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Abstract This paper presents a pixel-based hierarchical geostatistical modeling of submarine fan turbidite sandstone deposits in Tajin and Agua Fria fields of Chicontepec basin in the Gulf of Mexico. Methods are discussed for identifying and dividing the stack of heterogeneous siliciclastic sediments in these fields, using sequence stratigraphy, petrophysical well log characteristics, geological facies model and 3D seismic data.

An integrated multidisciplinary geostatistical reservoir characterization is conducted in two main steps. First, a large-scale reservoir framework of multiple sequence and subsequence surfaces is constructed based on the integration of data sources of geologic well markers, petrophysics, and seismic horizons. Second, high-resolution 3D distributions of reservoir properties are generated, accounting for inherent inter-relationship among reservoir property data and the three main data scales of log, sub-sequence layer and sequence interval.

At onset, shale volume content in Tajin field and total porosity in Agua Fria field are modeled. Block kriging, trend model, and conditional thickness-weighted Bayesian scheme are presented for the integration of data types and data scales. Facies distributions in Tajin are modeled by indicator kriging conditioned to Vsh content, and hence to seismic. Porosity distributions are by sGsim collocated with Vsh for each facies group, and water saturation distributions are collocated with porosity. Permeability distributions are function of porosity, water saturation, facies and sub-sequences. In Agua Fria, effective porosity and facies are by p-field related methods. Patterns of sand continuity and pay sand connectivity are derived and uncertainty in their prediction is evaluated.

Introduction There has been a great interest in the industry in the past decade to use multi-disciplinary geostatistical techniques for integrated reservoir characterization in various types of reservoir depositional environments1-3. Research in industry and academia is making advances in better utilization of seismic data for generating interwell data and information in reservoir areas where well data is non-existent4-6. Although seismic does not have the vertical resolution of well logs, its areal sampling coverage is dense, providing some details of reservoir unreachable by wells.

In the past several years, we have embarked on developing technology to integrate geological, geophysical and reservoir engineering information for reservoir management and field development of Chicontepec fields. It is recognized that development of an integrated geostatistical methodology, verified by field data, will be an appropriate approach for this purpose. As a case study, Tajin field and nearby Agua Fria and Coapechaca fields are selected for the development and benchmarking of this technology to be expanded later to other fields in this basin. Results of our initial work are documented in previous publications7-8.

Chicontepec basin, with a giant field area of 123 km in length and 25 km in width, has been formed by a complex system of submarine fan and turbidite sediments deposited in an eroded deep-water canyon originally formed in the Gulf of Mexico. The first field in the basin was discovered in 1931 and commercial production commenced in 1952. The Chicontepec reservoirs consist of Upper Paleocene-Lower Eocene alternating sandstone and shale bodies. These bodies do not present a continuous laminar extension throughout the field, and a wide variation in clay-shale content is recognized. It is crucial to improve reservoir characterization; especially distribution of sand-shale bodies and their pay connectivity, in order to optimize filed development planning and management of the Chicontepec reservoirs.

Geostatistical techniques can be categorized in two types: pixel-based and object-based methods. Pixel-based methods are largely used to characterize reservoir parameters and structures, but they are not designed to explicitly reproduce geometric shapes as their final goal. Object-based methods are suitable to represent geological features with certain geometric attributes, provided that adequate data on the geometry of geological features such as channels and turbidite

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Integrated Geostatistical Reservoir Characterization of Turbidite Sandstone Deposits in Chicontepec Basin, Gulf of Mexico Maghsood Abbaszadeh, SPE, Innovative Petrotech Solutions, Inc., Osamu Takano, Hiroshi Yamamto, Japan Petroleum Exploration Co., Tatsuo Shimamoto, SPE, Teikoku Oil Corp., Nintoku Yazawa, SPE, Japan National Oil Corp., Francisco Murguia Sandria, David H. Zamora Guerrero, Fernando Rodriguez de la Garza, SPE, PEMEX Exploration y Production

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lobes is available. The pixel-based approaches offer generality and can often generate results resembling actual geology of fluvial and turbidite deposits9.

This paper provides a comprehensive and integrated pixel-based geostatistical methodology for reservoir property distributions of Vsh, facies, effective and total porosity, water saturation and permeability in Tajin and Agua Fria fields. Geological, petrophysical and seismic attribute and horizon data are integrated within the framework of pixel-based geostatistics to generate 3D property distributions. Sand body continuity and pay sand connectivity are assessed by identifying connected low shale volume content areas (i.e., Vsh <0.4), which also meet pay cutoff criteria. It is found that upper Tajin and Agua Fria deposits are predominantly good quality turbidite channel type sands of limited lateral extent, while those of lower Tajin and Agua Fria are lower quality sheet like sands due to secondary diagenesis and cementation.

Geological Description Regional Geologic Setting The Paleogene Chicontepec Basin is located between the Sierra Madre Oriental and the Golden Lane Platform, extending northwest-southeast along the Gulf Coast in Mexico. The main reservoir rock of the basin is submarine fan turbidite sandstone derived from the Sierra Madre Oriental to the west of the basin. Previous sedimentological studies10 demonstrate that there were multiple sediment supply systems forming submarine fans along the western margin of the Chicontepec Basin (Fig. 1).

The Tajin, Coapechaca and Agua Fria oil fields are situated in the southern part of the basin to the west of Poza Rica, Veracruz. According to the previous studies, these fields are located in the depositional area of one of the submarine fans along the basin margin. In these oil fields, 184 wells have been drilled (111 in Tajin, 3 in Coapechaca, and 70 in Agua Fria) and 3D seismic data have been acquired, covering a large portion of these oil fields but not necessarily coinciding with the entire well coverage areas (Fig. 2). In this study, we utilized well-log and core data derived from the wells and the 3-D seismic data for the geological, petrophysical and geostatistical analyses.

Sequence Stratigraphy We conducted geological/sedimentological analyses based on the concept of sequence stratigraphy for the purpose of stratigraphic division and facies distribution modeling. Depositional sequences were recognized on well logs and seismic sections on the basis of sequence stratigraphic depositional models. Fig. 3 shows the result of sequence stratigraphic division in the Tajin, Coapechaca and Agua Fria fields. The reservoir unit in these fields is divided into twelve depositional sequences; these are, Sequence AF100, AF85, TAJ100, TAJ85, TAJ60, AF70-TAJ50, AF60-TAJ40, AF58-TAJ20, AF52, AF50, AF30 and AF10 in stratigraphic ascending order (Fig. 3). Sequence AF100 and AF85 horizons are absent in the Tajin field because they were eroded away after deposition. Sequence TAJ100, TAJ85 and TAJ60 horizons are absent in the Agua Fria area because of no deposition due to bypassing of sediments. Sequence AF52 horizon and the uppermost part of Sequence AF58-TAJ20 are

absent in the Tajin field because they were eroded away after deposition (Figs. 3 and 4).

Three important sequence stratigraphic surfaces of SB, MCS and TS within each depositional sequence were recognized. SB (Sequence Boundary) is the boundary between two vertically stacked depositional sequences. MCS (Minor Condensed Section) is a muddiest horizon in LST (Lowstand Systems Tract). TS (Transgressive Surface) is a boundary between LST and TST (Transgressive Systems Tract) of a depositional sequence (Fig. 3).

Facies Classification Facies were classified and divided based on log facies analysis and additional core descriptions. Log facies were classified mainly based on log patterns of gamma ray, resistivity and neutron-density logs, and then they were correlated to core facies in order to determine the lithology and intrinsic sedimentary facies. As a result, four major turbidite facies were recognized; these are SA, NA, MA and M. Fig. 5 describes main lithology; inferred sedimentary environments and characteristic log patterns for each facies.

