Abstract

Mathematical modeling is a method of simulating real-life situations with mathematical equations to forecast their future behaviour. The modeling of the microbiological parameters was done using SPSS 23 for descriptive statistics while E-view 10 software was used for pooled regression model. Crude oil-contaminated soil from Bodo in Ogoniland was sampled for treatment using bioremediation technology and seven treatment options designated as A to G were setup in triplicates in cells. Five were biostimulated with NH₄NO₃ and KH₂PO₄ while unamended and heat-treated served as control. The bioremediation lasted for 56 days with 50 % contaminated media amended with 1 % treatment material. The setup was sampled repeatedly at intervals for analysis within the study period. ES had highest THB count on day 28 while FS had the lowest counts on day 56. For hydrocarbon utilizing bacteria (HUB), CS had the highest count on day 42 while FS had the lowest HUB counts on day 56. For all the treatments options on day 0, the total petroleum hydrocarbon (TPH) ranged from 846.25 to 4406 mg/kg while polycyclic aromatic hydrocarbon (PAH) ranged from 2.02 to 202.70 mg/kg. In all the treatments by day 56, the TPH was < 405 mg/kg while PAH was < 6.5 mg/kg. By day 56, the percentage loss of TPH of treatment options as measured with GC-FID were AS (63 %), BS (72 %), CS (76 %), DS (95 %), ES (98 %), FS (59 %) and heat treated GS (47 % ). ES had the highest TPH (4403.91 mg/kg) on day 0 while CS recorded the lowest TPH (93.01 mg/kg) on day 56. By day 56, the percentage loss of PAH of treatments as measured with GC-FID were AS (98 %), BS (97 %), CS (93 %), DS (94 %), ES (96 %), FS (31 %) and heat treated GS (31 %). However, ES had the highest percentage loss (98 %) of TPH followed by DS (95 %) and lastly GS (47 %). FS had the highest PAH (201.67 mg/kg) on day 0 while AS had the lowest PAH (0.04 mg/kg) on day 56. The AS had the highest percentage loss of PAH (98 %) followed by BS (97 %) and lastly FS and GS (31 %). A total of 121 hydrocarbon utilizing bacteria were obtained which include Micrococcus sp 35 (28.93 %), Acinetobacter sp (9.92 %), Pseudomonas sp (28.93 %), Bacillus sp (14.05%), Alcaligenes sp (4.96 %), Proteus sp (1.65 %) and unidentified isolates (11.57 %). Regression model of bacteria showed the effect of time, nitrogen and phosphorous on microbiological and effect of HUB and THB on physicochemical parameters. Time and nitrogen had positive effect on HUB and THB while phosphorous had negative effect. A unit increase in time and nitrogen increased HUB by 0.0545 and 19.8826 while an increase in total phosphorus decreased HUB by 51.83. Time, HUB and THB affected TPH negatively. A unit increase in time, HUB and THB decreased TPH by 30.84, 74.75 and 145.1 unit respectively. These changes and effects by these mathematical models were statistically significant at P–value <0.05 and t-values. F-values implied overall models were statistically significant. These models have established that adjusting of limiting nutrients (nitrogen, phosphorous) is key to effective and efficient bioremediation of crude oil-contaminated media.

1. Introduction

Mathematical modeling has become an important tool to assist in analyzing and understanding complex environmental systems. Multitude of processes such as physical, chemical or biological nature, interact with each other. Mathematical modeling provides a rational framework to formulate and integrate knowledge derived from (i) theoretical work (ii) fundamental e.g. laboratory investigations and (iii) site-specific experimental work ¹. Furthermore, mathematical model is a method of simulating real-life situations with mathematical equations to forecast their future behaviour. Modeling is done to establish whether microbial activity is responsible for direct breakdown of organic contaminants or whether it is employed indirectly to alter geochemical conditions ¹.

Contamination of soils, ground water, sediments, surface water and air with hazardous and toxic chemicals is a problem facing industrialized and developing countries today. There are potential hazardous and chemical toxicant sites where it is estimated that a significant number of underground storage tanks ruptures, transport accidents and pipeline leaks and vandalism across countries of the world are leaking ^{2, 3, 4}. While regulatory steps have been implemented to reduce or eliminate the production and release to the environment of these chemicals, significant environmental contamination has occurred in the past and will probably continue to occur in the future. The need to remediate these sites has led to the development of new technologies (bioremediation) that emphasize the detoxification and destruction of the contaminants rather than the conventional approach of disposal ^{5, 6, 7, 8}.

