Modeling seismic velocity in Ekofisk chalk

Abstract

IntroductionThe Ekofisk formation in the Norwegian North sea has been under production for over 20 years. A project is under way to determine the feasibility of performing time lapse (4-D) seismic analysis to more accurately map the distribution of hydrocarbons. One part of this project was to model the seismic velocity of the chalk reservoir in terms of its porosity and fluid saturations. DiscussionIn order to create a model for the velocity-porosity transformation in chalks, we analyzed the data for well K13. Figure 1 shows porosity and water saturations versus depth. We first transformed velocity (Vp and Vs) to bulk and shear modulus using standard elastic equations. Next we transformed the log velocity to dry conditions using Gassmann's equations and the average solid and fluid properties given in Table 1.The velocity-porosity model we used connects the highest-porosity point with the zero-porosity point in the modulus-porosity plane. At the zero-porosity point the moduli will be those of the solid phase. For example, if at porosity , the mineralogical composition of the solid phase includes quartz, clay and calcite, the resulting effective bulk (K s ) and shear (G s ) moduli of the solid phase will be found using the Voigt-Reuss-Hill average of the individual components. This gives us the zero-porosity elastic moduli values. Density and modulus for the component minerals and fluids are shown in Table 1. The next step is to determine the highest-porosity elastic moduli values. There are at least two ways of doing this. The first one is to plot the dry-rock bulk and shear moduli (obtained from a typical well) versus porosity and pick these values. For example, for well K13, these values are about 4 GPa for both dry-rock bulk and shear moduli at porosity of 0.4. The second one is to use the contact cement theory (Dvorkin and Nur, 1996). The basic assumption behind this theory is that at high porosity chalk is made up by calcite grains enveloped by cement (calcite) rims. By using this theory one can accurately pick the high-porosity elastic moduli end members. Specifically, we recommend that the critical porosity value be selected at 0.42 for this data set. Then the end member elastic moduli values have to be picked at the critical porosity value minus 0.02. Next we describe the model that connects these end points in the moduli-porosity plane.The modified Upper Hashin-Shtrikman model (UHS) connects two end members in the elastic modulus -porosity plane. This approach is similar to one used by Anderson, 1997. One end member (K o , G o , M o ) is at the highest porosity point and can be calculated from the contact cement theory. The other end member is at zero porosity and is the modulus of the solid phase (K s , G s , M s ) calculated from VoigtReuss-Hill. In this text, K is for the bulk modulus, G is for the shear modulus, and M is for the compressional modulus:. For porosity that is between zero and , the dry-rock effective bulk and shear moduli ( and , respectively) are: The lower bounds for the dry-rock eff...

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