Facies SA consists of sandstone and sand-rich alternating beds of sandstone and shale, which are regarded as high-density turbidites. Upper fan, mid fan or distributary channel of a sandy radial fan, or a channel of a channel-levee system is inferred as a sedimentary environment. Facies NA includes normal alternating beds of sandstone and shale, and is regarded as low-density turbidites. Mid fan of a sandy radial fan or levee of a channel-levee system is inferred as a sedimentary environment. Facies MA consists of shale-rich alternating beds of sandstone and shale, and is also regarded as low-density turbidites. Lower fan of a sandy radial fan or levee of a channel-levee system is estimated as a sedimentary environment. Facies M is mainly shale including slump sediments, which was deposited in a slope or basin floor environment.

The results of petrographic analyses indicate that Facies NA and a part of Facies SA and MA tend to show promising reservoir quality.

Depositional Model Facies distribution maps of the Tajin and Agua Fria fields were created for each subsequence unit (SB-MCS, MCS-TS and TS-SB) by first plotting facies determined on well logs on a well-by-well basis and then estimating their distribution. Depositional systems, such as channels and lobes, were interpreted on the basis of the estimated facies distribution. In addition to the well-log facies plotting, seismic facies of 3D seismic data were used for estimating distributions of depositional systems for all 3D seismic areas. Seismic facies were categorized and mapped for each depositional sequence unit using Paradigm Geophysical software “Stratimagic”. Lastly, depositional models were constructed on the basis of the well-log-based facies distribution maps and the seismic facies maps.

Based on the interpreted maps, it is inferred that the western part of Tajin and Agua Fria fields corresponds to the slope adjacent to the western margin of the basin, whereas the eastern part is thought to be the central axis of the trough. Mostly clastics were supplied from the west or southwest

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through channels or depositional lobes of submarine fans (Fig. 6). In Sequence AF85, TAJ100 and TAJ85, distribution of turbidite sandstone tends to be sheet-like, whereas channel-levee type distribution patterns predominate in Sequence TAJ60, AF70-TAJ50, AF60-TAJ40, AF58-TAJ20, AF30 and AF10.

Diagenesis and Property Alteration Petrographic analysis was conducted to evaluate diagenetic factors controlling reservoir properties of the Chicontepec turbidites. First, cement and pore types of the turbidite sandstones were described using thin sections derived from selected wells. Based on the occurrence patterns of cement and pore types, diagenetic history for the Chicontepec turbidites was reconstructed. After deposition, the Chicontepec turbidites were buried approximately 1,000m deep. As the burial depth increased, quartz and calcite cement filled the original pores of sandstones, resulting in reduction of porosity. Then, unsaturated water dissolved calcite cement during uplift in the middle to late stage of diagenesis, resulting in recovery and enhancement of porosity.

Next, the distributions of cementation and dissolution were mapped by plotting the results of thin section descriptions for each subsequence unit. The results indicate that the lower part of the Chicontepec turbidite sequences tends to be highly cemented with exceptions of partly dissolved areas, whereas cementation intensity is low and dissolution is prominent in the upper part. Comparisons of the cement/dissolution maps with the facies maps reveal that the lower part is characterized by patch-like complex cementation patterns without controls of sheet-like facies distributions, whereas the cementation and dissolution tend to be clearly controlled by channel-like facies distribution patterns in the upper part.

Petrophysical Analysis Vsh from Logs Well log data from nearly all 184 wells in the study area were environmentally corrected and depth shifted at sampling interval of 0.25 m. The GR curve of each well had its own sand and shale lines, necessitating determination of individual well GR limiting values and normalization to an equal scale.

The calculation of shale volume, Vsh, was done mainly by using the normalized GR curves and standard petrophysical algorithms11. When a GR curve was poor, Vsh was calculated based on the normalized RHOB - PHIN or RHOB - DT difference. For these calculations: minimum GR recording for clean sand = 30 API, maximum GR recording for clean shale = 90 API, apparent shale neutron porosity = 0.320, apparent shale sonic porosity = 0.314, apparent shale density porosity = 0.107. A crossplot of GR readings vs computed Vsh indicated that Vsh<0.4 largely corresponds to facies SA+NA, and hence is used as a cutoff criterion for sand definition. Vsh>0.6 represents shale, and 0.4<Vsh<0.6 indicates shaley sand.

Porosity Model Total porosity φT, a combination of volume-weighted sand and shale porosities, is computed from sonic, neutron and density logs at 0.25 m resolution (about 1 ft) by standard petrophysical methods. An average of calcite and quartz theoretical

readings are used in these calculations; namely: matrix travel time of 52 msec/ft, the neutron porosity index of 2 % lower than clean quartz, and matrix density of 2.68 g/cc. The minimum porosity value is kept at 2%, consistent with core measurement and independent of tool selection. The best porosity value among these methods is the one requiring least manipulations to original logs. The corresponding φsh values in sonic, neutron and density log calculations are 0.314, 0.312, 0.107, respectively.

Two models of laminated shale and dispersed shale are applied for the calculation of φe from φT, depending on the facies types (Fig. 7). The laminated shale model considers more distinct alternating multilayer sandwiched beds of shale and sand for Facies SA and NA. Dispersed model applies to Facies MA and M, because the sands in these facies are so thinly bedded that they behave like dispersed sands within a shale environment:

Laminated Model: shsheshT V)V1( φ+φ−=φ (1) Dispersed Model: shsheT V φ+φ=φ (2) In comparing log data with core data, it would be

necessary to convert core-scale data to log-scale because the resolution of cores and logs are 2 in and 20 in, respectively, an order of magnitude different. This is done by using φlog-scale= NTG * φcore-scale, and noting that NTG = 1 - Vsh for SA and NA, and NTG=1 for MA and M facies. The same concept also applies to permeability. A crossplot of predicted porosity from log vs. core is shown in Fig. 8.

Permeability Model A comprehensive log-based permeability prediction model is developed for the fields of Tajin and Agua Fria as a function of six parameters. These include three log-derived petrophysical properties of φe, Vsh, Sw; geological facies classification, sub-sequence intervals within stratigraphic sequences, and four compartments of upper-lower Tajin and upper-lower Agua Fria. The permeability model, however, is not based on individual sequence intervals.

The non-parametric Alternating Conditional Expectation (ACE) algorithm12 is used to develop correlation functions between core permeability and the above six independent parameters. The ACE method extracts intrinsic relationships between the dependent and a series of independent variables without assuming a-priori regression model form. Fig. 9 compares permeability predicted by the ACE method vs. core permeability. The resulting correlation coefficient of Fig. 9 is about 95%, indicating a good permeability prediction model. High permeability streaks (largely in upper Agua Fria and Tajin) are predicted well, and the low permeability zones (mainly in diagenetically cemented lower Tajin) are predicted with a lesser accuracy.

Sensitivity studies of permeability prediction as a combination of various independent parameters show that porosity and sub-sequences are the most significant factors. Division of the fields into four compartments is important. Inclusion of Sw and Vsh are relatively important, while facies classification does not contribute much to the model.

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Geophysical Analysis Seismic Horizon Picking Major horizons corresponding to sequence boundaries were picked, and subsequently were refined through an iterative approach by matching them to well marker depth data. Depth conversion was achieved using an improved seismic velocity cube. The seismic horizon picking was performed every 10 lines and every 10 traces, guided by geologic sequence stratigraphic definitions. Because of limited seismic (roughly, +/- 25 m), it was not possible to pick sub-sequence surfaces of TS and MCS from the seismic signature.

Seismic Attribute Extraction Nine seismic attributes were extracted only at the scale of sequence intervals because of limitations in seismic resolution to define finer sub-interval layering. These attributes are classified into three groups; amplitude statistics, complex statistics and sequence statistics. The amplitude statistics group includes: average absolute amplitude, average peak amplitude, RMS amplitude, total absolute amplitude and total amplitude. The complex trace statistics consists of average reflection strength, average instantaneous frequency and average instantaneous phase. Only energy-half time attribute is included in the sequence statistics class. Reliable seismic inversion is not available for useful impedance attribute.

