the 18.3 m in the Z direction, while the majority of cells do not have sufficient fracturing to percolate through the 71 m cells in the X and Y directions.

The cell based fracture porosity n_f(i) was calculated by dividing the fracture volume by the cell volume:

n_i = _ A_ij t_ij /V_I (Equation 2-3)

where n_f(i) is the fracture porosity of cell i, A_ij is the area of the portion of fracture j in cell i, t_i is the thickness of fracture j in cell i, and V_i is the volume of cell i ( 275.5 m³ in the current analysis).

It is important to note that this fracture porosity n_f does not include the porosity of fractures smaller than 10 m in radius or larger than 50 m in radius, and also does not consider fractures which would be considered "non-conductive". As a result, the porosity n_f could be considered the porosity of the flowing fracture network, not including deterministically identified features.

Table 2-6 presents statistics on the fracture porosity and fracture intensity P₃₂ on a cell basis from the DFN model. The relationship between fracture intensity P₃₂ and porosity n_f is illustrated in Figure 2-26. The spatial variation of fracture porosity is illustrated in Figure 2-27.

Table 2-6 Grid Cell Fracture Porosity and Intensity

2.2.4.3 FraCluster Analysis

FraCluster analysis was used to derive dual porosity (matrix block) reservoir parameters, compartmentalization parameters, and tributary drainage volume parameters. FraCluster analyses were carried out directly

The matrix block calculation is illustrated in Figure 2-28, and is described in Dershowitz et al (1997). The sigma factor, block volume distribution, and Z-factor are summarized in Table 2-7, Figures 2-29, 2-30, and 2-31.

Table 2-7 Sigma Factor, Block Volume, and Z-Factor Statistics

Compartment size in a fractured reservoir is directly dependent on what is considered a "conductive" fracture. Thus, if all features are considered as conductive, the reservoir could be considered a single compartment. Conversely, if only features with a very high transmissivity are considered conductive, compartments would be coincident with these high transmissivity features, and there would be a large number of small compartments. Compartmentalization analysis algorithms are described in Dershowitz et al. (1997).

Table 2-8 summarizes the statistics for compartments identified in the conditioned DFN model for different transmissivity cutoffs. Compartmentalization analysis for Tract 17 is illustrated in Figures 2-32 and 2-33.

Table 2-8 Compartmentalization Analysis Summary

For a given transmissivity cut-off, FraCluster was used to derive the number of compartments, the distribution of compartment projected area, compartment volume, and the intensity of fractures within the compartments. Figure 2-34 illustrates the formation of compartments in the Yates Tract 17 model as a function of the transmissivity while is used to distinguish between "conductive" and "non-conductive features". For a transmissivity cutoff of 10^-6 m²/s, the entire DFN is connected, resulting in a single network. The maximum number of compartments is formed when a cutoff of approximately 4x 10^-4 is used. From there, increases in the transmissivity cutoff decrease the number of compartments dramatically. For Tract 17, a transmissivity of on the order of 10^-4 m²/s might be considered a reasonable cutoff, such that on the order of 200 hydraulic compartments would be found in the field, connected only by features of less than 10^-4 m²/s.

The projected compartment area distribution (Figure 2-35) is the key for the design of infill drilling. From the Tract 17 DFN model, the mean compartment volume at a transmissivity cutoff of 4 x 10^-4 m²/s is approximately 10,000 m². The compartment volume distribution is useful for assessing the oil producable for a given compartment (Figure 2-36). The compartment volume varies from on the order of 10⁴ m³ to 10⁹ m³, with a mean on the order of 10⁷ to 10⁸ m³. The variability between compartments is much greater than the variability in the mean compartment volume with transmissivity cutoff.

Intensity P₃₂, the fracture area per unit volume in compartments determines the area available for transfer of fluids from matrix storage to the fracture networks which feed well production. As P₃₂ increases, the fracture network becomes more efficient for gravity drainage of reservoir matrix storage. As shown in Figure 2-37, the mean compartment P₃₂ is fairly constant at 0.07 to 0.12 m²/m³. However, very large values of P₃₂ can occur, indicating a very effective drainage network, particularly for transmissivity cutoff less than on the order of 10^-3 m² /s.

