Petrel TIPS&TRICKS from SCM Knowledge Worth Sharing Truncated Gaussian Algorithm Rocks that transition from one facies or facies association to the next in a specific order are common. Examples include: Glacial deposition From: Significance of transition between Talchir Formation and Karharbari Formation in Lower Gondwana basin evolution A study in West Bokaro Coal basin, Jharkhand, India, by H N Bhattacharya, Abhijit Chakraborty, and Biplab Bhattacharya, in J. Earth Syst. Sci. 114, No. 3, June 2005, pp. 275 286. Progradational Parasequency Sets From: USC Sequence Stratigraphy Web (http://strata.geol.sc.edu/log stacking.html) 1
Reefs Building models that replicate this orderly facies transition has been difficult in Petrel. An algorithm called Truncated Gaussian simulation allows these ordered transitions to be modeled easily. The discussion below demonstrates the use of this algorithm on the African training data set and on data representing a pinnacle reef. The authors have used Truncated Gaussian simulation on a couple projects and found it simpler to use than the Truncated Gaussian with trends algorigthm (available in previous releases and still available) and that it produced better results than the other for that data. Because of the limited number of projects they have worked using this tool, the authors are not experts, but felt a tips and tricks article was important to make all aware of the new tool. Truncated Gaussian simulation The Algorithm Truncated Gaussian simulation is a stochastic algorithm. This means that it uses a seed and, if the seed is allowed to vary, will produce a different result upon re execution. Primary input include: Facies data as a property model up scaled from a facies log The facies to be modeled The order the facies are to occur (adjacency in the model) One variogram (used for all facies) The global fraction of each facies (tends to be dominated by Trends if they are used) Optional input data include: Vertical facies proportions from the Data Analysis process. Trend (3D, 2D, or 1D) for each facies Smoothing and whether data are honored during smoothing 2
Figure: Parameters available on the Truncated Gaussian simulation dialog. The algorithm basically models the probability of the facies in normal score space and then converts that modeled probability back to a facies code. Although the authors don t understand exactly how the algoirthm works, we have been able to pick up enough from the documentation to effectively use the tool. Our interpretation of the modeling process goes something like this (see figures below). Given Wells 1 and 2 and three stacks of cells in between them, the program: 1. Checks the probability of each facies and builds a cumulative probability function that totals 100% (0 10 = green, 10.01 to 40 = red, and 40.01 to 100 = yellow). Actually normal score values of 0 to 1 are used but percents are used in this example. 2. Assigns to each facies the percent at the center of its portion of the probability function and these are the values that are used to model that facies (5 for green, 25 for red, and 70 for yellow). 3. Builds a continuous model from the input data (probably using SGS). 4. Converts the modeled probability values back to facies space by comparing the value in the cell to the probability range and assigning to that cell the facies whose probability range it lies within. 3
Figure: Wells with midpoint probability values (displayed as %) that are passed to the modeling process. Stacks of cells (¼, ½, and ¾ of way between wells) with continuous probability values modeled (displayed as %). The probability values are converted to facies (color) based on which facie s probability range its value falls in. This example is based on only one probability number for each facies, that is, no trends or vertical proportions were used. The process gets more complex as trends etc. are added but the general approach is similar. African Model The African data set, commonly used for training, shows how the algorithm works. The model is first built using Sequential Indicator simulation and then using the Truncated Gaussian simulation. Figure: The same data modeled with Sequential Indicator simulation (left) and Truncated Gaussian simulation (right). The variograms were made as alike as possible (spherical left and gaussian right). Note the halo of yellow facies around the red facies. The order the facies were input to the Truncated Gaussian simulation algorithm was Grey, Yellow, and Red and this is the order the facies had to stay in when modeled because of how the algorithm works. Because it is a stochastic algorithm, you will still get a number of facies bodies that are unsupported by data but the data will be honored in all cases. 4
Figure: parameters used to build the African model with Truncated Gaussian simulation. 5
The larger the nugget the more fuzzy is the boundary between the facies. Figure: Model built with nugget =.001 (left) and nugget =.1 (right). Pinnacle Reef In the past it has often been said that Petrel is not friendly to modelers trying to build carbonate models. For this reason, we have built a Pinnacle reef model similar in style to pinnacles seen in the Michigan Basin. Since we didn t have data for Pinnacle reefs we studied the literature and manufactured our own. Structural Framework and the Mental Geologic Model The horizons modeled from top down are summarized in the table below. Below are cross section and 3D views showing the horizon geometry, pinnacle form, and layering used in the model. Normally there is 40% to 60% compaction in the carbonates (little or none in the evaporates) which creates a draping effect over the pinnacles. We did not take the time to build this compaction form into the model as it was not the goal of this study, although the drape would have created a more elegant and accurate facies model at boundaries between reef and evaporite. Layering was made proportional in the A 2 Carbonate and Lower Niagara and made to follow the top in the other zones. The shape of the horizons, the layering, and the approach used to model facies were all dictated by our mental image of how the reef should look and the distribution of the rocks in that mental image. The mental model used to guide this work was derived from work done by K.J. Mesolella, K.D. Robinson, L.M. McCormick, and A.R. Ormiston, 1974, Cyclic deposition of Silurian carbonates and evaporates in Michigan basin: AAPG Bulletin, v.58, P. 34 62. Model number 3 from this publication was used (two periods of growth separated by evaporate deposition. 6