Correlation of Attribute with Petrophysics The ACE algorithm is used to develop correlation functions between sequence interval seismic attributes and averaged Vsh (in Tajin field) and φT (in Agua Fria field) from well data. We used φT in Agua Fria field because the deposits in this field are more thinly laminated, and theoretical considerations indicate that φT would better relate well data to seismic response.

Theoretically, the independent variables of seismic attributes should have no correlation among each other for the ACE algorithm to apply. This is not the case for all nine seismic attributes because some of them have been obtained by certain mathematical manipulations from other attributes. Principal component analysis was performed on attribute data to transform them to a set of nine orthogonal principal components. The ACE algorithm was subsequently applied to these independent principal components, and correlations between seismic attributes and averaged petrophysical well data of Vsh and φT were developed.

Fig. 10 compares the predicted Vsh from seismic attributes with average Vsh from well data for five sequence intervals of TAJ-SQ40 to TAJ-SQ100. The y-axis represents Vsh calculated from the correlation functions built by the ACE algorithm. The overall correlation coefficient in Fig. 10 is 0.905, noting that a correlation coefficient of unity indicate perfect prediction of Vsh by seismic. Fig. 11 is for φT in Agua Fria field, with a correlation coefficient of 0.804.

Integrated Geostatistical Reservoir Characterization In this section we discuss pixel-based geostatistical techniques for 3D property modeling in the study area of Fig. 2. The reservoir model covers an area of 6,250 m by 20,000 m.

Reservoir Framework Construction The first step in building a geostatistical reservoir model is to construct a large-scale reservoir framework by imposing first-level geological controls on the reservoir architectural structure. The large-scale reservoir framework is primarily built on the sequence stratigraphy of the turbidite sand deposit systems, seismic horizon picks and well marker data. The goal is to mathematically describe the comprising sequence and sub-sequence surfaces, upon which subsequent detailed geological information is incorporated

Sequence Boundary Surfaces. The sequence boundaries

have been identified from well logs and seismic horizon picking, representing two different scales. The resolution of seismic horizon definition is around 20-30 m and that of well logs is about 1-2 m. Also, the two data types cover different areas of the fields with some common regions between the two of them, as seen in Fig. 2. Therefore, sequence boundary surfaces generated from either set of data “alone” will only be extrapolations in regions where data control from the other source type does not exist. Standard integration techniques of cokriging or collocated cokriging1,14 will not apply adequately. The following approach for the integration of partially overlapping well and seismic data types is offered.

Seismic and well data are combined into a single collective data set for each sequence, and fitted to a surface. The fitting is done by the Discrete Smooth Interpolation (DSI) technique13 used in the geological and reservoir modeling software GOCAD. The fitted surface is subsequently re-interpolated to more closely match the well marker data because of the scale difference between well and seismic information. This method has the advantage that it captures inherent trends in both seismic and well data everywhere.

After generating the sequence boundary surfaces, the thickness of sequence intervals is calculated and the inconsistent and overlapping surfaces are truncated or eroded based on geological information. For Tajin field, the surfaces in the lower Tajin are truncated against TAJ-SB100, which closely approximates the limiting wall of the Tajin canal. Fig. 12 shows an example of some of the surfaces generated.

Sub-Sequence Boundary Surfaces. At a second level of

sequence stratigraphy, data corresponding to TS and MCS events within each main sequence interval are used to impose additional geological control on the construction of reservoir framework. The resolution of seismic is too low to define the TS and MCS horizons within the sequence intervals, thus only well data is used to identify TS and MCS subsequences.

Surfaces TS and MCS surfaces are separately created from the corresponding well marker data. These surfaces are carefully constrained by the corresponding upper and lower sequence boundaries, SB. Overlapping is eliminated by truncation on the MCS surface. For Tajin field, if the lower SB of a sequence interval itself is already truncated against the Tajin canal base, the MCS and TS surfaces are also truncated against the canal base. In this fashion, some control from seismic through the SB surfaces is also imposed into the process of building the TS and MCS surfaces.

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Stratigraphic Gridding. The definition of stratigraphic grids (s-grid) follows the conceptual geological model as closely as possible. It includes truncation of surfaces and erosional events as dictated by geology. Calculations of variograms and geostatistical conditional simulations are conducted in s-grid in order to preserve geology and honor correlation structure of various depositional events.

The layout of geostatistical model for the study area is shown In Fig. 13, represented by 125 x 400 grid cells in the normalized transformed u,v coordinate system (nu=125, nv=400). The zero-degree azimuth refers to N-S direction and 90-degree azimuth is in the E-W direction. The Tajin field model is represented by 117 x 215 grid cells (nu=117, nv=215). Cell dimension is 50m x 50m, so there are approximately 8 cells between a well pair distance. Large variations in interwell heterogeneity characteristics of discontinuous turbidite clastic deposits necessitate such refined griding.

In the vertical direction and in the transformed normalized coordinate system of w, a variable griding system is used for each interval and sub-intervals at the scale of 0.5m to 1 m. This refined definition is also necessary to capture highly variable thin sand/shale laminations of turbidite deposits that are identified at the log scale. On average, at least 100 cells are used vertically for each sequence interval.

There are two main models of proportion and erosion for generating s-grid in the vertical direction. From the geological knowledge of deposition system in Tajin, the proportion model applies to the lower Tajin sequences. The erosion model is suitable for TAJ-SQ20 and TAJ-SQ40, where turbidite channel deposits or eroded surfaces are expected above TAJ-SB50. We consider that erosion mostly occurs at sequence boundaries. An example of s-grid for TAJ-SQ40 is shown in Fig. 14. S-grids inside the lower subsequence interval are by erosion model parallel to the top surface MCS, and those inside the upper interval are modeled as parallel to the base surface TS. Therefore, s-grids for the middle interval TS-MCS are of proportion type.

Integrating Data Scales There are three sources of static data in the study area from seismic, geological layering and petrophysics. The seismic attribute information is an average over a stratigraphic sequence interval, representing a vertical scale of roughly around 100m. The data is, however, densely sampled laterally, each measurement representing a 25m x 25m local area. The geological sub-layer information comes from well markers and geological insight as to the occurrence of TS and MCS surfaces. These layers are defined at the scale of about 30 m. Finally, fine-scale petrophysical information from logs along wells is available at the scale of 0.25 m.

Several techniques (cokriging, collocated cokriging, Markov-Bayes, Bayesian inference, trend modeling, etc.)14 exist for integrating data scales and data types. In this study in addition to 3D hard well data and 2D soft seismic information for each sequence interval, we also have sub-sequence TS and MCS geological layering data. Two methods of block kriging and trend model are presented to integrate available well data, geological layers and coarse-scale seismic data. In both methods the integration would require three steps: i) modeling properties at sequence interval-scale, ii) decomposing

sequence-scale into geologically-based sub-sequence scale (layers), iii) and down-scaling layer-averaged information to log-scale property distributions.

Modeling Properties in Tajin Field

Vsh Distributions. First Vsh distributions at stratigraphic sequence-scale are constructed for all sequence intervals: 1. Interpolate the seismic data to every cell of the 2D grid

which has the same XY dimensions as the final s-grid. Convert attributes at X,Y to principal components and use the correlations developed from seismic-petrophysics to compute seismic-derived Vsh at each s-grid 2D node.

