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DEVELOPMENT OF PREDICTIVE MODELS FOR DIFFUSION RATE OF SPILLED CRUDE OIL IN NIGER DELTA SOILS
ABSTRACT
Simplified predictive numerical models have been developed for diffusion rate of crude oil spilled into Niger Delta soils. The proposed model equations were developed using Fourier transformation, and Green’s function. The induction principles as well as the indicial matrix method of dimensional analysis were adopted in determining the functional parameters that could possibly influence their diffusion rates. These mathematical models correctly predict one – dimensional longitudinal diffusion rate, one-dimensional vertical diffusion rate coefficient, two-dimensional diffusion rate coefficient as well as the concentration distribution in the two spatial directions. The rates of diffusion as functions of volume of crude oil spilled and soil physical properties were correlated. Simple regression techniques were used for the validation of the models with experimental results. The results of the sorption experiment show that the linear isotherm describe the sorption mechanism of the six petroleum samples into the three soil types better with the following distribution coefficient (Kd) values: AF (sand) 0.00861; AF (top) 0.0707; AF (loam) 0.089; UT (sand)
0.1174; UT (top) 0.1324; UT (loam) 0.1352; EG (sand) 0.0697; EG (top) 0.0752; EG (loam)
0.0784; EW (sand) 0.0713; EW (top) 0.0740; EW (loam) 0.909; OBN (sand) 0.1030; OBN
(top) 0.1037; OBN (loam) 0.1051; ER (sand) 0.0784; ER (top) 0.0941; ER (loam) 0.1005. The proposed model equations, which are semi-empirical and generalized have, good stability behaviour and are easy to use with the aid of developed simplified and ready to use computational flow schemes.
TABLE OF CONTENTS
Page
| Title Page:…………………………………………………………………………… | i |
| Title Page:…………………………………………………………………………… | ii |
| Declaration: ………………………………………………………………………… | iii |
| Certification:………………………………………………………………………… | iv |
| Dedication:…………………………………………………………………………. .. | v |
| Acknowledgement: …………………………………………………………………. | vi |
| Abstract:…………………………………………………………………………….. | vi |
| Contents:…………………………………………………………………………….. | vii |
| List of tables:……………………………………………………………………….. | xii |
List of figures:……………………………………………………………………….. xiv
Nomenclature:………………………………………………………………………… xx
CHAPTER ONE: INTRODUCTION:………………………………………… 1
1.0 Introduction:………………………………………………………………… 1
1.1 Statement of the problem:…………………………………………………… 2
1.2 Objectives of the study:……………………………………..……..……….. 3 1.3 Scope of the work:…………………………………………………………… 3
CHAPTER TWO: LITERATURE REVIEW:…………………………………. 5
2.1 Theoretical background: …………………………………………………….. 5
2.2 Formation and structure of soils:…………………………………………….. 8
2.2.1 Weathering processes of soil:…………………………………………… 8
2.3 Flow of water in soils:………………………………………………………. 9
2.3.1 Principles of flow of fluid in saturated soils:…………………………. 10
2.3.2 Principles of flow of fluid in unsaturated soils:…………………………. 12
2.3.3 Equation governing flow of fluid in soils:………………………………. 12
2.4 Mechanism of mass transfer of contaminants in soils: ………………………. 16
2.4.1 Sorption mechanism: ……………………………………………………. 17
2.5 Migration of spilled petroleum in soils:………………………………………. 19
2.5.1 Principles of transport of spilled petroleum in soils medium:………… 20
2.5.2 Phase distribution of spilled petroleum in soils medium:…………….. 21
2.6 Factors affecting transport of spilled petroleum in soils medium:……………. 25
2.6.1 Properties of crude petroleum:………………………………………. 26
2.6.1.1 Petroleum density:…………………………………………… 27
2.6.1.2 Viscosity of petroleum:…………………………………………. 28
2.6.1.3 Interfacial tension:………………………………………….. 29
2.6.1.4 Vapour pressure:……………………………………………… 29
