A Petrel Plugin for Surface Modeling

Transcription

1 A Petre Pugin for Surface Modeing R. M. Hassanpour, S. H. Derakhshan and C. V. Deutsch Structure and thickness uncertainty are important components of any uncertainty study. The exact ocations of the geoogica picks are known ony at the wes which, in genera, are sparse. Athough the surface picks and thicknesses are ony known at sparse wes, 3D seismic data (time interpretation and time-to-depth seismic) and Geostatistica techniques can be used to assess the uncertainty in the surfaces and the thicknesses. A basic geostatistica assumption is that the base case surface is unbiased and that deviations from the base case foow a Gaussian distribution. If the distribution is known better, then a norma score transformation and back transformation woud repace the simpe (non)standardizing approach taken in this paper. Using Petre s Ocean API, the surface modeing engine has been written as Petre pugin. This aows Petre users to do surface modeing using the picks, base case surface and the uncertainty associated with time interpretation and time-to-depth seismic surfaces. In addition to Petre pugin the prototype code is aso presented. Introduction Structura modeing is one of the important steps in reserve cacuation, reservoir characterization and simuation and in genera in a reservoir uncertainty studies. The uncertainty in top and bottom reservoir surfaces has effect in the uncertainty of the reserve. In this paper a methodoogy is presented to mode the structura surfaces with reasonabe amount of uncertainty. The methodoogy is based on sequentia Gaussian simuation. Methodoogy Basicay the deviations from the base case surface are modeed. At we ocation since the picks are avaiabe the deviation is zero but far from the we we can assume that the deviations from base case are not zero and the distribution of the deviations foows Gaussian distribution. The required input parameters are isted beow: 1. The base case vaue (structure or thickness): (z b (u), u in A) a 2-D grid of vaues coming from the seismic. In genera these vaues are fitted to the we picks. 2. A goba estimate of the uncertainty in the base case surface σ Δ a singe number estabished from time interpretation uncertainty and time to depth uncertainty. It coud be cacuated from: σ = Δ σ + σ 2 2 TI TD Where TI refers to the time interpretation standard deviation and TD refers to the time-to-depth standard deviation. These woud be based on a review of the seismic data and, perhaps, differences between different interpretations. 3. Uncertainty in the mean cacuated from the number of independent data (widey spaced wes) or the spatia bootstrap σ σ = Δ Δ n i Where n i refers to the number of independent data

2 4. A map of ocay varying uncertainty coud be considered: (f (u), u in A) a 2-D grid of vaues coming from an understanding of the seismic variabiity. f (u) wi be 1 when the uncertainty is ike the goba estimate (point 2), it wi be higher than 1 in more uncertain areas and ess than 1 in more certain areas. These four parameters must be estabished from the avaiabe reservoir data. The simuation proceeds by estabishing a target mean, that coud be different from 0.0, simuating the deviations and adding them to the base case surface. The procedure for simuation can be summarized by the foowing steps: 1. Estabish a target mean for the simuation 1 a. Draw a random number and convert to a standard Gaussian vaue: y = G ( p ) b. Convert to a non-standard vaue reaization. Δ =, which is the target mean for this simuated y σ Δ 2. Estabish the conditioning data for the reaization. The conditioning data are aways zero, that is, we want to reproduce the data exacty; however, we need to use non-zero conditioning data so that the back transformed vaues are zero. The conditioning data are cacuated as: y ( u ) α = σ Δ Δ f ( u ) 3. Simuate standard norma vaues (sgsim with transformation turned off) using the conditioning data estabished in step 2. This provides (y (u), u in A). 4. Non standardize the standard norma simuated vaues and add to the base case: 5. Repeat steps 1 to 4 for many reaizations. ( u) = ( u) + ( u) ( u ) z zb y σ Δ f α There are some practica considerations. Firsty, different random numbers shoud be used at each step to avoid unwanted correations this is easy. Secondy, the conditiona simuation of step 3 amounts to condition to vaues that are a negative if Δ is positive and a positive if Δ is negative. Depending on the range of the variogram, this tends to work against a fu samping of the uncertainty. For exampe, if we draw a positive mean of 5m, the Gaussian vaues wi come out preferentiay negative and the back transformed mean wi be ess, say, 3 m. The uncertainty in the average may need to be increased to account for this. A typica workfow woud be to mode the top structure and work with isochore thicknesses down through the stratigraphic coumn. Care shoud be taken to ensure data conditioning and reasonabe standard deviations at each step. For the purposes of sensitivity study, the base case thicknesses coud be used for the reaizations of top structure, then the thicknesses coud be varied hoding the top structure at the base case. Of course, a vaues shoud be varied to quantify uncertainty