2. Average Vsh along wellbores for the whole sequence interval. Perform collocated cokriging to integrate seismic and obtain average Vsh map for the sequence interval. Some edge effects due to limited coverage of seismic data in the southeast part of the grid may result. Block Kriging Approach. Use block kriging to decompose

sequence-scale average Vsh values to both sub-sequence scale and further to log-scale within each sub-sequence scale. This is a reasonable approach because an averaged Vsh value for a sequence interval at a given location can be viewed as a block data. This in turn would constrain averaged information when determining individual sub-layer, and subsequently log-scale Vsh values at that location. The downscaling procedure continues from Step 2 as follows: 3. Average Vsh along wellbore for each sub-sequence layers

of SB-TS, TS-MCS, MCS-SB. Perform block kriging of these averaged well data with the map of Step 2 to obtain average Vsh map for each sub-sequence layer. There is an implicit assumption of vertical stationarity in this step.

4. For each sub-sequence layer, perform sequential Gaussian simulations sGsim with block kriging of well data using results of Step 3. This gives 3D distribution of Vsh within each sub-sequence layer.

Trend Model Approach. By necessity all (geo)statistical

models assume stationarity, and the trend model "relaxes" the assumption as much as possible. Dividing a sequence interval into its sub-sequence layers already provides a better control in capturing major geologic trends. We expect the trend method to produce reliable results because each sub-sequence should geologically be of similar sediment deposit characteristics over the field but the exact content of Vsh in each sub-sequence would differ areally.

The vertical Vsh trend is considered to be representative of the entire area of interest, and globally this trend is honored. Locally, this trend is informed by the areal trend of Vsh within the sub-sequences derived from available seismic and well information. The areal trend captures changes in the Vsh trend over all distances. It is also quite reasonable to assume that the vertical Vsh trend at smaller scale for each subsequence is also constant over the area.

The procedure of constructing Vsh distributions for each sub-sequence l at location ij, where ij is the index of lateral grid cells in the geostatistical model and l =1, 2, 3 (i.e., upper, middle, bottom) is as follows, starting from Step 2 above:

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3. Compute sequence and sub-sequence global wshV , w

,shV l

from well data. Calculate sequence-scale local (ij)Vwsh

average by thickness weighted averaging of sub-sequence global averages. This step introduces to each cell location ij geological trends of a sequence observed from well data.

4. Integrate seismic information by scaling sub-sequence local average Vsh to introduce both seismic and geological trend information:

)ij(wshV

)ij(sshVw

,shV)ij(s,shV ⋅= ll (3)

where, )ij(Vssh is the sequence interval average Vsh derived

from seismic data by collocated cokriging of Step 2. 5. Repeat the above procedure at fine-scale within each

subsequence to generate 3D distributions of Vsh (ijk). Use geological 2D maps of )ij(Vs

,sh l and vertical proportion curves of Vsh within each subsequence as trends.

6. Perform 3D non-stationary simple kriging using the trend model results of Step 5 as the varying nonstationary model mean in order to condition Vsh (ijk) to well data because the trend model is only an a-priori model.

The above procedure has two important features. It contains correct vertical average of Vsh at every location as dictated by seismic (or combined seismic and well data), and it preserves vertical trends observed in well data.

Results. Tables 1 and 2 provide parameters of vertical

and horizontal variograms of Vsh for all sub-sequences in Tajin. Azimuth is measured counter clockwise from the downward pointing v-axis. These variograms are based on the style of geological s-grid. We have found that with inappropriate geological s-grids the experimental variograms quickly degenerate and become unstable. Also, when sub-sequences are combined, the sequence-scale variograms show significant nugget effects and nested structures, as seen in Fig. 15 for TAJ-SQ85. This figure indicates areal anisotropy.

Table 2 shows that larger correlation ranges occur along the v-axis (roughly SE direction) for lower Tajin sequences, and that the pattern is reversed for upper Tajin sequences. These results are consistent with geological depositional settings that indicate high lateral sediment supply in the NE direction in lower Tajin for quick fill-up of the Tajin trough and subsequent migration of sediment flow in the SE-NW direction. For upper Tajin, the sediment supply is generally low and deposits tend to be aligned with the sediment supply route in the NE-SW direction, resulting in longer correlation lengths in that direction. Topographical variations and prior sedimentation add additional complexity to the interpretations of variograms. Other findings of these variograms are: i) The first short range correlation structure of the vertical

variogram model represents variability at the sand-shale lamination scale (in the order of 1-2 meters). The second long-range structure components with correlation ranges of 10-15 meter reflect variability at facies level.

ii) The anisotropy ratio of horizontal variograms varies between 1 and 3, indicating that these variograms do not greatly influence geometry of the modeled sand bodies.

iii) The correlation ranges are usually less than 1000 m, indicating that spatial correlation structure is restricted at most to 2-3 times of a well pair distance (about 400 m).

iv) The correlation ranges for upper Tajin are generally smaller than those of lower Tajin, suggesting more discontinuous sand body deposits in upper Tajin Maps of average Vsh distributions for sub-sequence layers

in TAJ-SQ40 are shown in Figs. 16. We note that the block kriging method generates distributions of averaged Vsh in regions beyond lateral correlation ranges that are essentially the same for all three sub-sequent layers. Thus block kriging cannot decompose sequence-scale Vsh into its sub-sequence scale components at distances beyond the correlation range of variograms (i.e., sufficiently away wells). The trend model, however, can accomplish this decomposition provided that the same averaged trends apply in non-drilled areas.

Facies Distributions. 3D facies distributions conditioned

to seismic data are constructed from Vsh distributions and Vsh-facies calibration data. The calibration is obtained from well data by corresponding probability of each facies to a given Vsh value. These facies probabilities are “prior” probabilities, which are updated to “posterior” probabilities. The posterior facies probabilities can guide the identification of sand bodies even in areas away from the well control influence where only seismic information is available. Fig. 17 shows an example of the calibration curve for the lower sub-sequence interval of TAJ-SQ40.

Sequential indicator kriging with locally varying mean (SISim-LVM) is used to update “prior” probabilities and generate multiple realizations of facies distributions. Prior facies probabilities are treated as local mean data, which vary spatially. Posterior facies probability distributions are computed from results of multiple realizations of SISim-LVM at each cell (ijk) by dividing the number of occurrences of each facies at that location by the total number of realizations.

Fig. 18 shows cross sectional distributions of posterior probabilities of Facies M and Facies SA+NA for TAJ-SQ40. It is seen that Facies M (shale) largely occurs in the upper sub-sequence interval and that the sandy Facies SA+NA occurs in the lower sub-sequence.

Effective Porosity Distribution. Multiple realizations of φe

distributions conditioned to Vsh distributions, as soft data, are created for each facies class. The method of Sequential Gaussian Simulation (sGsim) collocated with Vsh is used. The required correlation coefficients between φe and Vsh are constructed from well data, ranging from -0.3 to -0.7 and generally improving from lower deposits to upper deposits (for example for TAJ-SQ20, the correlation coefficients vary from -0.6 to -0.7, while those of TAJ-SQ100 range from -0.3 to -0.4, largely due to digenesis and cementation). Fig. 19 shows a typical variograms of normal score φe within Facies SA+NA in the lower sub-sequence of TAJ-SQ40.

SPE 84052 7

Water Saturation Distributions. Connate water saturation distributions are constructed by conditional sGsim collocated with φe, as soft information. Since porosity is constrained by facies and facies are in turn constrained by Vsh, (hence, seismic), hierarchical controls on Sw distributions are imposed. This operation proceeds by generating one realization at a time for each of Vsh, facies, φe and Sw parameters.

Permeability Distributions. An elaborate permeability prediction model was presented in the petrophysical analysis section. This model is a function of field compartments, sub-sequence intervals, φe, Vsh, Sw. and facies. Permeability values at each geostatistical cell are computed in a deterministic way from the permeability prediction model, using their φe, Vsh, Sw, facies, and knowledge of cell location within a field compartment and sub-sequence interval. In this way, higher geological and engineering controls on permeability distributions are exerted. Modeling Agua Fria Field Properties The general procedure for 3D modeling of properties in Agua Fria is similar to Tajin field, except that first distributions of φT constrained to seismic are obtained and used to construct φe and facies. Major steps are as follows: 1. Interpolate the seismic data to every cell of the 2D grid,

which has the same X-Y dimensions as the final s-grid. Convert attributes at X,Y to principal components and use the correlations developed from seismic-petrophysics to compute seismic-derived φT at each s-grid cell node.

