International Journal of Fuzzy Systems

, Volume 21, Issue 2, pp 488–502

# Bit Pressure Control During Drilling Operations Using a Direct Fuzzy Adaptive Controller

• Mahdi Imanian
• Aazam Ghassemi
• Mahdi Karbasian
Article

## Abstract

One of the high-risk parts in the oil industry is the drilling of oil and gas wells. At any moment, during drilling operations, there is the probability of well blowout due to the sudden entry of the formation fluid into the well. One of the methods used for preventing the blowout of wells is the online monitoring and control of bit pressure during the drilling operations. In this article, a direct fuzzy adaptive controller is used to control bit pressure. To evaluate the performance of this controller, the results are compared with three methods including the model reference adaptive controller, the self-tuning controller and the proportional–integral–derivative controller. Also, for the first time, the reference tracking scenario is used to investigate the ability of the controller to track bit pressure by changing the reference pressure of different formations during the drilling operations. The results show the superiority of the direct fuzzy adaptive control in controlling bit pressure based on the process output tracking criteria, control effort, controller tracking error and cost functions, as compared to other controllers.

## Keywords

Direct fuzzy adaptive control Bit pressure Blowout Reference tracking

## Model variables

$$p_{\text{p}}$$

Mud pump pressure (bar)

$$p_{\text{c}}$$

Choke manifold pressure (bar)

$$p_{\text{b}}$$

Bit pressure (bar)

$$q_{\text{p}}$$

Mud pump flow rate $$({\text{m}}^{3} / {\text{s}})$$

$$q_{\text{c}}$$

Chock manifold flow rate $$({\text{m}}^{3} / {\text{s}})$$

$$q_{\text{b}}$$

Bit flow rate $$({\text{m}}^{3} / {\text{s}})$$

## Initial values

$$p_{\text{p}}^{0}$$

Initial mud pump pressure (bar)

$$p_{\text{c}}^{0}$$

Initial choke manifold pressure (bar)

$$q_{\text{b}}^{0}$$

Initial bit flow rate $$({\text{m}}^{3} / {\text{s}})$$

## Model parameters

$$\beta_{\text{a}}$$

Annulus mud bulk modulus (bar)

$$\beta_{\text{d}}$$

Drill string mud bulk modulus (bar)

$$V_{\text{a}}$$

Annulus volume $$({\text{m}}^{3} )$$

$$V_{\text{d}}$$

Drill string volume $$({\text{m}}^{3} )$$

$$M_{\text{a}}$$

Mass coefficient of the annulus $$(10^{ - 5} \times {\text{kg/m}}^{4} )$$

$$M_{\text{d}}$$

Mass coefficient of the drill string $$(10^{ - 5} \times {\text{kg/m}}^{4} )$$

$$F_{\text{a}}$$

Annulus friction factor

$$F_{\text{d}}$$

Drill string friction factor

$$\rho_{\text{a}}$$

Annulus density $$(10^{ - 5} \times {\text{kg/m}}^{3} )$$

$$\rho_{\text{d}}$$

Drill string density $$(10^{ - 5} \times {\text{kg/m}}^{3} )$$

$$h_{\text{b}}$$

Vertical depth of the drill bit (m)

$$g$$

Gravity acceleration $$({\text{m/s}}^{2} )$$

$$q_{\text{r}}$$

Flow rate of reservoir fluids $$({\text{m}}^{3} / {\text{s}})$$

$$q_{\text{back}}$$

Back pump flow rate $$({\text{m}}^{3} / {\text{s}})$$

$$p_{0}$$

Pressure outside system (bar)

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