3 Petre Pugin Schumberger Ocean aows the Petre users to add their new deveoped agorithms to Petre as a pugin. The Petre pugin gets the required input from the user, reads the data from Petre, cas the DLL, receives the output from the DLL, and saves the data into Petre objects. In this work we used Ocean 2008 to generate surface modeing pugin for Petre. Since some parts of our agorithm (such as SGS) were previousy coded as a FORTRAN subroutine within GSLIB, we generated the main surface modeing engine in FORTRAN. The next step was to convert the surface modeing code to a DLL. This DLL was caed from the Ocean pugin. The surface modeing pugin user interface can be opened via the process menu or workfow manager in Petre. Figure 1 shows the surface modeing user interface. There are 11 parameters that shoud be specified before running the program. Base case surface (zb(u)), we data, and oca uncertainty map (f (u)) can be set by seecting an object and pressing the bue arrow or by dragging and dropping the object into surface modeing pugin window. Other parameters incuding uncertainty in base case surface, uncertainty in mean, random number seed, and number of reaization to generate can be specified in the reated boxes. Since there is no specific information to cacuate and mode the variogram for the variabe (deviation from base case surface) in this appication, a generic variogram structure may be considered. Gaussian and spherica variogram can be chosen for variogram type menu. Azimuth, maximum, and minimum ranges shoud aso be specified to define the variogram structure. Pressing appy or ok button wi run the program. The output wi be stored in a Piargrid object. Exampe In order to verify both the agorithm and the pugin the foowing case is examined. Consider an area with Easting of 920 m and Northing of 1300 m. Four vertica wes are dried in this area. The eevation of specific surface (such as top of Mcmurray) is known at a four wes. A seismic-derived base case surface is avaiabe for this area. Figure 2 shows the ocation of wes and the base case surface. A ocay varying uncertainty map is considered for this exampe. Figure 3 shows the ocay varying uncertainty map. Based on the oca uncertainty, three different cases of 0.1m, 0.3m and 0.7m are considered. For each case five reaizations are generated. For a cases the uncertainty in mean is set to A Gaussian variogram with isotropic range of m is assumed. Figure 4 to Figure 6 shows simuated reaizations for different base case surface uncertainty vaue. In order to check the vaidity of modes, each reaization is compared to the base case surface and the difference map (Δ) is cacuated. The mean and standard deviation of difference map is cacuated for a five reaizations. Tabe 1 shows the resuts for the first case (oca uncertainty of 0.1m). The averages of mean and standard deviation for five reaizations are (cose to zero) and (cose to 0.1), respectivey. The deviation of mean and standard deviation from 0.0 and 0.1 may be due to the data conditioning. Tabe 1. Summary statistics for five reaizations generated with oca uncertainty of 0.1m. Reaization Number Mean of Δ Standard Deviation of Δ Average Standard Deviation

4 References: Deutsch, C.V. and Journe, A.G., 1998: GSLIB - Geostatistica software ibrary and users guide. Oxford University press, 2 nd Edition. Deutsch, C.V., 2002: Geostatistica Reservoir Modeing. Oxford University press Neufed, C. and Deutsch, C.V., Programming Tips for Pugins. In Centre for Computationa Geostatistics, Paper 402, Annua Report 9, 2007 Manchuck, J., Neufed, C. and Deutsch, C.V., Petre Pugins for Decustering and Debiasing In Centre for Computationa Geostatistics, Paper 403, Annua Report 9, 2007 Schumberger Information Systems. Ocean 2008 Deveoper s Guide. Schumberger Information Soutions, Houston, Texas, Schumberger Information Systems. Ocean Porta. Figure 1. User interface for surface modeing Petre pugin

5 Figure 2. Location of wes in modeing area (eft) and base case surface map (right). Figure 3. Map of ocay varying uncertainty 408-5

6 Figure 4. The base case surface (top right) and five simuated reaizations with uncertainty of 0.1m in base case surface

7 Figure 5. The base case surface (top right) and five simuated reaizations with uncertainty of 0.3m in base case surface

8 Figure 6. The base case surface (top right) and five simuated reaizations with uncertainty of 0.7m in base case surface