2. Average φT along wellbores for each sequence interval, and perform collocated cokriging of well data with results of Step 1 to integrate seismic and obtain 2D averaged φT maps for sequence intervals.

3. Average φT along wellbore for each sub-sequence zone of SB-TS, TS-MCS, MCS-SB. Because there are severe truncation of surfaces and drastic changes in the thickness of sub-sequences in Agua Fria, block kriging is not suitable because of vertical nonstationarity. We devised a thickness-weighted porosity calculation scheme in order for averaged porosity of subsequence y)(x,Tlφ to satisfy

)(∑ φ=φ y,x y)(x,y)(x,w TTll , where w is weight factor.

First, sGsim is used to obtain )y,x(lµ and )y,x(2lσ of

normal distribution functions of y)(x,Tlφ . These parameters are then adjusted by constraining the joint probability functions of sub-sequence porosities to match sequence porosity φT(x,y). Subsequence y)(x,Tlφ distributions are obtained by randomly drawing from the adjusted normal distribution functions.

4. For each sub-sequence interval, perform sequential Gaussian simulations sGsim with block kriging of well data with results of Step 3. This gives 3D distribution of φT for each s-grid node.

5. Perform P-field simulation to obtain distribution of φe, using the information content of the scatter plot between φT and φe from well data, as shown in Fig. 20. Briefly,

Prob{φe|φT} are obtained along wells from well data and Fig. 20. sGsim is then used to generate 3D distributions of these probabilities. φe values at each cell location ijk are obtained from the inverse of Prob{φe|φT} for previously simulated φT values at that cell location.

6. Compute Vsh deterministically from Vsh=(φT- φe)/0.15. 7. Perform locally-varying truncated Gaussian simulations,

with truncating thresholds dependent on Vsh. First, a calibration plot of facies proportion vs. Vsh similar to Fig. 17 is constructed from well data for each sub-sequence layer, and is cumulated by nesting the facies according to geological ordering occurrence of facies (Fig. 21). Second, at a location along wellbore compute midpoint cdf value from Fig. 21 using Vsh and facies information at that location (call this F). Third, perform sGsim of F conditioned to well F data and obtain distributions of F in the reservoir. Finally, back calculate facies type from the knowledge of simulated F and Vsh at cell ijk in connection with Fig. 21.

Comparison with Deterministic Geological Models Geostatistically generated Vsh distributions in the fields of study area are analyzed for patterns of sand distribution and are compared with deterministically mapped distributions of facies from geology on the basis that facies SA+NA are sandier and that facies MA+M are shalier. Fig. 22 shows geostatistical Vsh distributions and geological facies maps for the lower subsequence interval SB-MCS of sequence AF60-TAJ40. The maps show the sediment supply routes, turbidite lobes and channels that are present at these locations.

Figure 22 shows general agreement between the geological model and the geostatistically-distributed properties. The low Vsh regions match areas defined by the SA and NA facies. The geostatistical maps, however, are more detailed and are extendable to larger areas. Thus we conclude that geostatistical modeling is applicable to Tajin and Agua Fria fields, and hence likely to other fields in Chicontepec basin.

Connectivity Analysis

Sand Continuity. Figs. 23 show sand volume geobodies and probability of sand occurrence for the lower sub-sequence intervals of SB-MCS of TAJ-SQ85 and TAJ-SQ40. A cdf of Vsh is constructed at each geostatistical cell location ijk from 50 realizations, and used to compute probability of sand occurrence, Prob{Vsh<0.4}. Probability maps of sand regions, (Vsh<0.40), provide a first level indication for sand distributions. These, however, do not necessarily indicate connectivity although in general one would expect that higher sand probability would also relate to higher probability of connectivity.

Geobodies represent conglomerate of sand volumes within each sub-sequence interval, and show more clearly the nature of sand distributions in these sequences. It is seen from Figs. 23 that the sandstones of TAJ-SQ85 are more sheet-like, and the sandstones of TAJ-SQ40 are more discontinues, representative of channelized environment there, both also supported by geologic depositional settings.

8 SPE 84052

Pay Sand Connectivity. We first specify petrophysical criteria for pay sand. For illustration purposes in this study, cutoffs are Vsh<0.4, φe>0.05 and Sw<0.7. The cutoff for porosity also relates to a cutoff in permeability because of the underlying k-φe relationship. Geobodies (i.e, connected sands) with the above-specified criteria are determined for each realization. Probability that cell ijk to be in a specified geobody ν is computed from 50 realizations as 50/np ijkijk

νν =

where, νijkn is the number of times to be in geobody ν. The

computed 3D probabilities are mapped as probability of connected sand body, and are considered an important parameter characterizing uncertainty. These probabilities not only are related to the continuity of sand bodies but also show the connectedness of pay sands. High probability areas of sands would relate to sweet spots, but not exactly.

An example of connected pay sand probability is shown in Fig. 24 for the middle sub-sequence interval of TAJ-SQ40. It is interesting to note that channel sand deposits follow the general topology of the formation and are oriented in the NW-SE direction. The turbidite channel sediment supply generally is laterally in SW-NE direction, but the local flow in TAJ-SQ40 is affected by the topography of this interval. The identified channel sand deposit in this interval, as seen in Fig. 24 in red color, would be an excellent location for infill drilling or placement of horizontal wells.

Fig. 25 shows probability of connected pay sands for the lower sub-sequence intervals of TAJ-SQ85 and TAJ-SQ40. The figure shows that the pay sands are fairly patchy despite continuity of sheet-like sands seen for TAJ-SQ85 in Fig. 25. So, what seems to be a continuous sand body in fact has a lot of discontinuities in pay geobodies, resulting from very irregular development of φe. Geological studies show that the lower layers are highly diagenetized (perhaps initially fully cemented and subsequently undergone geochemical dissolution processes), leading to patchy porosity distribution.

Conclusions 1. An architectural framework for Tajin, Coapechaca and

Agua Fria reservoirs was constructed from the integration of well marker data, geologic sequence stratigraphy and seismic horizons. Sub-interval surfaces of TS and MCS were also modeled to impose tighter geological controls on reservoir characterization models.

2. Good correlations between nine seismic attributes and average Vsh and φT petrophysical well data were obtained for all sequence intervals. The non-parametric ACE algorithm combined with principal component analysis generated these correlations.

3. A reliable permeability prediction model based on well logs has been developed for Tajin and Agua Fria fields. Permeability is a function of φe, Sw, Vsh, sub-sequence divisions and four reservoir compartments. The model effectively captures high permeability streaks.

4. High-resolution 3D distributions of reservoir properties are constructed using various geostatistical techniques and appropriate integration of data types and data scales. The hierarchical orders of property modeling are: Vsh, facies,

φe, Sw, k for Tajin and φT, φe, Sw, Vsh, facies, k in Agua Fria; respectively.

5. Block cokriging generates similar Vsh distributions for all subsequences in regions away from wells and at distances beyond correlation ranges of the underlying variograms. However, the trend model extrapolates information to outside the regions of well influence where seismic information is the only available data.

6. Although sands in the lower subsequences are blanket type they form discontinuous pay bodies due to diagenesis and cementation of primary porosity. The middle subsequence intervals are less sandy but they have high connectivity of pay sand bodies due to the preservation of porosity.

7. Channel type clean sands are present in upper sequences of Tajin and Agua Fria with minor alterations in porosity. The probability of sand occurrence correlates strongly with the probability of connected pay sand geobodies.