2.6.1.5 Soil distribution coefficient:…………………………………. 30
2.6.2 Properties of soil media:……………………………………………… 32
2.6.2.1 Soil texture:…………………………………………………… 32
2.6.2.2 Soil structure:………………………………………. ………… 35
2.6.2.3 Soil porosity:………………………………………………….. 36
2.6.2.4 Soil heterogeneity: …………………………………………… 38
2.6.2.5 Soil saturation:………………………………………………… 39
2.6.2.6 Soil wettability:………………………………………………. 41
2.6.2.7 Capillary pressure:……………………………………………. 43
2.6.2.8 Soil permeability:…………………………………………….. 44
2.6.2.9 Hydraulic conductivity: …………………………………………. 47
2.6.3 Estimation of volume of spill in soil medium:……….………………. 48
2.7 Soil transport differential equation:………………………………………….. 52 2.8 Solutions of soil transport differential equation:……………………………. 58
CHAPTER THREE: RESEARCH METHODOLOGY :………………………….. 60
3.1 Model formulations, Material and methods:…………………………………….. 60
3.1.1 Dimensional analysis of functional parameters:………………………. 60
3.1.1.1 Adoption of induction principle:……………………………… 61
3.1.1.2 Indicial matrix approach:……………………………………… 62
3.1.1.3 Models for the prediction of one dimensional longitudinal
diffusion coefficient:………………………………………….. 66
3.1.2 One-Dimensional longitudinal diffusion rate model:…………………. 69
3.1.3 Computational flow chart for outline solution of one-dimensional
longitudinal diffusion rate model:………………………….. ………… 75
3.1.4 Models for the prediction of one-dimensional vertical diffusion coefficient: 77
3.1.5 One-Dimensional vertical diffusive rate model:……………………… 77
3.1.6 Computational flow chart for the outline solution of one-dimensional
vertical diffusion rate model:……………………………………..……. 82
3.1.7 Model for the prediction of two-Dimensional diffusion coefficient:…… 84
3.1.8 Two-Dimensional diffusion rate model:…………………………………… 85
3.1.9 Computational flow chart for the out line solution of two-dimension
diffusion rate model:………………………………..………………….. 93
3.2 Soil survey and sample collection:…………………………………………….. 96
3.2.1 Identification of soil mapping unit:……………………………………. 96
3.2.2 General samples:……………………………………………………….. 96
3.2.3 Grid samples:…………………………………………………………… 97
3.2.4 Depth of sampling for general samples:……………………………….. 97
3.2.5 Laboratory determinations:…………………………………………….. 97
3.2.5.1 Pretreatment of soil samples:…………………………………. 97
3.2.5.2 Particle size distribution:……………………………….……… 98
3.2.5.3 Soil reaction:…………………………………………………… 98
3.2.5.4 Organic matter:………………………………………………… 98
3.2.5.5 Total nitrogen:…………………………………………………. 98
3.2.5.6 Exchangeable cations:………………………………………….. 99
3.2.5.7 Cations exchange capacity:……………………………………. 99
3.2.5.8 Exchangeable acidity:…………………………………………… 99
3.2.5.9 Available phosphorus and total phosphate content:…………….. 99
3.2.5.10 Bulk density:……………………………………………. 100
3.2.5.11 Extractable iron and aluminum:………….…………….. 100
3.2.5.12 Clay mineralogy:………………………………………… 100
3.3 Soil colour:……………………………………………………………………… 103
3.4 Experiment 1: Soil samples analysis:…………………………………………… 104
3.4.1 Materials:……………………………………………………………… 104
3.4.2 Experimental procedures:……………………………………………… 105
3.4.3 Classification of soil samples using the soil triangle:……… ………….. 105
3.5 Experiment 2: Crude oil analysis:………………………………………………… 106
3.5.1 Material:………………………………………………………………… 106
3.5.2 Experimental procedures:………………………………………………. 107
3.5.2.1 Determination of crude petroleum density:……………………… 107
3.5.2.2 Determination of crude petroleum viscosity:…………………… 107
3.5.2.3 Determination of water content of crude petroleum:…………… 108
3.5.2.4 Determination of interfacial tension of crude petroleum and
petroleum products:……………………………………………. 109
3.6 Experiment 3: soil sorption experiment:………………………………………. 110
3.6.1 Material:………………………………………………………………… 110
