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### A method for crude oil selection and blending optimisation based on Improved Cuckoo Search algorithm

Refineries often need to find similar crude oil to replace the scarce crude oil for stabilising the feedstock property. We introduced the method for calculation of crude blended properties firstly, and then created a crude oil selection and blending optimisation model based on the data of crude oil property.

**Yang Huihua, Ma Wei and Zhang Xiaofeng Guangxi**

Experiment Center of Information Science, Guilin University of Electronic Technology

Li Hu and Tian Songbai

Research Institute of Petroleum Processing, SINOPECExperiment Center of Information Science, Guilin University of Electronic Technology

Li Hu and Tian Songbai

Research Institute of Petroleum Processing, SINOPEC

**Viewed :**1789

**Article Summary**

The model is a mixed-integer nonlinear programming (MINLP) with constraints, and the target is to maximise the similarity between the blended crude oil and the objective crude oil. Furthermore, the model takes into account the selection of crude oils and their blending ratios simultaneously, and transforms the problem of looking for similar crude oil into the crude oil selection and blending optimisation problem. We applied the Improved Cuckoo Search (ICS) algorithm to solving the model. Through the simulations, ICS was compared with the genetic algorithm, the particle swarm optimisation algorithm and the CPLEX solver. The results show that ICS has very good optimisation efficiency. The blending solution can provide a reference for refineries to find the similar crude oil. And the method proposed can also give some references to selection and blending optimisation of other materials.

In order to cope with the changes in the variety, quantity and price of crude oils, refineries often need to find alternative crude oil which is similar to the scarce crude oil. And the crude properties should be considered firstly when selecting the substitutes. However, even crude oils coming from the same field may have different properties, and then it is very difficult to find alternative crude oil with similar properties. Thus, using the similar blended crude oil to replace scarce crude oil will be a good approach. The physical process of blending the crude oils is simple, but the selection of proper crude oils and the determination of proper blending ratios are difficult1. Some crude oil properties cannot be calculated by linear addition method, which brings certain difficulty in predicting the blended crude properties. In the last few decades, many empirical equations have been proposed to calculate the blended crude properties2-3. And all these approaches provide theoretical support for crude oil blending, and comparatively few studies have been done on the blending optimisation of crude oil. Ganji3 applied SQP method for calculating the optimum blending ratios. Bai4 proposed a two-level optimisation structure, and applied a hybrid algorithm with Tabu search and differential evolution to the determination of blending sequence and corresponding flow rates. Du5 considered the crude oil storage, transportation and blended properties simultaneously, and applied the genetic algorithm (GA) to identification of the blending ratios. Wang6 applied the improved particle swarm optimisation (PSO) algorithm to the multi-component naphtha recipe optimisation problem, which could give some references to the crude oil blending optimisation. Muteki7-8 built a PLS model, and solved it by branch and bound algorithm to determine the selection of crude oils and their blending ratios simultaneously. However, there are some drawbacks in all above methods, they either ignore the optimisation of crude oil selection or just build the model based on historical data which need a lot of pre-work to do.

The Cuckoo search (CS) was developed as a metaheuristic search algorithm by Yang and Deb in20099. It has less parameters to be fine-tuned, is very easy to realise programming, and works well on optimisation problems in many fields10-15. However, no technical literature has been proposing on using CS in the crude oil selection and blending optimisation problem up to now. We applied the improved CS (ICS) algorithm to solve the crude oil selection and blending optimisation model, and the blending solution can provide a reference for refineries to find alternative crude oil.

There are many methods for measuring the similarity between different individuals, such as inner product, cosine, correlation coefficient, and Dice coefficient, etc. Mc- Gill16 gave 67 methods for different cases. On the other hand, many new similarity measuring methods are being proposed with an increasing demand for new applications. It is very important to select a suitable method for measuring the similarity. Here, we apply the method based on distance to measure the similarity between different crude oils, which is described in Equation (1).

We assume that the two crude oils are OA and OB, the properties of which are A=(A1, A2, …, Am) and B=(B1, B2,…, Bm), respectively. Then, the weighted similarity between OA and OB is defined as follows:

where ωi is the weight of the ith property, which satisfies

Max(i) and Min(i) are respectively the maximum and minimum values of the ith property with the available crude oils. Ai and Bi are values between Min(i) and Max(i). Thus, the value of S(OA, OB) ranges from 0 to 1. Refineries can measure the similarity between OA and OB according to S(OA and OB). And S(OA and OB)=1 means that OA and OB are the same.

The crude oil properties can be divided into two categories as linear additivity and nonlinear additivity according to the relationship between the blended properties and raw material properties. For the linear additivity, some properties have additivity of mass, such as sulphur content, total acid number, and Conradson carbon residue, and others have additivity of volume, such as density, specific gravity, and refractive index parameter, etc.2 On the other hand, the nonlinear properties include viscosity, pour point, smoke point, etc.