8. Comparisons of geostatistical Vsh distributions with deterministic geological facies show general agreement between the two. However, the integrated geostatistical method is faster, generates detailed information and is readily applicable to other fields in Chicontepec basin.

Acknowledgement We thank the management of PEMEX and JNOC for permission to publish this paper. The work represents a portion of the collaborative research joint project for geostatistical modeling of Chicontepec deposits.

Nomenclature

a = correlation range in major azimuth direction b = correlation range in minor azimuth direction cc = sill of the variogram model c0 = nugget effect h = subsequence or sequence thickness k = permeability M = mud MA = mud alternating bed MCS = minor condensed section NA = normal alternating beds SA = sandy alternating shale SB = stratigraphic sequence boundary Sw = water saturation TS = transgressive surface Vsh = volume fraction of shale w = weight factor, Th/hw ll =

φ = porosity µ = mean of a normal distribution function σ2 = variance of a normal distribution function Subscripts e = effective T = total l = index fro subsequence (layer) Superscripts s = from seismic attribute w = from well data

SPE 84052 9

References 1. Journel, A.G. and Huijbregts, Ch.J., Mining Geostatistics,

Academic Press, New York, NY 1978. 2. Doyen, P.M., Boer L.D. and Pillet, W.R.: “Seismic Porosity

Mapping in the Ekofisk Field Using a New Form of Collocated Cokriging,” paper SPE 36498 presented at SPE Annual Technical Conference and Exhibition, Denver, CO, 6-9 October 1996.

3. Abbaszadeh, M. D., Koide, N. and Murahashi, Y.: "Characterization and Flow Modeling of a Complex Carbonate Reservoir in Daleel Field, Oman," SPERE (Sept. 2000)

4. Xu, X., Tran, T.T., Srivastava, R.M. and Journel, A.G.: “Integrating Seismic Data in Reservoir modeling: the Collocated cokriging Alternative,” SPE 24742 presented at the SPE Annual Technical Conference and Exhibition, Washington D.C., October 1992.

5. Journel, A.G.: “Conditioning Geostatistical Operations to (non)-Linear Volume Averages: Theory,” Stanford Center for Reservoir Forecasting (SCRF) Proceedings No. 11, Vol. 1, May 1998.

6. Doyen, P.M., Psaola, D.E., Boer L.D. and Jans, D.: “Reconciling Data at Seismic and Well Log Scales in 3-D Earth Modeling,” SPE paper 38698 presented at SPE Annual Technical Conference and Exhibition, San Antonio, TX, 5-8 October 1997.

7. Abbaszadeh, M., Takano, O., Shimamoto, T., Yazawa N., Sandria, M.F. and Guerrero Z.D.: “Geostatistical Modeling of Sandstone Distributions in Chicontepec Turbidite Deposits - Tajin Field, Vera Cruz, Mexico”, presented at EXITEP 2001 meeting, Mexico City, Mexico, Feb. 5-7, 2001.

8. Yazawa, N., Yamamoto, H., Takano, O., Shimamoto, T., Abbaszadeh, M., Sandria, M.F. and Guerrero Z.D:. “Geostatistical Modeling of Agua Fria, Coapechaca and Tajin Field – Chicontepec Basin”, presented at AIPM 2001 international meeting, Villahermosa, Mexico, June 14-17, 2001.

9. Doyen, P.M., Psaila, D.E. and Strandenes, S.: “Bayesian Sequential Indicator Simulation of Channel Sands from 3D Seismic Data in the Oseberg Field, Norwegian North Sea,” paper SPE 28382 presented at SPE Annual Technical Conference and Exhibition, New Orleans, LA, 25-29 Sept 1994.

10. Bitter, M.R., 1993, Sedimentation and provenance of Chicontepec sandstones with implications for uplift of the Sierra Madre Oriental and Teziutlan Massif, east-central Mexico. In Pindell, J.L. and Perkins, B.F., eds., Mesozoic and Early Cenozoic Development of the Gulf of Mexico and Carribean Region. Gulf Coast Section SEPM, 13th Annual Research Conference, 154-172.

11. Richard M. Bateman: ”Open hole log analysis and formation evaluation”, Boston, International Human Resources Development Corporation

12. Breiman, L. and Friedman, J.H.: “Estimating Optimal Transformations for Multiple Regression and Correlation, ”Journal of American Statistical Association (1985), 580-618.

13. Mallet, J.L.: “Discrete Smooth Interpolation,” ACM-Transaction on Graphics, Vol. 8, No. 2, pp 121-144, 1989.

14. Deutsh, C.V., Geostatistical Reservoir Modeling, Oxford University Press, New York, 2002

Table 1 - Vertical Variograms of Vsh, Tajin Field Sequence a1 cc1 a2 cc2 c0 Geological

Model SQ100 - L 0.045

4.05 0.61 0.41

36.92 0.39 0 Proportion style

SQ100 - M 0.05 1.53

0.55 1.0 15.34

0.45 0 Proportion style

SQ100 - U 0.08 2.64

0.27 0.95 16.5

0.73 0 Proportion style

SQ85 - L 0.09 1.78

0.55 1.0 8.91

0.45 0 Proportion style

SQ85 - M 0.1 2.5

0.5 1.0 12.5

0.5 0 Proportion style

SQ85 - U 0.1 2.55

0.28 1.0 12.74

0.72 0 Proportion style

SQ60 - L 0.09 1.61

0.3 1.25 8.92

0.70 0 Proportion style

SQ60, M+U 0.07 2.63

0.4 1.2 16.2

0.6 0 Proportion style

SQ50 - L 0.07 1.94

0.33 1.6 13.84

0.67 0 Proportion style

SQ50, M+U 0.05 2.52

0.36 1.2 28.83

0.64 0 Proportion style

SQ40 - L 0.05 3.55

0.4 0.5 22.98

0.6 0 Parallel to top s

SQ40 - M 0.1 2.13

0.32 8.5 10.66

0.68 0 Proportion style

SQ40 - U 0.05 1.04

0.24 1.0 10.44

0.76 0 Parallel to base

SQ20 - L 0.0452.03

0.29 4.0 14.80

0.71 0 Parallel to top

SQ20, M+U 0.07 1.5

0.35 2.5 10.05

0.65 0 Parallel to base

Table 2 - Areal Variograms of Vsh, Tajin Field

Sequence a b cc c0 Main Azimuth

SQ100 - Lower 0.09 (564m)

0.085 (889m)

1 0 105o

SQ100 - Middle 0.13 (815m)

0.1 (1045m)

1 0 105o

SQ100 - Upper 0.17 (1066m)

0.15 (1568m)

1 0 105o

SQ85 - Lower 0.11 (690m)

0.09 (940m)

1 0 105o

SQ85 - Middle 0.12 (752m)

0.1 (1046m)

1 0 105o

SQ85 - Upper 0.14 (1464m)

0.12 (752m)

1 0 15o

SQ60 - Lower 0.16 (1003m)

0.15 (1568m)

1 0 105o

SQ60 (Middle+Upper)

0.12 (758m)

0.12 (1255m)

1 0 105o

SQ50 - Lower 0.18 (1130m)

0.13 (1360m)

1 0 105o

SQ50 (Middle+Upper)

0.185 (1160)

0.185 (1936m)

1 0 105o

SQ40 - Lower 0.14 (878m)

0.13 (1360m)

1 0 45o

SQ40 - Middle 0.17 (1467m)

0.11 (948m)

1 0 45o

SQ40 - Upper 0.12 (1286m)

0.10 (584m)

1 0 0o

SQ20 - Lower 0.12 (1256m)

0.1 (682m)

1 0 15o

SQ20 (Middle+Upper)

0.12 (1255m)

0.09 (565m)

1 0 15o

10 SPE 84052

SIERRA MADRE ORIENTAL

A

B

C

Chicontepec Basin

Fig. 1- A,B: Location map of Tajin field. C: Paleogeographical map of the Paleogene Chicontepec Basin.