3.6.2 Experimental procedure:…………………………………… …………. 110
3.7 Experiment 4: Diffusion rate experiment:……………………………………… 111
3.7.1 Materials:………………………………………………………………. 111
3.7.2 Experiment procedure:…………………………………………………. 113
CHAPTER FOUR: RESULTS AND DISCUSSION:……………………………… 114
4.1 Result: ………………………………………………………………………….. 114
4.1.1 Soil and crude petroleum analysis:…………………………………….. 114
4.1.2 Sorption of spilled petroleum into soils media:………………………… 115
4.2 Discussion: …………………………………………………………………….. 135
4.3 Experimental / simulated diffusion rate of spilled petroleum in soils media:…… 140
4.3.1 Effects of crude petroleum physical properties on diffusion rate:………. 140
4.3.2 Effects of volume of spilled crude petroleum on diffusion rate:………… 145
4.3.3 Effects of diffusion coefficient on diffusion rate and extent of diffusion:… 150
4.3.4 Effects of soil physical properties on diffusion rate:……………………… 152
4.4 Validation of developed models:…………………………………………………. 157
4.4.1 Concentration distribution of six crude petroleum samples in top soil:….. 157
4.4.2 Concentration distribution of AF crude sample in Top, Loamy and
Sandy soils: ……………………………………………………………… 159
4.5 Correlation of alternate diffusion rate predictive models:………………………. 162
4.5.1 Diffusion of Afiesere petroleum sample in different soils media:………. 162
4.5.1.1 Relationship between M and volume of spilled petroleum and
soil physical properties:…………………………………………. 162
4.5.1.2 Relationship between Cn and soil physical properties:……………. 164
4.5.2 Diffusion of different petroleum samples in top soil:…………………… 166
4.5.2.1 Relationship between M and spilled petroleum physical properties: 167
CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS:…………….. 170
5.1 Conclusion:…………………………………………………………………………. 170
5.2 Contribution to knowledge: …………………………………………………….. 172
5.3 Recommendations and further works:…………………………………………… 174 References:……………………………………………………………………… 175
Appendix I: Description form for soil profile pit: ………………………….…… 186 Appendix II: Guidelines for rating soil characteristics:…………………………. 188 Appendix III A: Pictures illustrating soil profile pit at various locations:………… 191
Appendix III B: Pictures illustrating oil spillage sites visited at various locations: 193
Appendix IV: Computer simulations results:……………………………………. 194
CHAPTER ONE
INTRODUCTION
Nigeria is richly blessed with crude petroleum. It currently contributes more than 90% to the nation’s foreign exchange earnings (Akpofure et al., 2000). Exploration and exploitation of this natural resource brings problems of environmental pollution. All aspects of petroleum exploitation (starting from exploration to final processing) degrade the environment in one way or another. (Oghenejoboh, 2005). One of the major environmental problems arising from petroleum production activities is spillage. Between 1976 and 1980, 800 incidences of oil spills were recorded in the Niger Delta Area with more than 56.1 million barrels of oil spilled into soils and aquatic environment (Ayotamuno and Kogbara, 2007). Petroleum spillage is usually caused by leakages from underground pipes as a result of corrosion (aging), blowout from oil wells (as a result of uncontrolled high pressure) and deliberate human activities (sabotage in most cases). Petroleum when spilled on land degrades the environment and can elicit gross biological damage, physiological (pathological) effects on the biota (both plants and animals) and broad range of ecological changes (Akpofure et al., 2000). It also presents a significant source of groundwater contamination. It is therefore of utmost importance to quickly carry out remediation action to avoid long term degradation of the environment once there is petroleum spillage.