Many microorganisms possess the inherent ability to transform hazardous compounds. However, the long-term persistence of many of these contaminants in the environment is a testament to the fact that these naturally occurring processes often do not occur at rates that are fast enough to protect ecosystem and human health. Often, the microorganisms are limited by the availability of the pollutant or another key substrate or are not present in sufficient numbers. In many cases, bioremediation can overcome these limitations through careful engineering of the contaminated environment, thereby enhancing the rates of key microbial processes ^{2, 3, 7, 9}. Hence, successful bioremediation involves the integration of environmental microbiology and engineering techniques with other disciplines, such as geochemistry and hydrology.

In this research, the following treatment options were selected which include, crude oil-contaminated soil alone, crude oil-contaminated soil, various percentages of nitrogen and phosphorous and heat-treated crude oil-contaminated soil sample. All these treatment options were subjected to the same environmental conditions for a 56-day period.

2. Materials and Methods

The sample for this study was crude oil-contaminated soil. The sample was sourced from Bodo in (Ogoni) Gokana Local Government Area of Rivers State. The samples were collected using appropriate sterilized sampling containers. The samples were homogenized and transported to the laboratory to be processed.

Crude oil-contaminated soil were sampled and seven treatment options designated as A, B, C, D, E, F and G were setup in triplicates in cells. Five (A-E) were biostimulated with NH₄NO₃ and KH₂PO₄ while unamended (F) and heat-treated (G) served as control. The bioremediation investigation lasted for 56 days. The various treatment options and the controls were set up in triplicates in different cells using plastic bowls. For each treatment option, 2kg (wet weight) crude oil-contaminated soil/water was amended with 40 g of treatment material according to Abu and Ogiji ¹⁰. The heat-treated sample was autoclaved at 121°C for 15 minutes at 15psi.

In each treatment, parameters such hydrocarbon-utilizing bacterial count, total heterotrophic bacterial count, total organic carbon, total nitrogen, total phosphorous and hydrocarbon level were determined. Before the application of treatment materials, there was pretreatment analysis of the test samples (crude oil-contaminated soil) using the protocols listed above. This was done to establish baseline data of the samples.

In monitoring the conditions and bioremediation process in each set up, little quantities of different treatment options and the controls were collected and analyzed for total petroleum hydrocarbon (TPH) and polycyclic aromatic hydrocarbon (PAH), total nitrogen, total phosphorous and microbial population on day zero and subsequent analysis were carried out throughout the duration (56-day) of the study ⁷.

Statistical analysis was carried out on the data generated from the bacterial counts and hydrocarbon concentrations for the different treatments using analysis of variance (ANOVA) and Duncan Multiple Comparison test, to test for the significant difference between the various treatment options at 95 % (p<0.05) confidence level.

Triplicate set up and duplicate analysis was done to check precision and accuracy while blank analysis was done to check contamination. Calibrations of instruments were carried out to check sensitivity and precision of instruments. The Outliers test was to check systematic errors which include methodic, instrument and/or personal errors.

Enumeration/identification of total heterotrophic bacteria (THB) and hydrocarbon utilizing bacteria (HUB)

Counts for THB and HUB were carried out on baseline sample on day zero, 14, 28, 42 and 56 respectively. From each treatment option and control, 1g (wet weight) of crude oil-contaminated soil was homogenized in 9 ml of 0.85% of normal saline in tenfold serial dilution. Dilutions (tenfold) of the suspensions were plated out in duplicate on nutrient agar (Titan biotech ltd) and incubated at 37°C for 24 hours for the THB counts. For HUB counts, appropriate dilutions were selected and plated out in duplicate on mineral salt medium (MSA) of ^{13, 14}. Hydrocarbons were supplied through the mechanism of vapour phase transfer to hydrocarbon utilizing bacteria by placing sterile Whatman No. 1 filter paper saturated with sterile crude oil and aseptically placed on the surface of the lid of the inverted Petri dishes. The plates were incubated at 30°C for 7 days. Individual colonies of the hydrocarbon utilizing bacteria were examined for cultural characteristics and were picked out and subcultured for biochemical tests ^{13, 14}. The following biochemical tests: catalase, oxidase, indole production, citrate utilization, triple sugar iron utilization, methyl red-voges proskauer, starch hydrolysis, sugar fermentation; glucose, sucrose, lactose were used to identify and characterize the hydrocarbon utilizing bacteria. Other phenotypic tests done were motility test and Gram staining. The reductions of TPHs and PAHs were analysed on each sampling day using gas chromatograph with flame ionizing detector (GC-FID).