857 85983 3

835 83 7

83 981

1 813 81 5

81 780

2 80 1

80 3

80 5

80 7

82 6

82 4

822 82 1

82 3

82 5

848 84 4

84 2

843 845 849

76 9

86 8

86 6

86 4

86 2

861 86 5

867

78778 9

37835 8 352 355 357

33 8

33 4

332 33 1

33 3

335 337 339

318316 31 4

312 31 1

31 3

31 5

317 319

308 306 307

328 326 32 4

322 321 323 32 5

327

348 346 34 4

34 2

341 343 345 34 7

368 36 6

364 362 36 1

363 365 367388 386 384 38

238 1

383 385 387 389

698 696 69 4

69 2

691 693 695 697676 674 672 671 673 675 677

658 656 654 652 651 653

638 636 634 632 631 633

86 9

30 4

302 301 303 305

PS1

374

699

ENC 1

84 1846 847

35 6 33

6

35 1

1

3

635637

655 657

639

659679

758

36 9

349

329446

484

MIRANDA-1TAJ-168

76 7

74774 9

82 8

81 2

81 4

834

81 6

836856

858

733731

753

773

YATE- 1

704

714

724706

716

71 8

831

853 85 5

81 9 809

829827

2

Wells with well logsWells with coresand well logs

2km

AGUA FRIA

COAPECHACA

TAJIN

3D seismic

Fig. 2 - Detailed map of the Tajin, Coapechaca and AguaFria oil fields in the Chicontepec Basin, showing welllocations and 3-D seismic survey area.

Cretaceous

SB-AF100

SB-AF85

SB-TAJ100

SB-TAJ85

SB-TAJ60

SB-TAJ50

SB-TAJ40

SB-AF58 SB-TAJ20

MCS-AF100TS-AF100

eroded afterdeposition

TS-AF85MCS-AF85

bypassNo deposition

TS-TAJ100MCS-TAJ100

MCS-TAJ85

MCS-TAJ60

TS-TAJ85

TS-TAJ60

TS-TAJ50MCS-TAJ50MCS-AF70

TS-AF70

SB-AF70

eroded

TS-TAJ40MCS-TAJ40

PALE

OC

ENE

Chi

cont

e pec

Form

atio

n

Velasco Formation

Sequence AF100

Sequence AF85

Sequence TAJ100

Sequence TAJ85

Sequence TAJ60

Sequence TAJ50

Sequence TAJ40MCS-TAJ20

Sequence AF70

MCS-AF60TS-AF60

<Agua Fria> <Tajin>

SB-AF30

SB-AF10

SB-TAJ15

TS-TAJ20

Disc AF50Sequence AF52Sequence AF50

MCS-AF30

TS-AF30

Disc AF75

SB-AF52

MCS-AF10TS-AF10

SB-AF60 (B_AF60)

Sequence AF60

Sequence AF58 Sequence TAJ20MCS-AF58

eroded

Sequence AF30

Sequence AF10

eroded

Cretaceous

SB-AF100

SB-AF85

SB-TAJ100

SB-TAJ85

SB-TAJ60

SB-TAJ50

SB-TAJ40

SB-AF58 SB-TAJ20

MCS-AF100TS-AF100

eroded afterdeposition

TS-AF85MCS-AF85

bypassNo deposition

TS-TAJ100MCS-TAJ100

MCS-TAJ85

MCS-TAJ60

TS-TAJ85

TS-TAJ60

TS-TAJ50MCS-TAJ50MCS-AF70

TS-AF70

SB-AF70

eroded

TS-TAJ40MCS-TAJ40

PALE

OC

ENE

Chi

cont

e pec

Form

atio

n

Velasco Formation

Sequence AF100

Sequence AF85

Sequence TAJ100

Sequence TAJ85

Sequence TAJ60

Sequence TAJ50

Sequence TAJ40MCS-TAJ20

Sequence AF70

MCS-AF60TS-AF60

<Agua Fria> <Tajin>

SB-AF30

SB-AF10

SB-TAJ15

TS-TAJ20

Disc AF50Sequence AF52Sequence AF50

MCS-AF30

TS-AF30

Disc AF75

SB-AF52

MCS-AF10TS-AF10

SB-AF60 (B_AF60)

Sequence AF60

Sequence AF58 Sequence TAJ20MCS-AF58

eroded

Sequence AF30

Sequence AF10

eroded

Fig. 3- Sequence stratigraphy of the reservoir interval of thePaleocene Chicontepec Formation in the Tajin, Coapechacaand Agua Fria fields. The vertical axis of this chart isgeologic time domain. TS: Transgressive Surface, MCS:Minor Condensed Section, SB: Sequence Boundary

Sequence AF100

Sequence AF85Sequence TAJ85

Sequence TAJ100

Sequence TAJ60

Sequence AF70-T AJ50

Sequence AF60-TAJ40

Sequence AF58

Sequence AF52

Sequence AF50

Sequence AF30

Sequence AF10

AGUA FRIA COAPECHACA TAJIN Description of Litholigy

Normal Alternating beds of sandstone

and shale

Sandstone

Shale

Column

MA

Facies

M

SA

NA

(High density turbidite)

(Low density turbidite)

Shale-rich Alternating beds of sandstone and

shale

Sand-rich Alternating beds of sandstone

and shale

(Low density turbidite)

(Shaly Alternation)

(Hemipelagic sediments)

Inferred Sedimentary Environment

Upper fan / Mid fan distributary

channel of sandy radial fan

Mid fan of sandy radial fan

Channel of channel -levee system

Levee of channel -levee system

or

or

Lower fan of sandy radial fan

orLevee of channel

-levee system

Slope

Basin floor

Characteristics of well logGamma Ray Neutron Density

neutron phibulk density

bulk density

neutron phi

bulk densityneutron phi

Resistivity

neutron phi

bulk density

Core Facies

Facies 4Facies 5Facies 6

Facies 6

Facies 7

Facies 8

Facies 9

Facies 3

Facies 5

Conglomerate

Fig. 4 - Schematic illustrations of stacking patterns ofdepositional sequences in the Tajin, Coapechaca and AguaFria fields. The vertical axis is depth domain. Bold lines:major erosional surfaces.

Fig. 5 - Facies classification of the Chicontepec Formation inTajin field based on well log pattern and core description

SPE 84052 11

857 859

833 835 837 839

811 813 815 817

802801 803 805 807

826 824 822 821 823 825

848 844 842 843 845 849

769 868 866 864 862 861 865 867

787 789

378

358 3 52 355 357

338 334 332 331 3 33 335 337 339

318 316 3 14 312 311 313 315 317 319

308 306 307

328 3 26 324 322 321 323 325 327

348 346 344 3 42 341 343 345 347

3 68 366 364 362 361 363 365 367

388 386 3 84 382 381 383 385 387 389

698 696 694 692 691 693 695 697

6 76 674 672 671 673 675 677

658 656 654 652 651 653

6 38 636 634 632 631 633

869

304 302 3 01 303 305

PS1

374

699

ENC1

841846 847

356

336

351

1

3

635 637

655 657

639

659

679

758

369

349

329

446

484

M IR ANDA-1

TAJ-168

767

747 749

828

812

8 14

834

816

836

856858

733731

753

773

YATE-1

704

714

724

706

716718

831

853 855

819

809

829827

2

AGUA FRIA

TAJIN

Trough Margin

Trough Axis

Slope Zone

Slope Zone

Axis Zone

longitudinal supply

lateral supply

lateral supply

Multi-source submarine fan systems

with lateral and longitudinal

sediment supply

lateral supply

muddy

muddy

sandy

sandy

sandy

sandy

COAPECHACA

Fig. 6 - Generalized depositional model for the Chicontepecturbidites in the Tajin, Coapechaca and Agua Fria fields.

eφeφ eφeφ

(a): Facies SA and NA.

