CBS Engineering Properties in Simulated Downhole Environment

Expressing the right-hand side of Equation 15.4 in terms of the enthalpy A// and entropy 

The subscripts in Eq. 15.5 have the same meaning as in Eq. 15.4. The entropy is an explicit function of T, while the enthalpy depends on both T and P. The explicit temperature dependence on AG has been discussed in Chapter 6 and used to smdy its effect on alumina solubility in Chapter 11. Here, because the downhole pressure is very high, we extend the discussion of dependence of AG on P. 

When components of CBS slurry dissolve in water, their aqueous ions may have a different ionic size as compared to that in the unreacted crystal, and hence, the volume of the dissolved species may be different from that of the unreacted components. Thus, the total volume after dissolution Vf may be different from the total volume prior to dissolution Vq-This volume change will occur against the downhole pressure, because the slurry components will be mixed during pumping and wiU dissolve when they are placed in downhole conditions. Thus, the change in enthalpy of an individual component is given by 

Equation 15.6 is a generalization of Eq. (6.15) and includes the pressure effects. AHq is the change in enthalpy if the dissolution were to take place at normal temperature, while the rest of the terms on the right-hand side of Eq. 15.6 correspond to the change in enthalpy when the dissolution occurs at downhole temperamre and pressure. 

If we assume in Eq. 15.6 that the volume change AV does not depend on the temperature and pressure, we can write AVf = AVq, and the last two terms on the right-hand side reduce to (Pf — Pq)AVq. Calculations from this equation, based on the ionic radii of the right-hand side and the molecular radii of the left-hand side (see Ref. [4] for these data) of Eq. 15.3, indicate that AVq is very small even at a high pressure difference (Pf — Pq) Therefore, the pressure effects on the oxide solubility can be ignored, and the only variable one needs to consider while formulating the CBS slurry is the downhole temperature. 

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