Determination of Lamé parameters and LMR in one of the reservoirs in South of Iran

Lamé parameter (λ) and shear modulus (μ) are two most important parameters in the identification of fluids and reservoir rocks. Lamé parameter (λ) is sensitive to the fluid within the rock fabric whereas µ is sensitive to the rock matrix only. The combination of these attributes allows more accurate separation of the rock and fluid effects in the reservoir.
Wilkens et al. (1984) gave ultrasonic velocity values measured in single crystals of quartz and calcite. They reported values of about 44 GPa for the shear modulus of fused quartz, and 31 Gpa for calcite. They also measured λ to be about 8.4 Gpa for quartz and 55 Gpa for calcite. Lee (2005) reports measured values of 44 GPa for the shear modulus of sand, and 38 Gpa for bulk modulus (Lee, 2009), for which the value of Lamé parameter (λ) is 8.7 GPa. Helgerud et al (2009) calculated the shear modulus of gas hydrate to be 3.49 GPa (at 11°C and 1MPa). Goodway (2001) argued that the value of λ/μ was a more sensitive indicator than λ, λρ, Vp/Vs and Poisson's ratio. Goodway demonstrated that how LMR (Lambda-Mu-Rho) analysis could be used to identify gas sands. The gas in the rock does not affect rigidity and it has low values of λρ. The combination of the fluid compressibility along with the mineral properties and grain shapes result in different LMR values. Using petrophysical parameters to scale the results of LMR analysis, 3D seismic volumes can be converted into lithology cubes. Neither λ nor μ are powerful lithologic indicators by themselves, but used in combination can reveal a great deal about lithology. Gray and Andersen (2000) demonstrated that how LMR cross plot analysis could be used for lithology discrimination. Different lithologies can be identified by cross-plots of λρ versus μρ. Perez and Tonn (2007) were analyzed to model the LMR response of various reservoir qualities and fluid fills. LMR response separates shale zones from highly porous sand zones. Shaocheng et al. (2010) analyzed the equivalent isotropic elastic data of natural rocks in order to characterize λ values for common types of crystalline rocks in the Earth's crust and upper mantle. In the λ-ρ and μ-λ plots, the main categories of lithology can be clearly distinguished.
In this study, log analyses were used for a well from the South Pars gas field and the analysis of DSI was used to estimate shear wave velocity developed in a relationship with λ, μ and LMR. The reservoir zone of South Pars field consists of Kangan (K1 and K2) and Dalan (K3 and K4) Formations. Compressional and shear wave velocity values were determined for the estimation of Lamé parameters (λ and μ) for the reservoir zone. The crossplots λ/μ were used to identify the gas. The ratio λ/μ and the crossplot difference λρ-μρ provide some information about the presence of the gas in Kangan and Dalan Formations. The computed average Lamé’s constants, λ and μ parameters in Kangan Formation in K1 are 36.19 Gpa and 31.25 Gpa and are 32.59 Gpa and 27.02 Gpa in K2, respectively. Also the average values of λ and μ in K3 layer are 33.79 Gpa and 29.59 Gpa and 25.32 Gpa and 24.63 Gpa in K4, respectively.