3. Results

The values of the baseline bacterial (total heterotrophic (THB) and hydrocarbon utilizing bacteria (HUB), physicochemical parameters (Total nitrogen, nitrate, total phosphorous, phosphate and total organic contents), gas chromatographic analysis of total petroleum hydrocarbons (TPH) and polycyclic aromatic hydrocarbons (PAH) as well as the heavy metal contents in the crude oil-contaminated soil sample are presented in Table 2. The bacterial counts (for total heterotrophic bacterial (THB) and hydrocarbon utilizing bacterial (HUB) differs 10⁸cfu/g and 10⁶cfu/g respectively. This was indicative of the fact that the bacterial populations making up the THB and HUB were capable of utilizing petroleum hydrocarbons. The concentrations of the TPH and PAH in the crude oil-contaminated soil also showed that there is active bacterial population in the crude oil-contaminated soil that uses the hydrocarbons in the crude oil-contaminated soil as source of carbon and energy owing to their low concentration in this crude oil-contaminated soil that has high level of petroleum hydrocarbons. The baseline hydrocarbon contents in the crude oil-contaminated soil before bioremediation were 366.916 mg/kg and 215 mg/kg TPH and PAHs respectively but this was spiked with crude oil until 4800 mg/kg TPH and 235 mg/kg PAH.

During the 56-day bioremediation period under study, different trends were observed in all the biological and hydrocarbon parameters analyzed in the different amended and control crude oil-contaminated soil samples in cells in plastic bowls. The result of total heterotrophic bacterial counts for soil was presented in Figure 1 where ES had highest THB count (1.28 x 10⁸ Cfu/g) on day 28 for soil while FS had the lowest counts (3.45 x 10²Cfu/g) for soil on day 56. There was a general decrease for all treatments options and for all other treatments which were A, B, C, D, E, F and G that decreased from 10⁸cfu/g by day 28 to 10²cfu/g by day 56 when the experiment ended. The heat-treated control (hG) recorded no bacterial growth on day 0 but had few insignificant bacterial on day 42 and 56. The THB counts were not statistically significant at P < 0.05 using one way ANOVA.

Figure 2 represents the hydrocarbon utilizing bacteria (HUB) counts across all treatments including control during the 56-day bioremediation. HUB counts in all treatments increased from 10² cfu/g on day 0 to 10⁶ cfu/g on day 42 and decreased to 10⁴ cfu/g on day 56 except unamended FS that remained at 10² cfu/g ES had the highest HUB count of 2.95 x 10⁶ cfu/g on day 42 while FS the lowest count of 3.20 x 10² cfu/g on day 56. The heat-treated control hG showed no growth for THB and HUB on day 0, 14, 28, 42 but an insignificant growth on day 56.

The degradation of the hydrocarbons (TPHs and PAHs) present in the crude oil-contaminated soil samples amended with different nutrient sources (NH₄NO₃), the biotic and abiotic controls (F and hG) are shown in Figure 3 and 4. For all the treatment options on day 0, the total petroleum hydrocarbons (TPH) range from 846.25 to 4403.91 mg/kg crude oil-contaminated soil. By day 56, the TPH of all the treatment options were reduce to < 405 mg/kg. By day 56, the percentage loss of TPH of various treatment options as measured with GC-FID were AS (63 %), BS (72 % ), CS (76 %), DS (95 %), ES (98 %), FS (59 %) and heat-treated GS (47 %). Percentage loss of TPH of crude oil-contaminated soil in various treatment options showed that ES had the highest TPH (4403.91 mg/kg) on day 0 while CS recorded the lowest TPH (93.01 mg/kg) on day 56. However, ES had the highest percentage loss (98 %) of TPH of the crude oil-contaminated soil, followed by DS (95 %) and lastly GS (47 %). The percentage loss of TPH was statistically significant at 95% (P < 0.05) confidence interval using ANOVA and Duncan multiple test for significant different. The polycyclic aromatic hydrocarbons (PAH) for all the treatment options on day 0 range from 2.02 mg/kg to 201.67 mg/kg. By day 56, the PAH of all treatment options were reduce to < 6.5 mg/kg. By day 56, the percentage loss of PAH of various treatment options as measured with GC-FID were AS (98 %), BS (97 %), CS (93 %), DS (94 %), ES (96 %), FS (31 %) and heat treated GS (31 %). From Figure 4, FS had the highest PAH (201.67 mg/kg) on day 0 while AS recorded the lowest PAH (0.04 mg/kg) on day 56. However AS had the highest percentage loss of PAH (98 %) followed by BS (97 %) and lastly FS and GS (31 %).

