PAPER Z

NORMALISED Q_v - THE KEY TO SHALY SAND EVALUATION USING THE WAXMAN-SMITS EQUATION IN THE ABSENCE OF CORE DATA

I. Juhasz

Shell International Petroleum Maatschappij, The Hague, The Netherlands

ABSTRACT

In order to evaluate the water saturation of shaly sands from logs using the Waxman-Smits (W-S) equation the parameter Q_v (cation exchange capacity per unit total pore volume) must be known. Qv is normally obtained from a Q_v - total porosity (fT) relationship defined on the basis of either core-data, or log-derived Q_v and f_T values calculated via the W-S equation in water-bearing sands.

The constraints of applicability of such approaches are obvious:-

(i) either pertinent core data, or representative waterbearing sands must be available and, in addition,

(ii) the formation characteristics must be such that a good correlation between Q_v and porosity exists.

In this paper it will be demonstrated that the above mentioned constraints can be largely eliminated by replacing Q_v in the W-S equation with a dimensionless expression of Q_v defined as “normalised Q_v”: Q_vn = Q_v / Q_vsh. This parameter is shown to be equivalent to “shale-water saturation”: Q_vn = V_sh f_Tsh / f_T,  a parameter which can be derived from logs. Q_vsh, the Q_v value of the shales intimately associated with the sands can also be derived from logs as the difference between shale-water conductivity and formation-water conductivity divided by B, the specific conductance of the clay exchange cations. Q_v can thus be calculated from logs at any point in the section to be evaluated simply from the equation Q_v = Q_vn * Q_vsh.

By using the concept of the normalised Q_v the Waxman-Smits equation can be converted into a “normalised” form in which all parameters, with the exception of the saturation exponent n*, can be obtained from logs. From this, the water saturation can be expressed in the form of the familiar Archie equation.