“…The kinetic effect induced by pressure can be directly related to the activation volume of the reaction that passes through a transition state as shown in eq . Experimentally, the effect of pressure on reaction kinetics can be expressed in terms of the activation volume (Δ V ⧧ ), which is defined as the logarithmic pressure derivative of the rate constant. , Within transition state (TS) theory, the activation volume of, for example, barite nucleation (eq ), can be described as the difference in partial molar volumes between the TS ( V ⧧ ) and reactant species as indicated by eq . However, because of the complexity to measure the partial molar volume of the activated complex, experimentally the activation volume of the reaction can be determined from kinetic data using eq . where R is the gas constant, T (K) is the absolute temperature, and k (s –1 ) is the overall rate constant of barite formation at a given pressure under constant temperature. Induction time of mineral nucleation (hereafter nucleation time, t 0 ) and precipitation reaction rate are inversely proportional to each other; , therefore, eq can be modified to eq , where t 0 is the nucleation time of mineral precipitation, for example, barite.…”