Laminated shale model

(b): Facies MA and M.

Dispersed shale model

Fig. 7 – Schematic of models for porosity calculations formwell logs

0%

10%

20%

30%

0% 10% 20% 30%Log porosity adjusted by average core porosity

CORREL = 0.973(0.881)

0

200

400

600

log porosity shifted by average core porosity- average core porFig. 8 – Comparison of effective porosity predicted fromlogs vs, measured core porosity. Blue are data where coreand log data differ more than 3%

Fig. 9 - Evaluation of Permeability prediction Model, k =f(φe, Vsh, Sw, facies, sub-sequence, compartment)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Vsh form log

Vsh

from

sei

smic

TAJ S B10 0 - 8 5

TAJ S B8 5 - 6 0

TAJ S B6 0 - 5 0

TAJ S B5 0 - 4 0

TAJ S B4 0 - 2 0

Fig. 10 - Correlation of seismic attributes withVsh from well data, Tajin field

0. 0

0. 1

0. 1

0. 2

0. 2

0. 0 0. 1 0. 1 0. 2 0. 2 0. 3PHIT from log

PHIT

from

sei

smic

AFSB10- AFSB30AFSB52AFSB58- TAJSB20AFSB60- TAJSB40AFSB70- TAJSB50AFSB85AFSB100

Fig. 11 - Correlation of seismic attributes with φTfrom well data, Agua Fria field

12 SPE 84052

400 grids

125 g

rids

400 grids

125 g

rids

u

v

E, 90o

N, 0o

215 grids

TAJIN

400 grids

125 g

rids

400 grids

125 g

rids

u

v

E, 90o

N, 0o

E, 90o

N, 0o

215 grids

TAJIN

Fig. 13 – 2D geostat grid cells of the study area and Tajinfield with cell size 50m x 50m.

SB20

TS40

MCS40

SB40

Fig. 14 - Stratrigrahic correlations for TAJ-SQ40, Tajin

Lower SQ-85

Top SQ-85 Middle

All SQ-85

Fig. 15 – Horizontal variograms of Vsh for the lower sub-sequence interval TAJ-SQ85 (MCS to SB85)

AF58-SB-TAJ20

AF60-SB-TAJ40

AF70-SB-TAJ50

Disc 50 Erosion surface

AGUA FRIA TAJIN

Fig. 12 - Large scale reservoir framework modeling, AF70-TAJ15 to Disc

SPE 84052 13

Fig. 16 -– Average Vsh for TAJ-SQ40 by: trend model (upper set) and block kriging (lower set).

Lower_SQ-40, Tajin

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Vsh

Faci

es P

ropo

rtion

p: Mp: MAp: NA+SA

Fig. 17 – Calibration curves, facies proportion vs. Vsh for TAJ-SQ40(lower sub-sequence, SB50-MCS40)

14 SPE 84052

Vertical VariogramCOVARIANCE_MODEL 1 2SPHERICAL 135 0 0 1000 1000 0.045 0.6SPHERICAL 135 0 0 1000 1000 0.73 0.4

x 1000

Azimuth = 90 Azimuth = 120 Azimuth = 135 Azimuth = 150

Azimuth = 0 Azimuth = 30 Azimuth = 45 Azimuth = 60

x 1000x 1000x 1000x 1000

x 1000x 1000x 1000

Vertical VariogramCOVARIANCE_MODEL 1 2SPHERICAL 135 0 0 1000 1000 0.045 0.6SPHERICAL 135 0 0 1000 1000 0.73 0.4

x 1000

Azimuth = 90 Azimuth = 120 Azimuth = 135 Azimuth = 150

Azimuth = 0 Azimuth = 30 Azimuth = 45 Azimuth = 60

x 1000x 1000x 1000x 1000

x 1000x 1000x 1000

Fig. 19 - Taj-SQ40 (lower), Normal score Porosity on Facies NA+SA

Facies MFacies MFacies

SA+NAFacies

SA+NA

Fig. 18 – Cross sections showing posterior probability

eΦ

Tφ

<0.05

0.095

0.145

0.195

0 0.5 1

P-value

Fig. 20 - P-field simulation of φe

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.0000 =< Vsh < 0.020

0.0200 =< Vsh < 0.04

0.0400 =< Vsh < 0.060

0.0600 =< Vsh < 0.08

0.0800 =< Vsh < 0.10

0.1000 =< Vsh < 0.12

0.1200 =< Vsh < 0.140

0.1400 =< Vsh < 0.160

0.1600 =< Vsh < 0.180

0.1800 =< Vsh < 0.200

0.2000 =< Vsh < 0.22

0.2200 =< Vsh < 0.24

0.2400 =< Vsh < 0.26

0.2600 =< Vsh < 0.280

0.2800 =< Vsh < 0.30

0.3000 =< Vsh < 0.32

0.3200 =< Vsh < 0.34

0.3400 =< Vsh < 0.360

0.3600 =< Vsh < 0.38

0.3800 =< Vsh < 0.400

0.4000 =< Vsh < 0.420

0.4200 =< Vsh < 0.44

0.4400 =< Vsh < 0.46

0.4600 =< Vsh < 0.48

0.4800 =< Vsh < 0.500

0.5000 =< Vsh < 0.520

0.5200 =< Vsh < 0.540

0.5400 =< Vsh < 0.56

0.5600 =< Vsh < 0.58

0.5800 =< Vsh < 0.60

0.6000 =< Vsh < 0.62

0.6200 =< Vsh < 0.640

0.6400 =< Vsh < 0.660

0.6600 =< Vsh < 0.68

0.6800 =< Vsh < 0.700

0.7000 =< Vsh < 0.72

0.7200 =< Vsh < 0.74

0.7400 =< Vsh < 0.760

0.7600 =< Vsh < 0.78

0.7800 =< Vsh < 0.80

0.8000 =< Vsh < 0.82

0.8200 =< Vsh < 0.84

0.8400 =< Vsh < 0.860

0.8600 =< Vsh < 0.880

0.8800 =< Vsh < 0.90

0.9000 =< Vsh < 0.920

0.9200 =< Vsh < 0.94

0.9400 =< Vsh < 0.96

0.9600 =< Vsh < 0.98

0.9800 =< Vsh =<1.000

percentile

SandyAlt

Norm Alt

M udAlt

M ud

SQAF58 MCS-SB – WELL DATA

SA NA MA M

Vsh0 1

The facies have a relation ship between Vsh.

Vsh 0 1

1

0 cdf o

f fac

ies

Fig. 21 – Cumulative nested cdf offacies proportions, AF-58 (MCS-SB)

SPE 84052 15

(a) (b)(a) (b)

Fig. 22 - Comparison of deterministic geology with geostatistically generated Vs distributionsfor Sub-sequence SB-MCS of SQ-AF60,TAJ40. (a) geology and (b) geostatistics. Note goodcomparison of sand distributions and turbidite lobes.

Lowe

Fig. 23a – Sand continuity characteristics for TAJ-SQ85,Lower subsequence SB-MCS: (a) Sand geobody, (b)probability of occurrence Vsh<0.4,

Fig. 23b – Sand continuity characteristics for TAJ-SQ40,Lower subsequence SB-MCS: (a) Sand geobody, (b)probability of occurrence Vsh<0.4,

Fig. 24 - Connected pay sand probability forTAJ-SQ40 (middle sub-sequence interval,MCS-TS) also showing topology of pay channel

(b(a

Fig. 25 - Probability of connected pay sand geobody (φ>0.05, Sw<0.7). (a) Lower interval TAJ-SQ85, (b) Lower interval TAJ-SQ40.