1. Introduction - Firenze University Press

(Mg/Fe) of the mineral rock, Mg-silicate to AS mass ratio (S/AS), reaction temperature (T), time (t),
and the interaction of these effects.
It is important to point out the nature of the test data (statistical details are presented in Table 1).
The initial batch of tests were done using mostly Finnish serpentinite between 2008 and 2009, and
were reported in [15] and [16]. The aim at that time was to prove that Mg(OH)2 can be produced
from Finnish serpentinite, and efficiently too. After this, efforts were channeled towards applying
the method to different Mg-silicate rocks from worldwide locations[6, 20-22].
Table 1. Statistical overview of the parameter values tested in 82 experiments.
Parameters Minimum Maximum Median Average Standard Deviation
Mg/Fe (kg/kg) 0.31 5.90 2.16 2.81 1.32
S/AS (kg/kg) 0.40 4.0 0.67 0.85 0.6
T ( o C) 270 550 475 457 63
t (min) 10 120 22 32 27
Clearly, earlier tests did not focus on identifying reaction trends as experiments were performed at
varying reaction conditions chosen almost at random - targeting to cover a broad range of each
parameter. However, after testing a range of values of each of the factors, it now becomes necessary
to identify which parameters have the most significant effects on Mg extraction and Mg(OH)2
production. More so, parameter cross-correlation effects would be determined as well. A better
understanding of these effects and their interactions is essential for optimization of Mg(OH)2
production from Mg-silicate minerals for the purposes of fixing CO2 as carbonate(s).
Due to the range of values parameters considered (Table 1) the choice of a reasonable reference
point was important in order to design a two-level fractional factorial design. We used a reference
level “0” condition to classify each factor according to levels: high (+1) or low (-1) (in Table 2).
The first “0” level was chosen to reflect the median value of the parameters while a second “0”
level was chosen at values of the parameters at near optimal conditions. The response parameter
(dependent variable) in this analysis is % Mg extraction (% Mg ext). The % Mg extraction is the
amount of Mg (grams) extracted from the Mg-silicate rock divided by the total amount of Mg
(grams) present in the Mg-silicate, expressed as percentage. The motivation for focusing on the
parametric analysis of Mg extraction is the fact that the amount of Mg(OH)2 produced from the
process strongly correlates with values for Mg extraction[16].
Table 2. Reference level “0” conditions for evaluation of factors and their interactions.
Parameters
Levels
Mg/Fe (kg/kg)
A
high
(+1)
low
(-1)
S/AS (kg/kg)
B
high
(+1)
236
low
(-1)
T ( o C)
C
high
(+1)
low
(-1)
t (min)
D
high
(+1)
Condition Iᵝ > 2.16 ≤ 2.16 ≤ 1 > 1 ≥ 480 < 480 > 25 ≤ 25
Condition IIᵝ > 2.16 ≤ 2.16 ≤ 0.67 > 0.67 ≥ 440 < 440 > 60 ≤ 60
ᵝ Condition I reflects the median of the data. ᵝ Condition II is chosen at near optimal
experimental conditions. “+1” and “-1” are the high and low levels respectively.
3.1 Fractional factorial design
Fractional factorial design (2 n-1 , where n represents the number of parameters) enables the analysis
of only a subset of treatment combinations, while still obtaining a meaningful result that is
statistically representative of the entire data set. In this analysis n=4 (A, B, C and D in Table 3) and
the objective function is Y which represents % Mg extraction. The fractional factorial design is
constructed by partitioning the runs into two blocks; one block, which is a contrast of the other, is
completely sacrificed [23]. Instead of using a full 2 n design with 16 design points, the 2 n-1 design
low
(-1)