Tributary drainage volume analysis is similar to compartment analysis, except that it focuses on compartments as they intersect specific well fields. The Tract 17 well field analyzed includes all of the currently installed vertical wells (Figure 2-38). Results of this analysis are summarized in Table 2-9.

Table 2-9 Tributary Drainage Volumes

Figure 2-39 illustrates the distribution of tributary drainage volume for the Tract 17 DFN model based on the well field analyzed. A single compartment of on the order of 10⁹ m³ is accessed the wells analyzed within the Tract 17 DFN model region if all fractures above approximately 10^-5 to 10^-4 m²/s are considered conductive. For a transmissivity cutoff greater than 10^-4, this compartment is seen as multiple smaller compartments, and therefore more, smaller compartments are identified in the tributary drainage volume calculation.

The exchange surface area for the tributary drainage volumes are shown in Figure 2-40. Figure 2-40a shows the variation in fracture intensity with the transmissivity cutoff. Figure 2-40b shows the total connected fracture surface area available for fluid transfer from matrix storage to the flowing fracture network. On the order of 10⁷ m² are available for fluid exchange with a transmissivity cutoff of 10^-5 to 10^-4 m²/s.

Tract A tributary drainage volumes are visualized in Figure 2-41.

2.2.4.4 Flare Analysis

Tract 17 reservoir permeability-thickness was calculated from wells simulated into the Tract 17 conditioned DFN model Permeability thickness kh was calculated as the total transmissivity from all the fractures seen in a 15 m interval, using a representative sample of 9 of the actual Tract 17 vertical wells.

The cumulative density function for permeability thickness from this analysis is presented in Figure 2-42 for intervals with permeability thickness greater than 10^-7 m²/s. Table 2-10 summarizes simulation results statistically for intervals with permeability thickness greater than 10^-7 m²/s. Based on this analysis, the median permeability thickness is 4.3 x 10^-4 m²/s, which corresponds to 1.16 x 10⁵ mD-ft. The median permeability is the permeability for which 50% of intervals tested have greater permeability thickness.

Table 2-10 Permeability Thickness (m²/s) for 15 m Production Intervals

2.2.5 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:

• Seventh Quarterly Report (Dershowitz et al, 1998a)
• Annual Report (Dershowitz et al., 1998b)
• Research Report, Fracture Data Analysis (Dershowitz et al.,1998c)
• Additional data provided by Marathon (Figures 2-1 through 2-13)

2.2.6 Task 5.2.1: Progress Reports

The annual report for the period March 1, 1997 to March 1, 1998 was prepared during the quarter, and was posted to the WWW.

2.2.7 Task 5.2.2: Research Reports

No new research reports were completed during the quarter.

2.2.8 Task 5.2.3: Presentations

The following presentations were made during the quarter:

• La Pointe, P.R., T. Foxford, and V. Ivanova, 1998. Improved Estimation of Reservoir Compartmentalization, Tributary Drainage Volume and Connectivity Through Discrete Fracture Network Modeling. Annual Meeting American Assoc. Petrol. Geol., May 17-20, 1998, Salt Lake City, UT.
• Dershowitz, W., T. Eiben, and T. Cladouhos, 1998. Linking Dual Porosity Continuum and Discrete Feature Network Models for Fractured Reservoirs. Annual Meeting American Assoc. Petrol. Geol., May 17-20, 1998, Salt Lake City, UT.
• La Pointe, P.R. and W. Dershowitz, 1998. Discrete Fracture Network Modeling for Petroleum Exploration and Reservoir Engineering in Fractured Reservoirs. Railroad Commission of Texas, Technology Transfer Seminar, May 20, Dallas, TX.

2.2.9 Task 5.3.1: Workshop Preparation

During the quarter, alternative venues for the project technology transfer workshop were explored. It was initially hoped that the workshop could be held in conjunction with an SPE, AAPG, and SEG meeting. However, due to the constraints of the project schedule, it was decided to hold the workshop in Seattle, WA on September 15, 16, and 17. The workshop announcement and registration form were posted to the project web site. The preliminary workshop schedule is provided in Table 2-11.

The Inn at the Market in downtown Seattle http://www.innatthemarket.com has been booked for the workshop.

Table 2-11 Technology Transfer Workshop

2.2.10 Task 6: Management

No significant project management activities were carried out during the quarter.