Novel De-Oiling of Oil-Water

Corresponding Author: Emmanuel Ewa Ekeng Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria Email: ekengemmanuel@yahoo.com Abstract: The study anchors on developing a mechanistic model for oilwater separation. Over the years, researchers have been working on how to improve the quality of produced water effluent especially from oil and gas operations sent to the receiving waters. Despite the standard set for compliance by regulatory bodies like united nation agency, ministry, departments and other agencies both state and federal government including non governmental agencies the problem of meeting stipulated bench marks still persist. This study however looks into some variables perceived as being relative to improving or affecting produced water effluent from oil-water separator. Modeling of oil-water separation was based on the philosophy that a mathematical model can be established for the physical problems under investigation. These mathematical problems formulated were based on laws of conservation. Solving the model equation analytically however pose some problems. Hence they were solved by simulation using a computer soft ware SIMULINK a graphical extension of MATLAB with positive outcome since it has the ability to model nonlinear systems. From the simulated analysis, increased flow rate creates turbulence in the system with resultant poor effluent quality, whereas also, from the simulated analysis, gradual increases in temperature improves oilwater separation from lower temperature of the fluid upstream thereby aiding improvement in effluent quality.


Introduction
Petroleum is vital to many industries and in the manufacture of a wide variety of materials. It also accounts for a large percentage of the world's energy needs and thus it is a critical concern for many nations (Shahryar, 2017). Wastewater or oil-water effluent management practices can be implemented by prevention (improved operation or operating procedures), source reduction or waste minimization (material elimination, inventory control and management, material substitution, process and equipment modifications), reuse, recycling/recovery, treatment and disposal. Setting and enforcing environmental regulations in the oil and gas industry are important for minimizing potential environmental impacts and protecting human health and the environment (Shahryar, 2017). The function of an oil production facility is to separate the oil well stream into three components or phases (oil, gas and water) and process these phases into some marketable products or dispose of them in an environmentally acceptable manner (Sayda and Taylor, 2007). The major research task of modeling oil-water separation involved, constructing and simulating flow in the paradigm. The physical model constructed with Perspex glasses about 5mm in thickness also included the internals like baffles and the hydraulic weir. However, the gravity settling approach requires very long cylinder which is not practical and inconsistent with space restriction in the laboratory (Kharoua et al., 2013). Produced water is the largest waste stream generated in oil and gas industries. It is a mixture of different organic and inorganic compounds (Fakhru'l-Razi et al., 2009). Modelling of oil-water separation might not be new. However, a model may be seen as a description of a system using mathematical concepts and language. Hence this would metaphor into a statement of an equality containing one or more variables called equations. This study is expected to improve on mathematical formulation describing oil-water separation due to high cost of improving produced water treatment through chemicals. This study might also help explained liquid-liquid separation in a gravity vessel both analytically and the effect of different components. If this is achieved, the study would impart positively or 180 benefit oil and gas industries in terms of optimization of oil production, reduction in pollution of receiving waters, produced water re-injection, design and cost reduction in terms of produced water treatment. Utilities companies, water treatment entities including the academia and the reading public are not left out as direct beneficiaries of this study.

Aim and Objectives
The aim of this research is the formulation, solution and simulation of mathematical relationships describing oil-water separation.

Methodology
In developing a mathematical model for the multiphase oil-water separation, the following assumptions were adopted for the mechanistic model: Applying the basic principles of conservation of mass in the first instance which states that for any system closed to all transfer of matter and energy, the mass of the system must remain constant over time. The model under study, where the total mass and energy cannot be generated neither do they disappear, so that mass balance would give a differential equation which is ordinary. This ordinary differential equation contains one or more functions of one independent variable and its derivatives. The equation relates some functions with it derivatives. These functions which are physical quantities include, concentration, flow rate, mass, density, velocity, area, temperature etc. While the derivative would represent the rate of change and the equation to be derived would define the relationship between the two. For example the Equation (2.1) (Luyben, 1990): where, i, j are the densities of inlet and outlet streams; Fi, Fj are volumetric flow rates of the inlet and outlet streams. However, the differential equation will accompany set of additional constraints called boundary conditions: However, the accumulation term will supply the time derivative and produce a differential equation.
Component mass balance gives:

Rate of Accumulation
Applying Product Rule to Equation (2.7) we have: where, (-rA) = Rate of Disappearance of component A. Simplifying, we have: Collecting like-terms, we have: Dividing throughout by Volume, V, we have: where, 'r' = rate of disappearance of component A or reaction rate. The reaction rate expression used in dynamic modeling are typically based on the principles of mass action (Luyben, 1990). Hence Arrhenius expression must be incorporated when rate constants depend on temperature., otherwise, the energy balance will not adequately describe temperature change. Hence Arrhenius Equation ( Furthermore, another equation was also formulated still from the law of conversation that is for total energy balance. It states that the total energy of an isolated system remains constant and it is said to be conserved overtime (Luyben, 1990).
All models will include one or more balance equations. Most will also use a set of constitutive equations to better define specific terms in the balance equation. Luyben (1990) listed some common constitutive relationships to include: Property relation and equation of state, reaction rate expression etc. The mass flow into or out of the separator carries certain amount of energy, associated with how fast it is moving (kinetic energy), how high off the ground it is (potential energy) and its (internal energy).
However an increase in temperature typically increases the rate of reaction. An increase in temperature will raise the average kinetic energy of the reactant molecules of oil and water. Therefore a greater proportion of the molecules will have the minimum energy necessary for an effective collision hence aiding separation. According to (Smith et al., 1996;Luyben, 1990): (2.14) Where: Also considering the concentration of the produced water in terms of component species, we equally introduce 182 the component energy balance. This is the first law of thermodynamics which states that for any bounded system. Energy In -Energy Out across the boundaries = Energy accumulated inside the boundaries.
Using this definition, we can easily express the rate of temperature change in a insulated system/vessel as a function of mass flow through the tank, the fluid heat capacity, density and tank volume.
Component energy balance state as follows: .

Rate of Energy Rate of Accumulation
Energy Input
However, the two model Equations (2.13), (2.25) were solved by simulation using Simulink a graphical extension of MATLAB software since it has the ability to model non-linear system and the ability to take on initial conditions. From Fig. 1 to 4 it was seen that from the simulation according to the first model equation there were responses in the CA-value representing the outlet concentration that is the effluent. This was achieved by keeping other variables constant and varying a particular parameter one at a time like, the retention time, flow rate, sample volume, temperature, etc. For example, increasing flow rate creates turbulence with resultant poor effluent quality. In the course of simulating with the software, input values ranges between plus and minus. This was geared towards improving the effluent quality at a particular set value from the micro model and comparing it with a macro system. This in turn verified the fact that results were in agreement with the macro results that varying the variables actually influences oilwater separation effluent quality. That is at certain set values considering the variables in model Equation (2.13) and Equation (2.24) the produced water or effluent quality can greatly be improved if applied.   Fig. 5 shows the effluent quality from output response during simulation which was time dependent. At a concentration of 1.0 mg/l, there was a steady profile for a long while before the curve started declining. Whereas Fig. 6 with reduced concentration of 0.25 mg/l with same simulation time, a far more quality effluent was achieved.
We also observed that increasing the volumetric flow rate creates turbulence in the system hence resulting in decreasing effluent quality. Figure 7 shows a more prolong time in the gravity separation since retention time is a major determinant in oilwater separation hence improved produced water. Whereas, Fig. 8 shows a short time response which inevitably leads to poor separation.
Furthermore, Fig. 9 shows the effect of increasing temperature on oil-water separation from 450 k. The produced water quality shows a significant improved quality considering the same time duration as compared with that in Fig. 10 at a temperature of 350 K.

Conclusion
The simulation from the Simulink software an extension of MATLAB using the model equations shows, how the variables of temperature, volumetric flow rate, sample concentration affects, influences oilwater effluent or produced water from oil and gas industries. This work is in agreement with the work of (Abdulkadir and Hernandez-Perez, 2010) where CFD