We assume that Pmix is the blended property, Pi is the property of ith crude oil, and Ri is the mass fraction of the ith selected crude oil.

With respect to the properties of mass additivity, we can use Equation (2) to calculate Pmix,

With respect to the properties of volume additivity, we use Equation (3) to calculate Pmix. And we consider the properties of volume additivity as nonlinear in this case.

As for the nonlinear properties such as viscosity, pour point, and flash point, a lot of literature information have proposed experiential methods to predict the blended properties. In this paper, we use the method proposed in the literature2,

in which Ind is the index of properties and some of them are summarised in Table 1.

We assume that X(N, M) is the property matrix of the available crude oils (in which N is the number of available crude oils, and M is the number of properties). X(n, m) is the property matrix of selected crude oils (in which n is the number of selected crude oils, and m is the number of measured properties). The mass fraction of crude oils used in the crude blend is R=(R1, R2, …, Rn).

Oobj is the objective crude oil, and Omix is the blended crude oil. Then, the crude oil selection and blending optimisation model is described as follows:

Equation (5) is the objective function, and its objective is to maximise the similarity between the blended crude oil and the objective crude oil. The calculation method of similarity is Equation (1), and the blended properties are calculated by Equation (2) through Equation (4).

Equations (6) and (7) are the constraints of binary decision variables. Here δi will be set as 1 if the crude oil is selected, or otherwise will be set as 0. Nmax and Nmin are the upper and lower limit of the number for selected crude oils, respectively.

Equations (8) and (9) are the constraints of decision variable Ri. Rui and Ril are respectively the upper and lower limit of blending ratios for the selected crude oils. Furthermore, the total ratio of Ri must be 1.

In general, the model is a mixed-integer nonlinear programming with constraints. And it belongs to the class of NP-hard optimisation problems, which cannot be solved efficiently by any known algorithm in a practically acceptable time scale. In the most cases, we can use metaheuristic search algorithm to get proximate optimum solution. On the other hand, only the decision variable R is left when the available crude oil number N is equal to both the upper limit Nmax and the lower limit Nmin (which means Nmax=Nmin=N), and then, the problem will be transformed into the blending ratios optimisation only, and this belongs to a nonlinear continuous optimisation problem which is easier to solve.

Basic CS algorithm is very effective in solving continuous optimisation, but has no capacity to solve the problem with mixed-integer variables. Thus, for establishing the crude oil selection and blending optimisation model, we have improved the encoding scheme and the Lévy flights in order to deal with the 0-1 mixed-integer problems. The main idea of ICS is described as follows: 1) A real-coded scheme is proposed, which takes into account the binary variables δ and the continuous variable R. And this measure can avoid the complex operation with binary variables; 2) The continuous variables by Lévy flights are updated, while keeping the binary variables constant; 3) The binary variables are updated by abandoning nests with a probability.

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**Introduction**In order to cope with the changes in the variety, quantity and price of crude oils, refineries often need to find alternative crude oil which is similar to the scarce crude oil. And the crude properties should be considered firstly when selecting the substitutes. However, even crude oils coming from the same field may have different properties, and then it is very difficult to find alternative crude oil with similar properties. Thus, using the similar blended crude oil to replace scarce crude oil will be a good approach. The physical process of blending the crude oils is simple, but the selection of proper crude oils and the determination of proper blending ratios are difficult1. Some crude oil properties cannot be calculated by linear addition method, which brings certain difficulty in predicting the blended crude properties. In the last few decades, many empirical equations have been proposed to calculate the blended crude properties2-3. And all these approaches provide theoretical support for crude oil blending, and comparatively few studies have been done on the blending optimisation of crude oil. Ganji3 applied SQP method for calculating the optimum blending ratios. Bai4 proposed a two-level optimisation structure, and applied a hybrid algorithm with Tabu search and differential evolution to the determination of blending sequence and corresponding flow rates. Du5 considered the crude oil storage, transportation and blended properties simultaneously, and applied the genetic algorithm (GA) to identification of the blending ratios. Wang6 applied the improved particle swarm optimisation (PSO) algorithm to the multi-component naphtha recipe optimisation problem, which could give some references to the crude oil blending optimisation. Muteki7-8 built a PLS model, and solved it by branch and bound algorithm to determine the selection of crude oils and their blending ratios simultaneously. However, there are some drawbacks in all above methods, they either ignore the optimisation of crude oil selection or just build the model based on historical data which need a lot of pre-work to do.