A variety of bacteria genera were isolated from the amended and unamended crude oil-contaminated soil during the 56-day period of bioremediation. All the bacteria genera were from genera of bacteria known to have the ability to degrade petroleum hydrocarbons. A total of 121 hydrocarbon utilizing bacteria were obtained from crude oil-contaminated soil, one hundred and seven (107) of which were assigned tentative identities and belonged to the genera of Bacillus, Proteus, Pseudomonas, Alcaligenes, Micrococcus and Acinetobacter. Fourteen bacterial isolates could not be given tentative identities and were designated unidentified bacterial isolates. The frequency of occurrence of the genera of the bacteria identified in the study and percentage loss of TPH and PAH is given in Table 3 and Table 4 respectively.

The modeling of the microbiological parameters was done using Statistical Package for Social Sciences (SPSS 23) for descriptive statistics while Econometric View (E-view 10) software was used for the pooled regression model. The result of regression model revealed the effect of variables such as time (T), nitrogen (TN) and phosphorous (TP) on microbiological parameters and the effect of microbiological parameters on physicochemical variables.

Table 5 shows bacteria regression model of hydrocarbon utilizing bacteria (HUB) and total heterotrophic bacteria (THB) of microbiological parameters and time for crude oil-contaminated soil. The result revealed that when the effect of the explanatory variables, time (T), total nitrogen (TN) and total phosphorus (TP) were not considered, HUB was 0.1238 (constant). Time and total nitrogen had direct relationship with HUB. But total phosphorus had an inverse relationship with HUB. That is, a unit increase in time increased HUB by 0.0545. Also a unit increase in total nitrogen increased HUB by 19.8826 while an increase in total phosphorus decreased HUB by 51.83.

The value of total heterotrophic bacteria (THB) when the effect of time, total nitrogen and total phosphorous were not considered was 1.1957. Time and total nitrogen affected THB positively but total phosphorous affected THB negatively. A unit increase in time and total nitrogen increased THB by 0.0293 and 27.5203 respectively while an increase in total phosphorous decreased THB by 70.9670.

4. Discussion

Crude oil-contaminated soil was sampled and seven treatment options designated as A, B, C, D, E, F and G were setup in triplicates in cells. This experimental design was adopted with slight modifications from ^{7, 11, 12} for crude oil-contaminated soil. Five (A-E) were biostimulated with ammonium nitrate (NH₄NO₃) and potassium dihydrogen phosphate (KH₂PO₄) while unamended (F) and heat treated (G) were controls. The bioremediation investigation lasted for 56 days with 50 % contaminated media amended with 1 % treatment material (ratio 50:1). For each treatment options, 2 kg (wet weight) crude oil-contaminated soil was amended with 40 g of treatment material. This nutrient amendment is in agreement with work of ^{7, 10, 15}. Physicochemical parameters, total heterotrophic bacterial (THB) counts and hydrocarbon utilizing bacterial (HUB) as well as gas chromatographic analysis were carried out on the nutrient amended and control samples over a 56 day period as the experiment progressed. The FS (unamended control for natural attenuation) was composed of the crude oil-contaminated soil and indigenous bacteria only while the heat-treated GS were sterilized using autoclave to monitor the effect of environmental factors during bioremediation ^{7, 15}.

