Unlike siliciclastic rocks, carbonate rocks are much more susceptible to dissolution. Dissolution of carbonate rocks is significant in many aspects of geosciences, including the quality of reservoirs, carbon dioxide sequestration, reefs and platforms stability. Many factors including mineralogy, temperature and time influence the rate of carbonate dissolution. Response surface method (RSM) is a useful statistical technique which has been applied in research in complex variable [1,2].

The method is suitable for application when the output is influenced by several input factors [3]. The area is one of the most important gas provinces in the area [4]. The formation of these carbonate buildups started in the Miocene [5] and is following structural highs. Epting [4] described the architecture of the carbonate platforms in Central Luconia (Figure 1) as to be controlled by four major processes, namely: (i) the rate of skeletal carbonate production, (ii) subsidence, (iii) relative sealevel fluctuation and (iv) the supply of clastic material from the Borneo delta [6]. The sedimentation of these carbonates is suggested by [7] to be caused by turbidity currents sourcing from different platforms.

Figure 1: Location map of Central Luconia Province.

Most of the studies in the area were directed towards the genesis of these carbonate buildups, their genesis, architecture, and potentiality. Studies addressing the disintegration of these buildups mainly scoped to the physical weathering due to turbidity currents. There is a remarkable lackness in the studies regarding dissolution phenomenon in that area, and the response of different microfacies. Therefore, the aim of this paper is to predict short term response of three carbonate microfacies in those buildups as bases to understand long term impact of dissolution. The proposed method here, the response surface method is used to examine the relationship between one or more response variables and a set of quantitative experimental variables or factors [8].

Samples of limestone from different locations were selected for this study. The carbonate rocks are taken from the Central Luconia area offshore Sarawak. A number of three facies identified based on their composition, texture and structure; these included: Moldic Wackestone, Mudstone, and, [9] Crystalline-Sparistone. Initially, dissolution was run for the different samples under three different temperatures, namely: 25, 50, and 75 C to evaluate the response of dissolution of different microfacies under different temperatures. The solvent used was diluted Hydrochloride acid (0.1), with pH level maintained constant. Dissolution process was carried out for a time period of 100 minutes. Dissolution rates for different samples were measured in terms of the release of calcium and magnesium iron (Ca⁺² and Mg⁺²), and is expressed in part per million (ppm). Concentrations were measured continuously at an interval of 10 minutes using inductive couple plasma (ICP) device.

In order to study the effect of time and temperature, data were transferred into Sigma Six, Minitab package for analysis. A response surface method (RSM) was selected under design of experiment (DOE) option. The method was best described, is an empirical modeling approach for determining the relationship between various operating variables and response variables. It provides a sequential experimentation strategy for building and optimizing an empirical model. Thus, RSM is a collection of mathematical and statistical procedures that are useful for the modeling and analysis of problems in which the response is affected by operating variables.

After parameters identified, model type was selected based on the items to be fit. The simplest one is that includes the effect of individual parameter, A B C D. Square model studies the combined effect for the factor A*B, A*C, B*C, etc. (Figure 2).

Figure 2: Screen shot showing model type selected based on the factors/parameters.

By setting a quadratic model, different relationships can be obtained, including single parameter (A) effect, two factors effect (A*B), and squared effect of the same factor (A*A). Different setting parameters of the response surface are shown in Table 1. The setting of the response surface method included with the selecting of tow input factors. According to that selection, the number of runs will be identified.

Table 1: Design of the experiment.

The design of experiment for two factors, the setting design of the experiments to be carried out obtained is shown in Table 1. Parameters of the model were set and nominated for calcium and magnesium individually, temperature as A, and time as (B) all through the experiment. Other settings such as the number of runs, display units were set to the default (Table 2).

Table 2: Setting model parameters for calcium.

