Method of controlling static pressure in the reservoir of a liquefied gas and proppant blender

A method for dynamically adjusting a feedback control for proportional-integral-derivative (PID) control loops tuning gains in a fracturing fluid that is utilized in stimulation of an underground formation, wherein the loop output regulates the head pressure in a proppant reservoir comprising:

• supplying proppant or proppant slurry from a sealed, pressurized proppant reservoir to a fracturing fluid stream;
• supplying a fluid flow of liquefied gas and measuring the flow rate of said fluid by a flow meter, and providing a feedback signal to a computer;
• combining the proppant or proppant slurry with the liquefied gas stream forming a fracturing fluid containing proppant and measuring a concentration of the proppant in said fracturing fluid downstream by a concentration meter, and providing a feedback signal to the computer;
• and
• adjusting a PID controller for adjusting proportional, integral, and derivative gains of the PID control loops based on the feedback signals of flow and concentration to the computer, wherein the PID controller is given the following formula:
• u
• ⁡
• (
• t
• )
• =
• K
• P
• *
• e
• ⁡
• (
• t
• )
• +
• K
• I
• *
• ∫
• 0
• t
• ⁢
• e
• ⁡
• (
• τ
• )
• ⁢
• d
• ⁢
• ⁢
• τ
• +
• K
• D
• *
• de
• dt
• Equation
• ⁢
• ⁢
• 1
• where u is the control signal and e is the control error and is the reference of the set point, and where the tuning parameters are based on the following:
• Kp=f(GFR,PC)=C1*GFR+C2*PC+C3 Equation 2
• KI=f(GFR,PC)=C4*GFR+C5*PC+C6 Equation 3
• KD=f(GFR,PC)=C7*GFR+C8*PC+C9 Equation 4
• where GFR is the liquefied gas flow rate, PC is the proppant concentration, and C1_9 denotes predetermined constants.