## 3 Results and Discussion
### Experimental and ANOVA Results
The increase in chelation of the released Mg and Ca ions with Oxalic ions at higher temperatures (above 40 \({}^{\circ}\)C) and adsorption of the chelates on the rock surface may be behind the inhibition of further dissolution of the minerals in the acid solution at higher temperatures. Figure 3: Solubility (%) versus % Oxalic acid at 50 \({}^{\circ}\)C.  
Figure 2: Solubility (%) versus temperature (with concentration of Oxalic acid 4%). The above phenomenon may be clarified in Figure 3, which shows that increasing the concentration of Oxalic acid from 3.2% to 12% resulted in decrease in the solubility (%) of the rock samples. The situation may be attributed to increasing the formation of the chelates with increasing the concentration of oxalate ions. The chelating compounds could potentially precipitate on the particle surfaces and thus inhibit dissolution. The optimization and modeling were performed based on what was elucidated in Section 2.1.2 Experimental macro-design. The plots in regard are illustrated in Figures 4 and 5. Ten matrix acidizing experiments were run based on the central composite experimental design depicted in Table 1. The solubility of the samples and the % increase in the density of the acid after each experiment were determined. The numerical values of solubility % and % increase in density of the combined acid after the acidizing process were analyzed by ANOVA (Analysis of Variance) by the software (Portable statgraphics centrion, 15.2.11.0.exe). Figures 4 and 5, respectively. All the plots in Figures 4 and 5, the polynomial equations, the optimum solubility % and the % increase in the combined acid density are the output of analysis by the software. The Pareto charts (Figure 4a,b) display the absolute value (magnitude and the importance of the standardized effects of the operating variables represented by bars). If a bar crosses the reference line, it reflects that the effect of the factor is statistically significant at the 0.05 level. The Pareto chart (Figure 4a) shows that the Oxalic acid concentration has a significant effect on solubility (%), while temperature is statistically of less significance. The negative sign of the effect reflects that the solubility (%) decreases with increase in Oxalic acid concentration, while the positive sign of the effect of temperature revealed that solubility (%) increases with temperature increase. The situation is supported by the plots of the standardized effects (Figure 4b). On the other hand, Figure 4c shows that there is an interaction between the two factors reflected by the non-parallel and the crossing of the factor effects. The interaction is obvious at a high concentration of Oxalic acid and high temperatures. Figure 4d shows the three-dimensional response surface plots that illustrate the effect of Oxalic acid concentration and temperature, and their mutual interaction. Similar trends are shown in Figure 5 for the effects of the Oxalic acid concentration and temperature on density of the combined acids after the acidizing process. However, the temperature impact was more effective on the acid density increase compared to its effect on solubility (%). The increase in acid density is due to dissolution of the carbonate in the acid. The mathematical models estimated from ANOVA for solubility (%) and (%) increase in density of the combined acids after acidizing were estimated with high regression coefficients \(\text{R}^{2}\,78.52\%\) and \(90.06\), respectively. Response surface methodology using ANOVA can be useful for better data evaluation and model development [33]. The high values of regression coefficients confirmed the accuracy of the models and their high capability to explain the experimental results.