Crude oil is a naturally occurring flammable liquid that consists of a complex mixture of hydrocarbons of different weight and other liquid organic compounds found in geological formations underneath the earth's surface (Wikipedia, 2011). Its properties depend on the chemical composition and structure of the molecules.
The rate of oil and gas production has diminished as a result of limited enhanced recovery techniques to recover the large percentage of trapped oil (Sun et al. 2007) .In order to develop more enhanced recovery techniques, an understanding of phase behaviour of crude oil is necessary, as this is "fundamental to the design and analysis of oil and gas behaviour in the reservoirs" (Manning et. al. 1995). This can be achieved by developing a robust and accurate equation of state that is capable of predicting the thermodynamic properties of crude oil, basically, the phase behaviour of crude oil.
Unfortunately, the complexity of crude oil makes it difficult to model the phase equilibrium behaviour both in terms of the number of undefined components and the large percentage of these undefined components (Sun et al. 2007). Usually, the undeï¬ned components are determined by true boiling point distillation analysis and characterized by an average normal boiling point and speciï¬c gravity (ibid.). Such fractions are expected to have paraffin, naphthalene, and aromatic molecules; but it is very tricky to experimentally determine the chemical nature and concentrations of these molecules (ibid). As result of these, a large number of undeï¬ned components cannot be characterized. Hence, the difficulties lie in the determination of the most accurate way to assign the crude oil a controllable number of pseudo components and the parameters of these pseudo components from inadequate experimental information (ibid).
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However, several methods of grouping pseudo component have been proposed based on different assumptions. For instance, Lee et al.(1981) proposed that fractions should be group based on the slopes of available properties like density and molecular weight with respect to their boiling points. On the other hand, Li et al. (1984) set a constant number of pseudo component at every decade of Watson K factors (Watson K factor is the ratio of cube root of mean average boiling point in Radian to the specific gravity (Tuv nel Ltd. n. d)). In the same spirit, Pedersen et al.(1983) grouped the fractions together based on the assumption that each pseudo component has equal weight fraction and used weight fraction average for the description of their properties. In addition, Cotterman et al. (1985) employed continuous distribution in an index property such as boiling point, carbon number or molecular. This approach is more accurate and faster than previous techniques. More so, Kehlen et al. (1985) supported this in a formal mathematical analysis of continuous thermodynamics. In the quest of looking for appropriate way of grouping the pseudo components, Behrens and Sandler (1988) suggested a truncated exponential distribution function to model oil mixtures; they showed that it can be defined by applying Gaussian Quadrature method to the distribution function and they combined this method with Peng Robinson equation of state and applied the method to saturation curve calculations. Subsequently, to ameliorate the semi continuous thermodynamic method, Willman and Teja (1987) recommended that to distinguish the between various isomers of a compound, an effective carbon number as a single characterization parameter must be used, since in the previous thermodynamic methods, the distribution variables used cannot distinguish between different isomers of a compound; example of this distribution variable is molecular weight, so it makes it more difficult to distinguish between various isomers. Unfortunately all these propositions do not have a rigorous basis, although they can be done within shorter period which make it better than the usual trial and error methods that are time consuming. In addition to the limitation of these propositions, is their inability to take into consideration the shape, size and association interactions between the constituent molecules. Moreover, Polling et al (2000) have critically reviewed the group contribution techniques that have been employed to provide an accurate ways of predicting the properties of heavier molecules based on the information about the composition and structure of the pseudo components. However, SAFT equation of state has proven to be a versatile theoretical model for describing thermodynamic properties of a fluid because of the fundamental way in which it accounts for molecular shape, size and association interactions between the constituent molecules (Sun et al. 2007). Furthermore, this equation of state has been successfully employed to predict phase behaviour of a broad range of vital industrial fluids and their mixtures (ibid.).