There are several challenges in modelling rate and transport of spilled petroleum in soils medium. Hydraulic conductivity, sorption and heterogeneity of soils are some of the major parameters needed to effectively analyse transport of petroleum in soils, and accurate measurement of these parameters are difficult. Another factor that makes predicting transport spilled petroleum in soils difficult is its different chemical constituents, some of which are highly volatile. Once petroleum is spilled into soil its constituents become part of biological cycles that affect all forms of life. Constituents of petroleum hydrocarbon in soil move in one or more of the following directions (Glasson et al., 1999):
| (a). | They may vaporise into the atmosphere without chemical change. |
| (b). | They may be absorbed by the soil |
| (c). | They may move downward through the soil in liquid or solution form and be lost from the soil by leaching. |
| (d). | They may be broken down by soil micro-organisms. |
| (e). | They may be washed into streams and rivers in surface run-off |
| (f). | They may be taken-up by plants or animals and introduced into the food chain. |
All the above phenomena are governed by the physical properties of the crude petroleum involved and the properties of the geologic medium (soil). The exact mechanism by which spilled petroleum is bonded to soil matrix is not clearly understood. This is because the types of interaction between soil organic matter and soil matrix include physical adsorption or interaction through van der waals forces, electrostatic interactions (cation and anion exchange processes), chemical adsorption and hydrogen bonding.
An adsorption isotherm describes the relation between the concentration of crude petroleum in solution and the quantity of petroleum on the surface at constant temperature. This isothermal interaction between a liquid and solid medium is known as sorption and is determined through experimentation. Sorption determines the extent to which movement of spilled petroleum in soil medium is retarded. Sorption kinetics (isotherms) describing sorption process can either be linear or non-linear (Wu and Gschwend, 1986).
1.1 Statement of the Problem
In most predictive works, sorption of non-conservative contaminants such as crude petroleum into soils medium are generally assumed to follow the linear isotherm model without experimental proof. Though correct as those assumptions may be, sorption of most contaminants do not readily follow the linear equilibrium partitioning models generally assumed. Hence the need for experimentation to determine the actual sorption mechanism that fits a particular contaminant sorbing into soil. The diffusion rate models of the contaminants also make use of diffusion coefficients by describing the diffusion process of spilled petroleum in soils medium, based on the combined physical properties of crude petroleum and the soil porous media as well as the determination of the functional parameters that may affect the diffusion mechanism.
1.2 Objectives of the Study
The development of a predictive tool for the prediction of diffusion rate of spilled petroleum in soils is the main motivation for this study. Both qualitative (experimental) and quantitative (simulation) approaches will be employed. The Niger Delta soils will be used to validate our models. With this aim in mind, the objectives of this study are identified as follows:
- To establish the effects of volume of soil on both the longitudinal and vertical diffusion of spilled crude petroleum in different soil media.
- To investigate the sorptive pattern of spilled crude oil of different physical properties
in soils.
- To establish concentration/time relationship of longitudinal and vertical diffusion of crude oil as a function of petroleum physical properties and soil physical properties.
- To develop predictive empirical models for the prediction of diffusion rate and diffusion coefficient of both longitudinal and vertical diffusion of spilled petroleum in soil media.
1.3 Scope of the Work
The thesis will focus mainly on the effects the volume of crude oil, its physical properties and soil physical properties have on the concentration distribution of crude oil once spilled into soil media as well as the determination of the best sorption mechanism for the transport of spilled petroleum in soils. Theoretical models are developed to predict spatial diffusion of spilled crude oil in soils.
DEVELOPMENT OF PREDICTIVE MODELS FOR DIFFUSION RATE OF SPILLED CRUDE OIL IN NIGER DELTA SOILS
