Discrimination of fizz water and gas reservoir by AVO analysis: a modified approach

Abstract

Amplitude versus offset response is analogous to variation in P-wave velocity resulting from different pore fluid saturations. However, the input parameters of fluid mixtures such as fluid modulus and density are often estimated using volume average method, and the resulting estimates of fluid effects can be overestimated. In seismic frequency band, the volume average method ignores the heat and mass transfers between the liquid and gas phases, which are caused by pore pressure perturbations. These effects need to be accounted for the interpretation of the seismic events and forward modeling of fizz water reservoirs. The conventional model is corrected in present study by considering the thermodynamic properties of the fluid phases. This corrected model is then successfully applied on a gas producing field in the North Sea. AVO response, based on the corrected model is highly affected by pressure related variations in bulk modulus of multi-phase formation fluid. Velocity push down effect appears, as the free gas saturation generates stronger AVO response than obtained by a conventional AVO model. The, present research reveals that such response is helpful to discriminate fizz water from commercial gas, to detect primary leakage of gas (CO₂ or CH₄) from geological structures and to model free gas effects on seismic attributes.

Appendix: Relaxed two-phase compressibilities calculated from an equation of state (EOS)

This appendix describes the method used in this paper to compute the isothermal and adiabatic (or isentropic) bulk moduli of thermodynamically-equilibrated (or relaxed) co-existing liquid and gas phases using an equation of state (EOS) and expressions for the enthalpies of the liquid and gas phases (Whitson and Brulé 2000). These moduli, labeled respectively with subscript T for isothermal and S for adiabatic, are related by the following formula, valid both in single-phase and in the two-phase regions

$$ K_{f} = \biggl[ K_{T}^{ - 1} - \frac{\alpha_{P}^{2}TV}{C_{P}} \biggr]^{ - 1}. $$

(A.1)

In (A.1), V is the total volume (V=V _l +V _g in two-phase conditions), α _P =1/V(∂V/∂T) _P is the isobaric thermal expansivity, and C _P the isobaric heat capacity. (In these partial derivatives, the overall mixture composition is kept unchanged.) In the one-phase region, α _P , C _P and the isothermal bulk modulus

$$ K_{T} = 1/\beta_{T} = \bigl[ - 1/V ( \partial V/\partial P )_{T} \bigr]^{ - 1} $$

(A.2)

are easily obtained from an EOS. In (A.2), β _T is the isothermal compressibility of the fluid. In the two-phase region, β _T and α _P are obtained numerically by determining phase compositions from a phase-split (flash) calculation and then computing the phase volumes V _l and V _g at fixed temperature and neighboring pressures (to obtain β _T ), and at fixed pressure and neighboring temperatures (to obtain α _P ).

Similarly, the two-phase heat capacity C _P is obtained as the derivative with respect to temperature of the enthalpy of the two-phase system. The enthalpies of the liquid and gas phases are the sum of an ideal term and a departure term directly related to the equation of state. The only ingredients needed for calculating the departure terms are the phase compositions obtained by the flash calculation and the phase volumes. The ideal terms are the combination (weighed by the molar fractions) of the ideal enthalpies, whose values had obtained from Reid et al. (1988). The two-phase C _P is obtained numerically from the two-phase enthalpies calculated at two neighboring temperatures.

The EOS used for the aqueous fluids is the Peng-Robinson modified by Soreide and Whitson (1992) EOS. This EOS provides accurate phase compositions. The molar volume of the liquid (aqueous) phase is calculated by using the following relation

$$ V_{l}(T, P) = V_{\mathrm{H}_{2}\mathrm{O}}(T, P)x_{\mathrm{H}_{2}\mathrm{O}} + V_{j}(T)x_{j}, $$

(A.3)

where $V _{\mathrm{H}_{2}\mathrm{O}}$ is the molar volume of pure water at given T and P, and V _j is the apparent partial molar volume of the non-aqueous component j. We have used the values of V _j deduced from the density measurements by Hnedkovsky et al. (1996). The molar volume of the non-aqueous phase is obtained by using the Lee and Kesler (1975) equation for the compressibility factor.