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SAFT is an equation of state for associating fluids. The residual molar Helmholtz energy, Ares (the difference between total molar Helmholtz energy, Atotal and an ideal molar Helmholtz energy, Aideal at the same temperature and molar density) is represented as a sum of three terms each accounting for different intermolecular forces; segment-segments interactions, chains (formation of covalent chain bonds among the segments) and site-site association among the segments (Muller et al. 2001). This equation of state was by Chapman et al (Chapman et al. 1989; Chapman et al. 1990). This can be written mathematically as
The quantities at the right hand side of (2) are functions of Îµ (the strength of segment-segment Van der Waal's force), Î» (the range of force), and Ïƒ (segment diameter). There are many variants of SAFT theory but in this project we would be considering SAFT-VR (Statistical associating fluid theory for potentials of variable range) and a square well potential is assumed. SAFT-VR models an alkane chain as a chain of tangentially touching spherical segments, where the segment-segment interaction is hard sphere with square well potentials (using parameters such as Îµ, Î», Ïƒ). Then the segment term corresponds to a fluid of free segments (perturbation theory to second order in Îµ) and the chain term is the Helmholtz energy change on combining the segments into chains, while the association term takes care of hydrogen bonding, thus it is zero for hydrocarbons, since hydrocarbon mixture is a non associating chain fluid.
A completely different but fundamental way of predicting the properties of a system is to conduct Molecular Dynamics Simulations (DL-Poly). In this project we propose to use this technique in combination with SAFT-VR. It is much more computationally intensive but, on the other hand, gives much more detailed and reliable information. DL-Poly is a molecular simulation package developed to meet the needs of the United Kingdom's CCP5 (computer simulation of condensed phases) for a general purpose MD (molecular dynamics) code by T.R. Forester and W. Smith at Daresbury Laboratory (Todorov, I. n. d.).. It was first released in 1994 and had 11 updates between 1995 and 1999 (ibid.). In this simulation package, the user provides various forms of forces that exist between the molecules, and then the program will estimate the molecular trajectories which by averaging over time yield the system's thermodynamics properties.
TraPPE is an acronym that represent Transferable Potential for phase Equilibrium, the term transferable means a force field parameters should be transferred between different molecules for a given interaction site. It is widely used both in academia and industry. This force field is based on three levels, namely; TraPPE-UA, TraPPE-EH, TraPPE-POL. For the purpose of this project, we are going to consider TraPPE-UA. TraPPE-UA uses united-atom representation for alkyl segments and Lennard-Jones and coulombic terms (The Siepmann Group n. d.). It is a force field that gives an accurate prediction of vapour-liquid coexistence curve and the critical point for wide range of alkanes(Martin et al. 1998).
2.2 Research Hypothesis and Objectives
We intend to provide a robust and accurate equation of state for complex hydrocarbon mixtures such as crude oil through the use of SAFT theory. The DL-Poly molecular simulation package will be used to optimize the SAFT parameters. This will involve;
Improving the parameters such as Îµ, Î», and Ïƒ of SAFT theory for pure and multiple components systems.
Addition of new term to the SAFT theory basically the third order perturbation term in Aseg that is the contribution to Helmholtz energy due to segment-segment interaction between the monomers to improve the description at critical point.
Reducing the complex oil mixture to a small number of pseudo components to which SAFT may be applied.
2.3 Programme and Methodology
A simulation would be run with a DL_Poly molecular simulation for 1-component system based on the literature potentials (Martin et al. 1998) over a specified temperature range to determine the phase diagram which would be compared with experimental phase diagram. If agreement is achieved, DL-Poly for 1-component system will be used to generate a broader database of thermodynamic data.
Further simulations would be run with a DL_Poly for 2-components system based on the literature potentials (Martin et al. 1998) at a specified temperature range to determine the phase diagram which would be compared with experimental phase diagram. If an agreement is achieved, then DL-Poly 2-components system will be used to generate a broader database of thermodynamic data.