Data layout

After data were imported to the software, response surface method module was selected. After the design was set, a model for the dissolution was selected from the “Fittings” column. The fittings gave the modeled value of dissolution while the Residuals (Res) represented the difference between the actual values of dissolution and predicted one (Figure 3).

Figure 3: Screen shot of the actual values, predicted ones, and residuals.

Qualitative description of dissolution

From the 3D surface plot, a qualitative description can be obtained that can show the trend of dissolution with time and temperature. Dissolution data obtained experimentally are shown for different samples. Patterns of dissolution for Mg⁺², the curves show less fluctuation compared to that of Ca⁺². In general, dissolution of Ca⁺² is much more compared to that of Mg⁺² which shows low dissolution, where it ranges from 10 to 340 ppm and from 2-30 ppm respectively (Figure 4).

Figure 4: Impact of time-temperature (C) on Ca and Mg release, sample 1.

Calcium release model

Data on Estimated Regression Coefficients can be helpful in the analysis of calcium release. Statistical data were shown in Table 3

Table 3: Statistical data of calcium release model.

From which, dissolution model can be constructed:

Analysis of variance: The p value (to the right side of the results shows that individual factors (i.e. Time, and temperature), and the effect of temperature* temperature are significant as they reflect values lower than 0.05 (the significance limit). The effect of time*time and time*temperature are less significant as they show values of 0.8 and 0.09 respectively. This also indicates that Time*Temp effect is more significant as compared to the effect Time*Time.

Magnesium model

Statistical data and model for magnesium is shown in Table 4. For Mg, the model fit is stronger as compared to calcium. The variance analysis for the model shows that the impact of all factors (Temp. Temp*Temp, and Temp*Time) is quite significant, with p value equivalent to zero; except for Time and Time*Time (p value =0.25 and 0.26).

Table 4: Statistical data and model for magnesium (mg).

Effect analysis

Normal Probability Plot utilizes residuals remaining from prediction and compares it to a hypothetical straight line of normal data. Normal probability plot provides a measure of outliers also which can be used in determining the points of maximum effect. An example taken here is sample 2 (Figure 4.1) to show the fluctuation of residuals around the hypothetical straight line. The data plotted in the probability plot shows some curvature instead of straight line; the thing that indicates alternative sources other than normal distribution. Effect analysis graphs were obtained directly from ANNOVA test. A comparative plot the effect of both time and temperature on Mg release (Figure 4.2).

Figure 4.1: Impact of time-temperature on Ca and Mg release, sample 2.

Figure 4.2: Impact of time-temperature on Ca and Mg release, sample 3.

Dissolution optimization

The response optimization helps identify the combination of input parameters setting that results in a maximum single or a group of outputs (responses). In order to achieve that, Response Optimizer module was applied for both calcium and magnesium released. Individual desirability (d) was obtained for each individual response. Minimum and maximum values are set for the output before the response was maximized. The‘d’ value for both calcium and magnesium was found to be 0.73 and 0.64 respectively. The Results obtained (Figures 5 and 6).

Figure 5: Effect analysis of both Time and Temp for Mg, Sample No 2.

Figure 6: Optimization plot showing the individual desirability of Ca and Mg.

Response surface method was applied to investigate the combined effect of temperature and time factors on the dissolution of calcium and magnesium that principally compose carbonate rocks in the area. Dissolution of carbonate rocks indicated by the release of calcium and magnesium ions was evaluated for a number of six samples of carbonate rocks representing three microfacies. The main objective of this paper was to evaluate the individual and collective effect of time and temperature on the dissolution trends for any facies. Dissolution was measured progressive periods of time under different temperature ranges, and time represented the factors, while amounts of calcium and magnesium released (in ppm) represented the responses. Dissolution was carried out experimentally under a constant pH of 0.1 m Hcl, continuous stirring. The resulting data in terms of concentration (ppm) of the Ca and Mg was used as input data for the model. Response surface method provided models for the dissolution of carbonates, optimization of dissolution, and individual-and-combined effect of each factor (Time and temp).