The Cuckoo search (CS) was developed as a metaheuristic search algorithm by Yang and Deb in20099. It has less parameters to be fine-tuned, is very easy to realise programming, and works well on optimisation problems in many fields10-15. However, no technical literature has been proposing on using CS in the crude oil selection and blending optimisation problem up to now. We applied the improved CS (ICS) algorithm to solve the crude oil selection and blending optimisation model, and the blending solution can provide a reference for refineries to find alternative crude oil.

**Crude Oil Selection and Blending Optimisation Model**

Crude oil similarityCrude oil similarity

There are many methods for measuring the similarity between different individuals, such as inner product, cosine, correlation coefficient, and Dice coefficient, etc. Mc- Gill16 gave 67 methods for different cases. On the other hand, many new similarity measuring methods are being proposed with an increasing demand for new applications. It is very important to select a suitable method for measuring the similarity. Here, we apply the method based on distance to measure the similarity between different crude oils, which is described in Equation (1).

We assume that the two crude oils are OA and OB, the properties of which are A=(A1, A2, …, Am) and B=(B1, B2,…, Bm), respectively. Then, the weighted similarity between OA and OB is defined as follows:

where ωi is the weight of the ith property, which satisfies

Max(i) and Min(i) are respectively the maximum and minimum values of the ith property with the available crude oils. Ai and Bi are values between Min(i) and Max(i). Thus, the value of S(OA, OB) ranges from 0 to 1. Refineries can measure the similarity between OA and OB according to S(OA and OB). And S(OA and OB)=1 means that OA and OB are the same.

**Blended properties calculation**The crude oil properties can be divided into two categories as linear additivity and nonlinear additivity according to the relationship between the blended properties and raw material properties. For the linear additivity, some properties have additivity of mass, such as sulphur content, total acid number, and Conradson carbon residue, and others have additivity of volume, such as density, specific gravity, and refractive index parameter, etc.2 On the other hand, the nonlinear properties include viscosity, pour point, smoke point, etc.

We assume that Pmix is the blended property, Pi is the property of ith crude oil, and Ri is the mass fraction of the ith selected crude oil.

With respect to the properties of mass additivity, we can use Equation (2) to calculate Pmix,

With respect to the properties of volume additivity, we use Equation (3) to calculate Pmix. And we consider the properties of volume additivity as nonlinear in this case.

As for the nonlinear properties such as viscosity, pour point, and flash point, a lot of literature information have proposed experiential methods to predict the blended properties. In this paper, we use the method proposed in the literature2,

in which Ind is the index of properties and some of them are summarised in Table 1.

Blending optimisation modelBlending optimisation model

We assume that X(N, M) is the property matrix of the available crude oils (in which N is the number of available crude oils, and M is the number of properties). X(n, m) is the property matrix of selected crude oils (in which n is the number of selected crude oils, and m is the number of measured properties). The mass fraction of crude oils used in the crude blend is R=(R1, R2, …, Rn).

Oobj is the objective crude oil, and Omix is the blended crude oil. Then, the crude oil selection and blending optimisation model is described as follows:

Equation (5) is the objective function, and its objective is to maximise the similarity between the blended crude oil and the objective crude oil. The calculation method of similarity is Equation (1), and the blended properties are calculated by Equation (2) through Equation (4).

Equations (6) and (7) are the constraints of binary decision variables. Here δi will be set as 1 if the crude oil is selected, or otherwise will be set as 0. Nmax and Nmin are the upper and lower limit of the number for selected crude oils, respectively.

Equations (8) and (9) are the constraints of decision variable Ri. Rui and Ril are respectively the upper and lower limit of blending ratios for the selected crude oils. Furthermore, the total ratio of Ri must be 1.

In general, the model is a mixed-integer nonlinear programming with constraints. And it belongs to the class of NP-hard optimisation problems, which cannot be solved efficiently by any known algorithm in a practically acceptable time scale. In the most cases, we can use metaheuristic search algorithm to get proximate optimum solution. On the other hand, only the decision variable R is left when the available crude oil number N is equal to both the upper limit Nmax and the lower limit Nmin (which means Nmax=Nmin=N), and then, the problem will be transformed into the blending ratios optimisation only, and this belongs to a nonlinear continuous optimisation problem which is easier to solve.

**Improved Cuckoo Search Algorithm**Basic CS algorithm is very effective in solving continuous optimisation, but has no capacity to solve the problem with mixed-integer variables. Thus, for establishing the crude oil selection and blending optimisation model, we have improved the encoding scheme and the Lévy flights in order to deal with the 0-1 mixed-integer problems. The main idea of ICS is described as follows: 1) A real-coded scheme is proposed, which takes into account the binary variables δ and the continuous variable R. And this measure can avoid the complex operation with binary variables; 2) The continuous variables by Lévy flights are updated, while keeping the binary variables constant; 3) The binary variables are updated by abandoning nests with a probability.

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