HydroGeoSphere/2-D Random Fracture Generator

The 2-D Random Fracture Generator can be used to generate random fracture networks in two dimensions, currently only in the xz-plane. Nevertheless, in the y-direction, more than one block can be used. Begin 2D random fractures...End Causes grok to begin reading instructions that describe the generation of 2-D random fractures until it encounters an End instruction. • • • The following optional instructions can be used to modify the default behaviour of the fracture generator: Number of random fractures n rfractures Number of random fractures to generate. By default, the 2-D random fracture network will consist of 80 fractures. • • • Use constant seed the_seed Seed for the 2-D Random Fracture Generator. Causes the 2-D Random Fracture Generator to use a constant seed the_seed to produce the same random fracture network each time grok is run. By default, the 2-D Random Fracture Generator is seeded with a time-dependent value, based on the current system time. In that case, it produces a different fracture network each time grok is run. In either case, the seed value is written to the prefixo.eco file and can be used to generate the same random fracture network many times. • • • Generate orientation distribution or_n_classes Number of orientation classes. or_first_class middle Middle of the smallest orientation class. or_last_class middle Middle of the largest orientation class. or_sigma Standard deviation of both Gaussian distributions. or_my1 Mean of the first Gaussian distribution. or_my2 Mean of the second Gaussian distribution. Causes grok to read the parameters that are used to define the distribution of fracture orientation, which follows a double-peaked Gaussian distribution according to: 25(Equation 5.1) where the normal distribution for a variable with mean and variance has the probability function 25(Equation 5.2) for the domain . By default, the values given in Table 5.1 are used to define these relationships: +Table 5.1Table 5.1: Default Values for 2-D Random Fracture Orientation Parameter Value Unit Number of orientation classes 13 - Middle of the smallest orientation class 30 degrees Middle of the largest orientation class 150 degrees Standard deviation of both classes 15 degrees Mean of the first Gaussian distribution 60 degrees Mean of the second Gaussian distribution 120 degrees • • • Generate aperture distribution ap_n_classes Number of aperture classes. ap_first_class_middle Middle of the smallest aperture class. ap_last_class_middle Middle of the largest aperture class. ap_lambda of the exponential aperture distribution. Causes grok to read the parameters that are used to define the distribution of fracture aperture, which follows an exponential distribution, according to: 25(Equation 5.3) Note that for a high value of , the exponential distribution becomes steeper and small apertures are more numerous, whereas a small value of favours larger apertures. By default, the values given in Table 5.2 are used to define these relationships: +Table 5.2Table 5.2: Default Values for 2-D Random Fracture Aperture Parameter Value Unit Number of aperture classes 10 - Middle of the smallest aperture class 50 microns Middle of the largest aperture class 300 microns of the exponential aperture distribution 9000 - • • • Generate log-normal length distribution le_n_classes Number of length classes. le_first_class_middle Middle of the smallest length class. le_last_class_middle Middle of the largest length class. lognormal_m of the log-normal distribution. lognormal_s of the log-normal length distribution. Causes grok to read the parameters that are used to define the distribution of fracture length, which follows a log-normal distribution according to: 25(Equation 5.4) By default, the values given in Table 5.3 are used to define these relationships: +Table 5.3Table 5.3: Default Values for 2-D Random Fracture Length, Log-normal Distribution Parameter Value Unit Number of length classes 10 - Middle of the smallest length class 0.1 min() † m ‡ Middle of the largest length class min() m of the log-normal distribution 2.9 - of the log-normal length distribution 0.45 - † The symbols and denote the length of the simulation domain the x- and z-directions respectively. ‡ Although metre units of length are shown in this table they may be defined differently by the user as outlined in Section 5.1.2. It should be noted that the log-normal distribution results from the curve by: Stretching of in the x-direction. Stretching of in the z-direction. Thus, larger values for will move the peak to the right. Altering the standard deviation will have an impact on the scattering of the distribution where a small leads to less scattering and a sharper peak. • • • Exponential length distribution Causes grok to use an exponential distribution of the fracture trace, as opposed to the default log-normal distribution. • • • Generate exponential length distribution le_n_classes Number of length classes. le_first_class_middle Middle of the smallest length class. le_last_class_middle Middle of the largest length class. le_lambda of the exponential length distribution. Used in conjunction with the Exponential length distribution instruction, this causes grok to read the parameters that are used to define the distribution of fracture length, which follows an exponential distribution according to: 25(Equation 5.5) Note that for a high value for , the exponential distribution becomes steeper and short fractures are more numerous whereas a small favors longer fractures. By default, the values given in Table 5.4 are used to define these relationships: +Table 5.4Table 5.4: Default Values for 2-D Random Fracture Length, Exponential Distribution Parameter Value Unit Number of length classes 10 - Middle of the smallest length class 0.1 min() † m ‡ Middle of the largest length class min() m of the exponential length distribution 0.05 - † The symbols and denote the length of the simulation domain in the x- and z-directions respectively. ‡ Although metre units of length are shown in this table they may be defined differently by the user as outlined in Section 5.1.2. • • • Output random apertures Writes the generated aperture distribution data and individual fracture apertures to the output file prefixo.rfrac.apertures. • • • Output random lengths Writes the generated length distribution data and individual fracture lengths to the output file prefixo.rfrac.lengths. • • • Output random orientations Writes the generated orientation distribution data and individual fracture orientations to the output file prefixo.rfrac.orientations. • • • Output random fractures Writes fracture zone aperture, conductivity and location data to the output file prefixo.rfrac.fractures. • • • Default distributions Figure 5.3 gives an overview of the default distributions which the 2-D Random Fracture Generator employs. The orientation distribution (Figure 5.3a) is based on the assumption that tectonic stress results in the creation of two fracture families as depicted in Figure 5.3b. However, upon assigning identical values for and , the distribution collapses to a one-peak distribution. The default distribution for the aperture (Figure 5.3c) is exponential and can be modified by the user. By default, the fracture traces are distributed log-normally (Figure 5.3d), which can be changed to exponential. Note that the fracture trace distribution depends on the domain dimensions. Here, a block has been used with  = 100 m,  = 1 m and  = 50 m. Figure 5.3thumb|none|800px|Figure 5.3: Default Random Fracture Distribution Example irregular fracture network The following instructions were used to generate the irregular fracture network shown in Figure 5.4. Note the dominance of the two orientations 80° and 135°: !_______________________ grid definition generate uniform blocks 100.0 200 1.0 1 50.0 100 adapt grid to fractures 3 end ...etc... !_______________________ fracture media properties use domain type fracture properties file eval.fprops begin random fractures use constant seed 0.5 number of random fractures 70 exponential length distribution generate orientation distribution 10 60. 150. 10. 80. 135. output random apertures output random lengths output random orientations output random fractures end read properties fracture Figure 5.4thumb|none|800px|Figure 5.4: Example for an Irregular Fracture Network