Simulative Analysis of Emitted Carbon during Gas Flaring Based on Quantified Magnitudes of Produced and Flared Gases

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3.1. Model Formulation

Computational analysis (using C-NIKBRAN: ^[14]) of results in Table 1 indicates that

(1)

Substituting the values of K, N and S into equation (1) reduces it to;

(2)

(3)

Where

K, N and S_,are equalizing constants

(ξ) = Carbon emitted (Tonnes)

(₰) = Total gas produced (Mscf/d)

(ϑ) = Total flared gas (Mscf/d)

3.1.1. Boundary and Initial Conditions

The ranges of carbon emitted, total gas produced and flared are 164.61-990.3 tonnes, 1062-9009.35 and 1062-6389.02 (Mscf/d) respectively. The flow rate of the gas was assumed constant.

3.1.2. Model Validation

Table 2. Variation of ξ - 30.7738 with 0.0513 ₰ + 0.0776 ϑ

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The validity of the derived model was rooted in equation (2) where both sides of the equation are correspondingly approximately almost equal. Furthermore, equation (2) agrees with Table 2 following the values of ξ - 30.7738 and 0.0513 ₰ + 0.0776 ϑ evaluated from Table 1.

Furthermore, the derived model was validated by comparing the model-predicted emitted carbon and that obtained from the experiment. This was done using the 4^th Degree Model Validity Test Techniques (4^th DMVTT); statistical graphical, computational and deviational analysis.

Figure 1. Variation of emitted carbon with total gas produced as obtained from experiment [1]

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Figure 2. Variation of emitted carbon with total gas produced as obtained from derived model

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Figure 3. Variation of emitted carbon with total gas flared as obtained from experiment [1]

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Figure 4. Variation of emitted carbon with total gas flared as obtained from derived model

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3.2. Statistical Analysis
3.2.1. Standard Error (STEYX)

The standard errors incurred in predicting emitted carbon for each value of the TGP & TGF considered as obtained from experiment and derived model were 14.2963 and 7.4141 & 1.3657 and 7.4084 % respectively. The standard error was evaluated using Microsoft Excel version 2003.

3.2.2. Correlation (CORREL)

The correlation coefficient between emitted carbon and TGP & TGF were evaluated (using Microsoft Excel Version 2003) from results of the experiment and derived model. These evaluations were based on the coefficients of determination R² shown in Figure 1 - Figure 4.

(4)

The evaluated correlations are shown in Table 3 and Table 4. These evaluated results indicate that the derived model predictions are significantly reliable and hence valid considering its proximate agreement with results from actual experiment.

Table 3. Comparison of the correlations evaluated from derived model predicted and experimental results based on TGP

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Comparative analysis of the correlations between emitted carbon and TGP & TGF as obtained from experiment; derived model and regression model indicated that they were all > 0.99.

Table 4. Comparison of the correlations evaluated from derived model predicted and experimental results based on TGF

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3.3. Graphical Analysis

Comparative graphical analysis of Figure 5 and Figure 6 show very close alignment of the curves from the experimental (ExD) and model-predicted (MoD) emitted carbon.

Figure 5. Comparison of quantities of emitted carbon (relative to TGP) as obtained from experiment and derived model

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Figure 6. Comparison of quantities of emitted carbon (relative to TGF) as obtained from experiment and derived model

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It is strongly believed that the degree of alignment of these curves is indicative of the proximate agreement between both experimental and model-predicted values of the emitted carbon.

3.3.1. Comparison of Derived Model with Standard Model

The validity of the derived model was further verified through application of the Least Square Method (LSM) in predicting the trend of the experimental results. Comparative analysis of Figure 7 and Figure 8 shows very close alignment of curves and areas covered by emitted carbon, which precisely translated into significantly similar trend of data point’s distribution for experimental (ExD), derived model (MoD) and regression model-predicted (ReG) results of emitted carbon.

Also, the calculated correlations (from Figure 7 and Figure 8) between emitted carbon and TGP & TGF for results obtained from regression model gave 0.9992 & 1.0000 respectively. These values are in proximate agreement with both experimental and derived model-predicted results. The standard errors incurred in predicting emitted carbon for each value of the TGP & TGF considered as obtained from regression model were 14.8230 and 0.0039% respectively.

Figure 7. 3-D Comparison of emitted carbon (relative to TGP) as obtained from ExD, MoD and ReG

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Figure 8. 3-D Comparison of emitted carbon (relative to TGF) as obtained from ExD, MoD and ReG

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3.4. Computational Analysis

Computational analysis of the experimental and model-predicted emitted carbon was carried out to ascertain the degree of validity of the derived model. This was done by comparing the emitted carbon per unit TGF obtained by calculation from experimental result and model-prediction.

3.4.1. Emitted Carbon per unit TGF

The emitted quantity of carbon per unit TGF was calculated from the expression;

(5)

Equation (5) is detailed as

(6)

Where Δξ = Change in emitted carbon at two values of TGF ϑ₂, ϑ₁.

Considering the points (1062, 164.61) & (6389.02, 990.3), (1062, 167.67) & (6389.02, 988.74) and (1062,163.88) & (6389.02, 990.08) as shown in Figure 8, then designating them as (ζ₁, ϑ₁) & (ζ₂, ϑ₂) for experimental, derived model and regression model predicted results respectively, and also substituting them into equation (6), gives the slopes: 0.155, 0.154 and 0.155 Tonnes/ Mscfd^-1 as their respective emitted carbon per unit TGF.

3.5. Deviational Analysis

Critical analysis of the emitted carbon obtained from experiment and derived model show low deviations on the part of the model-predicted values relative to values obtained from the experiment. This was attributed to the fact that the flow properties of the flared gases and the physico-chemical interactions between the flared gases and the emitted carbon which played vital roles during the flaring process were not considered during the model formulation. This necessitated the introduction of correction factor, to bring the model-predicted emitted carbon to those of the corresponding experimental values.

The deviation Dv, of model-predicted emitted carbon from the corresponding experimental result is given by

(7)

Where ϑ_ExD and ϑ_MoD are TGF obtained from experiment and derived model respectively.

Figure 9. Variation of model-predicted quantity of emitted carbon (relative to TGP) with associated deviation from experiment

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Deviational analysis of Figure 9 and Figure 10 indicate that the precise maximum deviation of model-predicted emitted carbon from the experimental results is 2.71%. This invariably translated into over 97% operational confidence for the derived model as well as over 0.97 reliability response coefficients of emitted carbon to TGP and TGF.

Consideration of equation (7) and critical analysis of Figure 9 and Figure 10 show that the least and highest magnitudes of deviation of the model-predicted emitted carbon (from the corresponding experimental values) are – 0.16 and - 2.71%. Figure 9 and Figure 10 indicate that these deviations correspond to emitted carbon: 988.74 and 459.18 Tonnes, TGP: 9009.3 and 3745 Mscf/d, as well as TGF: 6389.02 and 3045 Mscf/d respectively.

Correction factor, Cf to the model-predicted results is given by

(8)

Critical analysis of Figure 9, Figure 10 and Table 5 indicates that the evaluated correction factors are negative of the deviation as shown in equations (7) and (8).

Figure 10. Variation of model-predicted quantity of emitted carbon (relative to TGF) with associated deviation from experiment

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Table 5. Variation of correction factor (to model-predicted emitted carbon) with TGP and TGF

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