As water migrates through porous rock, any changes in pressure or temperature, as well as changes in fluid composition, may lead to changes in the solubility of dissolved minerals. We examine the reactions which may develop in such a system, following the injection of water of one temperature and composition into a reservoir with different temperature and equilibrium composition. We examine the structure of pressure, temperature and compositionally induced reactions.
Connate water in reservoirs is often saturated in calcium carbonate. Like many minerals, the solubility is highly dependent on temperature, pressure, and the ion concentrations of other species (Mg2+, NaCl, pH etc.) (1) (Schlecter 1992). In this simplified model, we attempt to explain some of the different flow induced processes which may lead to the formation or dissolution of limescales in reservoirs; we focus on the effects of changes in pressure, temperature or composition as fluid is injected and migrates through the reservoir. In order to understand the different processe, we present a series of simplified models, to account for the reaction fronts associated with compositional and temperature changes. We then illustrate how the effects of pressure dependent solubility, coupled with the gradual pressure gradients which develop in a flowing reservoir, lead to a spatial rather than frontal generation or dissolution of precipitate.
Precipitation will occur if the saturation S, defined as the ratio of concentration to equilibrium concentraion (S=C/Ceq), exceeds a critical value. Because nucleation creates a potential barrier, this value may be greater than 1. Zhang (2) gives an expression of R=k(S1/2 –1)2, where k is a rate contant and R is the precipitation rate. However, the pressure dependence of the rate constants and saturation level is not well characterised.
In our simplified model, we assume that the equilibrium saturation is directly proportional to the pressure and temperature, and that the precipitation rate increases linearly with the supersaturation of the liquid, i.e. R=?(S-ßp)-?T. This is a gross simplification, as the behaviour is likely to be highly non-linear, especially as the pressure is reduced and dissolved CO2 reaches bubble point. However, for the purposes of understanding the fluid dynamics of the system and the nature of the reaction regimes, our simplification will be useful.
We first analyse a depletion front reaction, in which undersaturation of the injected fluid leads to an advancing dissolution front in the rock. We then examine the migration of a thermally induced reaction, which can develop when water of a different temperature to the reservoir is injected into the reservoir. We then describe the different regimes of interaction between these two reaction fronts. We then turn to precipitation reactions induced by supersaturated in the injected water, which leads to clogging of the rock near the site of injection, in contrast to the dissolution driven traveling depletion front. Finally, we consider the effect of changes in solubility resulting from the pressure changes which water experiences as it migrates through the reservoir. We illustrate that with a decrease in solubility as the pressure falls, precipitation occurs throughout the reservoir, but is maximized downstream, near a low pressure producing well, and it is in this region that the rock will tend to clog first.
In the simplest example of a depletion or dissolution front, we assume that the injected fluid is compositionally undersaturated at reservoir conditions and that a small fraction of the matrix is composed of soluble mineral which, on dissolution, can restore the liquid to equilibrium. If the composition difference between the injected and formation fluid is co and the fraction of the matrix composed of soluble mineral is so, then the reaction front will advance a distance ?ut while the injected fluid will advance a distance ut/f, where ? is given by the mass balance
here ß is the stochiometric constant expressing the ratio of the mass of mineral which dissolves per unit mass of composition dissolved in solution.