Super-linear approximation of dynamic property values in a process control environment

1. A system comprising:

a processor; and

a non-transitory computer-readable medium comprising computer-executable instructions for generating a process simulation using said processor, said instructions comprising:

creating a mathematical model,

generating a super-linear Taylor series expansion of the mathematical model, the super-linear Taylor series expansion comprising calculations comprising:

determining a rigorous value,

generating a linear difference between a current independent property value and a previous independent property value, the current independent property value representing a property value during a current time, the previous independent property value representing a property value during a previous time,

generating a linear derivative of the linear difference,

generating a negative of the linear derivative,

generating a logarithmic difference between a logarithm of the current independent property value and a logarithm of the previous independent property value,

generating a logarithmic derivative of the logarithmic difference, and

determining a super-linear approximation by adding the rigorous value, the linear derivative, the negative linear derivative, and the logarithmic derivative, wherein the rigorous value, the linear derivative, the negative linear derivative, and the logarithmic derivative are all first-order terms;

determining, using the determined super-linear approximation, a solution for values of variables used in a simulated process of at least one piece of equipment of a real-world equipment processing system, and

transmitting data related to the solution to the at least one piece of equipment of a real-world equipment processing system, the solution data comprising instructions that controls operations of the at least one piece of equipment at the processing system.

2. The system of claim 1 , wherein obtaining the super-linear approximation value in the adding step further comprises:

determining an error of said super-linear approximation,

updating the super-linear approximation value in the adding step when the super-linear approximation error is greater than a predetermined threshold, and

using the super-linear approximation obtained in the adding step when the super-linear approximation error is less than a predetermined threshold.

3. The system of claim 2 , wherein determining the super-linear approximation error further comprises:

adding the negative linear derivative and the logarithmic derivative.

4. The system of claim 2 ,

wherein determining the super-linear approximation error further comprises:

obtaining a simple-linear error by generating the absolute value of the sum of the rigorous value and the linear derivative,

obtaining a super-linear error by generating the absolute value of the sum of the negative linear derivative and the logarithmic derivative, and

performing a percent error operation using the simple-linear error and the super-linear error to obtain the super-linear approximation error.

5. The system of claim 1 ,

further comprising a simulation module;

said simulation module configured and arranged to generate a simulation using values obtained from one of:

the mathematical model; and

the super-linear Taylor series expansion of the mathematical model.

6. The system of claim 5 ,

wherein the simulation module comprises:

at least one solution engine;

at least one module interface; and

at least one modeling engine.

7. The system of claim 1 ,

wherein values obtained from at least one of the mathematical model and the super-linear Taylor series expansion of the mathematical model are used for at least one of:

displaying results on a client device; and

controlling process components comprising at least one of a pump and a valve.

8. The system of claim 1 ,

wherein the independent property value is at least one of temperature, pressure, and composition.

9. A method comprising:

creating, by a computing device on a network, a mathematical model;

generating, by a computing device, a super-linear Taylor series expansion of the mathematical model, the super-linear Taylor series expansion comprising calculations comprising:

determining a rigorous value;

generating a linear difference between a current independent property value and a previous independent property value, the current independent property value representing a property value during a current time, the previous independent property value representing a property value during a previous time;

generating a linear derivative of the linear difference;

generating a negative of the linear derivative;

generating a logarithmic difference between a logarithm of the current independent property value and a logarithm of the previous independent property value;

generating a logarithmic derivative of the logarithmic difference; and

determining a super-linear approximation by adding the rigorous value, the linear derivative, the negative linear derivative and the logarithmic derivative, wherein the rigorous value, the linear derivative, the negative linear derivative, and the logarithmic derivative are all first-order terms;

determining, by the computing device, using the determined super-linear approximation, a solution for values of variables used in a simulated process of at least one piece of equipment of a real-world equipment processing system, and

transmitting, by the computing device over the network, data related to the solution to the at least one piece of equipment of a real-world equipment processing system, the solution data comprising instructions that controls operations of the at least one piece of equipment at the processing system.

10. A non-transitory computer-readable storage medium tangibly encoded with computer-executable instructions that when executed by a computing device, perform a method comprising:

creating, by the computing device on a network, a mathematical model;

generating, by a computing device, a super-linear Taylor series expansion of the mathematical model, the super-linear Taylor series expansion comprising calculations comprising:

determining a rigorous value;

generating a linear difference between a current independent property value and a previous independent property value, the current independent property value representing a property value during a current time, the previous independent property value representing a property value during a previous time;

generating a linear derivative of the linear difference;

generating a negative of the linear derivative;

generating a logarithmic difference between a logarithm of the current independent property value and a logarithm of the previous independent property value;

generating a logarithmic derivative of the logarithmic difference; and

determining a super-linear approximation by adding the rigorous value, the linear derivative, the negative linear derivative and the logarithmic derivative, wherein the rigorous value, the linear derivative, the negative linear derivative, and the logarithmic derivative are all first-order terms;

determining, by the computing device, using the determined super-linear approximation, a solution for values of variables used in a simulated process of at least one piece of equipment of a real-world equipment processing system, and

transmitting, by the computing device over the network, data related to the solution to the at least one piece of equipment of a real-world equipment processing system, the solution data comprising instructions that controls operations of the at least one piece of equipment at the processing system.