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A SAFT model for 1-component would be run using literature parameters or initial guess for Îµ, Î», and Ïƒ at a specified range of temperature to get the value of Ares in terms of temperature, molar density and number of mole; this will then be added to the of Aideal (T, Ï, N) to estimate the total molar Helmholtz energy of the system (ATotal (T, Ï, N)). Hence, the chemical potential, pressure, density and other important thermodynamics properties can be calculated. For instance, first derivative of ATotal (T, Ï, N) with respect to N and V will give chemical potential (Âµ) and pressure (P) of the system respectively. Therefore, with the specified temperature range, the corresponding values of the molar density would be estimated from (3) & (4) below and a plot of temperature against molar density could be achieved to predict the phase behaviour of the system.
Hence, we would validate the phase diagram from SAFT for 1-component system with the experimental phase diagram and/or the DL-Poly with 1-component system. If this does not fit with experimental phase diagram, the SAFT parameters will then be adjusted such that the prediction from SAFT is close to the experimental data/ data generated by DL-Poly for one component system.
Another SAFT model would be run for 2-components system using literature parameters at a specified temperature range to estimate the value of Ares(T, Ï, N); this will then be added to Aideal (T, Ï, N) to calculate the total molar Helmholtz energy of the system (ATotal (T,Ï,N)). Hence, the chemical potential, pressure, density and other important thermodynamics properties can be calculated. Therefore, with the specified temperature range, the corresponding values of the molar density would be estimated from (3) & (4) above. Hence, a plot of temperature against molar density could be achieved to predict the phase behaviour of the system.
Furthermore, we would validate the phase diagram from SAFT for 2-components system with the experimental phase diagram and/or the DL-Poly with 2-components system. If this does not fit with experimental phase diagram, the SAFT parameters will then be optimized such that the prediction from SAFT is close to the experimental data/ data generated by DL-Poly for one component system.
In the same way, the procedures 2(a) above would be repeated for multi components systems using n-components SAFT and n-components DL-Poly depending on the number of pseudo components.
(2) SAFT theory with second order perturbation term predicts accurately phase behaviour of crude oil below or above the critical point; our objective is to develop theory that can accurately predict the phase behaviour of crude oil at the critical point or very close to the critical point. To do this, a third order perturbation term in powers of Îµ will be added to the Aseg term in the original SAFT theory. The improve Aseg will then be added to the Achain term to estimate the residual Helmholtz energy for the system and from this total Helmholtz energy for the system and other thermodynamics properties could be determined. Even small increment in these properties could lead to prediction of phase behaviour of crude oil close to the critical point or even at the critical point.
(3) Following the proposition of Behrens and Sandler (1988), we would represent crude oil fraction with a truncated distribution function. The challenge is to find a robust and appropriate way of splitting this complex mixture of hydrocarbon into a set of pseudo components which will yield an accurate equation of state without any undue numerical effort when fed into a generalized SAFT algorithm.
Milestones of the proposed research
Phase diagram from DL-Poly simulation for 1-component system.
Phase diagram from DL-Poly simulation for 2-components system.
Phase diagram from SAFT model for 1-component system.
Phase diagram from SAFT model for 2-component2 system.
M2: Improved Aseg term for the system.
M3: The number of pseudo components and their corresponding values of carbon number and mole fractions.
2.4 Relevance to Academic Beneficiaries
The major objective of this proposed Research is to optimize SAFT theory so as to provide a robust and accurate equation of state that is capable of predicting thermodynamic properties of crude oil, basically its phase behaviour. After paramerization has been done successfully, the research community will have an understanding of how to accurately predict many thermodynamic properties of crude oil. Furthermore, many researchers can be trained on how to use the optimized model. In addition, researchers would be able to discover more enhanced recovery techniques; thereby having a positive impact on the rate of production of crude oil as the larger percentage of trapped crude oil will be recovered. In addition, the resulting model could be applied to many more complex mixtures, for instance, that involve in nuclear waste reprocessing.