Figure: Section (left) through the horizons modeled for the Pinnacle reef study. Reef is found in the Niagara and A 1 Carbonate zones. A 3D view of the top Niagara with the cross section cutting it is shown in the right view. Figure: Section showing the layering used to guide the correlations in each zone. 7
Table: List of horizons modeled and description of rock lying below each horizon. Horizon Zone rock description A 2 Carbonate Coarse grained, dense carbonate, unfossiliferous. A 2 Evaporite Halite with occasional thin dolomite beds capped by few feet of dense anhydrite A 1 Carbonate Dense fine grained, unfossiliferous, argillaceous, thin bedded carbonates. A 1 Evaporite Clear, coarsely crystalline halite thinly interbedded with anhydrite and dolomite, commonly capped with a foot or two of anhydrite. Niagara Dense argillaceous, micritic carbonate, ranging from massive tan dolomite to gray micritic crinoidal limestone to light gray nodular limestone. Top Lower Niagara Same as the Niagara but without having any reef development (zone added to separate the lower non reef Niagara from the upper reef bearing Niagara. Base Lower Niagara Base of model so no rocks modeled beneath. (top Clinton) Facies Modeling The facies modeled are listed in the figure below. Not all facies were found in each zone. In fact it was necessary to model each zone separately so that facies from one zone would not blur into a zone they did not belong in. One of the most important aspects of using the Truncated Gaussian simulation algorithm is to use horizons or some other means to restrict the modeling areas to have just those facies that match the style (adjacency order) of the algorithm. The Well section below shows the facies distribution in each well and zone. Based on the distribution and relationship of the facies, the following algorithms were used to model each zone: A 2 Carbonate Truncated Gaussian simulation (limestone and dolomite) A 2 Evaporite Sequential Indicator simulation (salt and anhydrite) A 1 Carbonate Truncated Gaussian simulation (reef and carbonate) A 1 Evaporite Sequential Indicator simulation (salt and anhydrite) Niagara Truncated Gaussian simulation (reef and carbonate) Lower Niagara Assign value (Interreef mud) The A 2 Carbonate could have been modeled with either Sequential Indicator or Truncated Gaussian equally well as there were only two facies in the zone. 8
Figure: Line cut by the Well section through the wells (top left), list of the Facies that are being modeled (top right), and the Well section with facies log displayed (bottom). Data Analysis vertical proportions were used on all zones to assist in distributing the rock. 2D Trend grids were used to force facies to be positioned laterally with respect to the reef in the proper percents. These trends were made to range in value from 0 to 1.0. Although the trends should sum to 1.0, no effort was made to force this (some places they summed to.5, some places to 1.0 other places to 1.5). When a particular facies wasn t positioned correctly, its trend was adjusted to increase or decrease its proportion in that area. The authors have found that trends are the primary tool for positioning the rock and creating the desired geologic effect when working with this algorithm. In most cases, 2D Grids work fine but in some cases, specially built 3D Grids are needed to create the desired effect. Because the wells were preferentially drilled into the reef the percent of each facies in a zone did not match the modeled percent. This was expected 1) because the model covered both reef and non reef areas, 2) vertical proportions were used which sometimes force the distributions to vary a bit from the wells, and 3) trends were 9
used which dramatically impact the percent of each facies. Needless to say, the model was worked until its geologic features (facies distributions) looked acceptable, and matched the mental image of the geology. Figure: Data Analysis dialog for the two reef zones (remember, layering is set to follow top). Figure: Trends used to model the A 1 Carbonate (top row): Reef Rock, Reef Talus, Dolomite, Limestone and Niagara (bottom row): Reef Rock, Reef Talus, and Interreef Mud. 10
Figure: Facies modeling parameters used to model the A 1 Carbonate. Figure: J index section with a 1:1 vertical exaggeration showing the final facies model. Figure: I index section (top left, 5:1), J index section (top right, 5:1), K index (bottom left, through A 1 Carbonate), and 3D view of reef rock and talus (bottom right 5:1), all showing the finished model. 11
Experiments Some experiments were made to see what the effect would be if trends were not used, if the Sequential Indicator simulation algorithm was used with the same trends, and if the reefs and the intermediate evaporate were all modeled as one zone. The figures below show these scenarios compared to the best case model. It was found that for this data, SIS and TGS could both be used to produce acceptable results but that the trends were more rigorously followed with TGS. Figure: Models built with Truncated Gaussian simulation: without trends (left) and with trends (right). Figure: Models built with trends: Sequential Indicator simulation (left) and Truncated Gaussian simulation (right). Trends tend to be honored more rigorously with Truncated Gaussian simulation but both produce acceptable forms with this data. 12
Figure: Models built with Sequential Indicator simulation: one zone from top A 1 Carbonate down to Base Niagara (left) and separate zones (right). 13