The result of total heterotrophic bacterial counts was presented in Figure 1 where ES had highest THB count (1.28 x 10⁸ Cfu/g) on day 28 for soil while FS had the lowest counts (3.45 x 10²Cfu/g) for soil on day 56. There was general increase in count for all treatments options by day 0 to day 28 and it decreased from 10⁸cfu/g by day 28 to 10²cfu/g by day 56 when the experiment ended. Control hG had no bacterial growth on day 0 but had little insignificant bacterial growth on day 42 and 56. The THB counts were not statistically significant at P < 0.05 using one way ANOVA. HUB counts in all treatments increased from 10² cfu/g on day 0 to 10⁶ cfu/g on day 42 and decreased to 10⁴ cfu/g on day 56 except unamended FS that remained at 10² cfu/g ES had the highest HUB count of 2.95 x 10⁶ cfu/g on day 42 while FS the lowest count of 3.20 x 10² cfu/g on day 56. The heat-treated control hG showed no growth for THB and HUB on day 0, 14, 28, 42 but an insignificant growth on day 56. From the result, it was clear that the indigenous bacteria in the crude oil-contaminated soil was already acclimatized to hydrocarbons since there was also loss of TPH and PAH in the control as bioremediation progressed. These findings are in agreement with report of Ibekwe and Okpokwasili ⁷ in bacterial treatment of drill cuttings. Odokuma and Dickson ¹⁶ and Chikere et al. ¹⁵ observed similar results.

The linear regression model of hydrocarbon utilizing bacteria (HUB) and total heterotrophic bacteria (THB) showing the effect of time, TN and TP on microbiological parameters for crude oil-contaminated soil as showed in Table 5. The result revealed that when the effect of the explanatory variables time (T), total nitrogen (TN) and total phosphorus (TP) were not considered, HUB was 0.1238 (constant). Time and total nitrogen had direct relationship with HUB while total phosphorus had an inverse relationship with HUB. That is, a unit increase in time increased HUB by 0.0545. Also a unit increase in total nitrogen increased HUB by 19.8826 while an increase in total phosphorus decreased HUB by 51.83. This is significant at 95% confidence levels indicated by the t-values of 13.7655, 7.4856 and -5.8124 with p-values < 0.05 except the constant which the p-value was > 0.05 ¹⁷. Finally, time, total nitrogen and total phosphorus were responsible for 65% of total changes observed in HUB; the remaining 35% were accounted by variables not included in the model. The F value of 71.19 showed that the overall model was significant (P < 0.05). These changes and effects revealed by these mathematical models were statistically significant at P –value <0.05 and t-values ^{18, 19}. Montgomery et al. ¹⁸ and Harvey and Author ¹⁹ stated that any approach to modeling the relationship between a dependent variable Y and one or more independent variables denoted X, such that the model depends linearly on the unknown parameters to be estimated from the data.

The value of total heterotrophic bacteria (THB) when the effect of time, total nitrogen and total phosphorous were not considered was 1.1957. Time and total nitrogen affected THB positively but total phosphorous affected THB negatively. A unit increase in time and total nitrogen increased THB by 0.0293 and 27.5203 respectively while an increase in total phosphorous decreased THB by 70.9670. These values were significant at p-value < 0.05 and t-values 7.4288, 10.3460 and -7.9670 respectively. The effect of time, total nitrogen and total phosphorous accounted for 64 % of the changes observed in THB and the remaining 36 % came from variables not included in the model. The F value (67.28) which was the F calculated is an indication of the expression of overall model which was significant at p – value <0.05 ^{18, 19}. Montgomery et al and Harvey and Author stated that any approach to modeling the relationship between a dependent variable Y and one or more independent variables denoted X, such that the model depends linearly on the unknown parameters to be estimated from the data.

These models have established that adjusting of limiting nutrients (N, P) is the key to effective and efficient bioremediation of crude oil-contaminated soil.

5. Conclusions

i) The concentration of the toxicants- TPH, PAH were reduced below acceptable limit which suggest that the technology was effective.

ii) Different experimental setup showed varying degrees of remediation with ES being the most efficient and effective.

iii) Environmental factors also played a role in the remediation as shown by heat-treated setup.

iv) Crude oil-contaminated soil only (FS), if left for natural attenuation will take a longer time to degrade hence the need for bioremediation.

v) The global problem of crude oil-contaminated soil is what this study has proffered solution to, through bioremediation technology and mathematical model.

vi) It is important to increase nitrogen and reduce phosphorous in bioremediation crude oil-contaminated soil.

vii) Adjusting of limiting nutrients (Nitrogen, Phosphorous) is the key to effective and efficient bioremediation of crude oil-contaminated soil.

References