Introduction of Kinetic Effects into the Thermodynamic Modelling of CaCO3 Scale Precipitation
Authors: Silva Duarte J. , Sorbie K. S. , Mackay Eric J. 
Published: June 2018

Abstract
Calcium carbonate (CaCO3) scale can form through an "auto-scaling" process in production systems with a CO2-rich environment due to fluid (water/oil/gas) depressurisation. Thermodynamic modelling is used to estimate the amount and severity of CaCO3 scale precipitation in this context in order to design scale inhibitor or other types of treatments. However, field experience has indicated that thermodynamic calculations often lead to an overestimation of the calcite scale problem. One possible source of this discrepancy may be due to kinetic effects; i.e. that the calcite is somewhat oversaturated (Saturation Ratio, SR &gt;1) but the driving force is not sufficiently large and so the deposition is kinetically "slow". The industry response to this situation has been to come up with some simple heuristics based on field observations, and "rules of thumb" have been developed to account for this apparent overestimation of calcite deposition. The central objective of this paper is to try to address the problem of using such an arbitrary field procedure for calcite scale prediction by introducing the kinetics of calcite deposition in a thermodynamically consistent manner. We view the calcite auto-scaling system as one which moves from SR &lt; 1 (non scaling) incrementally to one that is slightly supersaturated (SR slightly &gt; 1). By making the deposition rate a function of SR, this would give slow rate of deposition initially, but as the system moved into the more scaling regime in the production system (SR &gt; 1) then the deposition rate would increase. However, throughout the system, this kinetic formulation must limit correctly (i.e. it must be consistent with) the underlying equilibrium thermodynamics of the full brine/oil/gas system. Thus, we replace the idea of using heuristic estimates of when calcite scaling occurs by one where an estimate (or measurement) of the kinetics is made; indeed, a range of kinetics rates can easily be run to give an envelope of calcite scaling profiles in the wellbore and throughout the production system.
In this paper, we present a model that incorporates a fully consistent kinetic formulation into a general thermodynamic scale prediction model. This model can then calculates scaling profiles in production systems considering both kinetic and thermodynamic effects. In particular, a rate law for the precipitation of CaCO3 based on the respective degree of super-saturation is coupled with the Heriot-Watt FAST Scale Prediction model (HW FAST). HW FAST uses the Pitzer equations and the Peng-Robinson Equation of State to model, respectively, the aqueous and hydrocarbon phases (gas and oil), and it has been developed to calculate CaCO3 scaling profiles caused by a de-pressurisation effect in CO2-rich production systems.
First, we present an equilibrium thermodynamic example calculation showing that CaCO3 scale precipitates in CO2-rich production systems due to a de-pressurisation effect, and that precipitation is more severe topsides where the pressure is low than it is downhole where the pressure is high. It is explained that the amount of scale precipitated in this auto-scaling process must be plotted as a cumulative amount, in order to avoid the calculation of a potentially misleading scaling profile. This calculation is then repeated, but also considering kinetic effects for systems with varying temperatures and water flowrates. In the example presented here, we show that this system with sufficiently "low" water flowrates can be approximated by a thermodynamic calculation, and that systems with "high water" flowrates must take kinetic effects into consideration. This scaling profile can then be used to more accurately design scale inhibitor treatments, thus avoiding under or over-treatments (e.g. opting for continuous scale inhibitor injection instead of the more expensive squeeze treatment).
Our approach focuses on calculating the correct scaling profile in auto-scaling processes, both qualitatively and quantitatively, by coupling a kinetic formulation to a thermodynamic model, and it can be readily extended to other auto-scaling processes. Further, our kinetic model can be easily integrated with commonly available scale prediction software.