# Entropy Production in Pipeline Flow of Dispersions of Water in Oil

## Abstract

**:**

**PACS Codes:**5; 47; 82

## 1. Introduction

_{lost}is the rate of lost work, T

_{o}is the surroundings temperature, and Ṡ

_{G}is the total rate of entropy generation due to internal (within control volume) and external (outside the control volume) irreversibilities. According to the second law of thermodynamics, Ṡ

_{G}>0 for any irreversible process. Ṡ

_{G}= 0 only when the process is completely reversible (no internal and external irreversibilities). The importance of Equation (1) is aptly described by the following statement of Smith et al. [1] “The engineering significance of this result is clear. The greater the irreversibility of a process, the greater the rate of entropy production and the greater the amount of energy that becomes unavailable for work. Thus every irreversibility carries with it a price.”

_{destruction}is the total rate of exergy destruction. The thermo-mechanical exergy associated with a fluid stream per unit mass is given as follows:

_{o}and s

_{o}are specific enthalpy and specific entropy of fluid in dead state, respectively, V is fluid velocity, g is acceleration due to gravity, and z is elevation of the fluid stream with respect to the dead state. According to the second law of thermodynamics, ψ̇

_{destruction}> 0 for any irreversible process. Thus irreversibilities in a process cause production of entropy and destruction of exergy.

_{G,step}/∑Ṡ

_{G}for different steps.

## 2. Theoretical Background

_{o}to the control volume be Q̇

_{o}. Let the temperature of the control volume boundary be uniform at T

_{b}. Entropy balance on the control volume gives:

_{G,total}= 0.

_{sh}is the rate of shaft work. For adiabatic incompressible flow in a horizontal pipe in the absence of any shaft work, Equation (10) simplifies to:

_{Darcy}= 4 f

_{Fanning}). In this article, the Fanning friction factor is used throughout. From Equations (15) and (16), it follows that:

^{1/4}; this form of the Blasius equation is equivalent to Equation (19) where the Fanning friction factor is used (f

_{Darcy}= 4 f

_{Fanning}). Substitution of the friction factor expressions from Equations (18) and (19) into Equation (17) leads to the following relations for entropy production in pipe flows:

## 3. Experimental Work

^{3}) equipped with baffles, two high shear mixers, heating/cooling coil, and a temperature controller. The mixers used were Philadelphia model PDV-13 (0.5 hp variable speed motor with a maximum speed of 1750 rpm) and Philadelphia model PD-14 (0.25 hp motor with a fixed speed of 1750 rpm). One of these mixers (Philadelphia model PDV-13) had two S.S. propellers (3-blade, diameter of 0.082 m) mounted on the same S.S. shaft and the other mixer (Philadelphia model PD-14) had one S.S. impeller (3-blade, 0.089 m). The heating/cooling coil used in the tank was helical in shape and was made from stainless-steel. The coil was connected to hot and cold water lines at one end (via solenoid valves) and to drain at the other end. The opening or closing of the solenoid valves on the hot and cold water lines was controlled by a temperature controller (YSI Thermistemp temperature controller—71A) which had a temperature sensor (YSI thermistor probe) mounted on the side wall of the tank near the bottom. The set point (desired temperature) of the controller could be selected anywhere from −10 °C to 120 °C.

^{3}and a viscosity of 2.41 mPa.s at 25 °C. No chemical emulsifier or surfactant was used in the preparation of emulsions. The experiments were started with pure oil into which a required amount of water was added to prepare an emulsion. The concentration of water was increased from 0 to 41% vol. The experimental work was conducted at a constant temperature of 25 °C. The temperature was maintained constant in the flow loop with the help of a temperature controller installed in the mixing tank. The emulsions were sheared in the tank as well as the pumping system for more than 3 h before collection of any data. The volume fraction of the dispersed-phase in the emulsion was determined by collecting several emulsion samples from the mixing tank and other locations of the flow loop. The samples were collected in graduated cylinders (about 1–2 L) and were allowed to undergo complete separation into oil and water phases before recording the volumes of the individual phases.

## 4. Results and Discussion

_{w}+ (1 − φ)ρ

_{o}, where ρ

_{w}and ρ

_{o}are the densities of water and oil, respectively and φ is the volume fraction of water (dispersed-phase). The emulsion viscosity was determined from the pipeline data in the laminar regime using the Hagen-Poiseuille law.

## 5. Conclusions

## Acknowledgment

## Conflicts of Interest

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**Figure 3.**${\dot{S}}_{G}^{\prime}$

**versus**Re plot for 10.51% by vol. W/O emulsion flow in a 8.89 mm diameter pipeline.

**Figure 4.**${\dot{S}}_{G}^{\prime}$

**versus**Re plot for 17.49% by vol. W/O emulsion flow in a 8.89 mm diameter pipeline.

**Figure 5.**${\dot{S}}_{G}^{\prime}$

**versus**Re plot for 26.72% by vol. W/O emulsion flow in a 8.89 mm diameter pipeline.

**Figure 6.**${\dot{S}}_{G}^{\prime}$

**versus**Re plot for 32.47% by vol. W/O emulsion flow in a 8.89 mm diameter pipeline.

**Figure 7.**${\dot{S}}_{G}^{\prime}$

**versus**Re plot for 38.14% by vol. W/O emulsion flow in a 8.89 mm diameter pipeline.

**Figure 8.**${\dot{S}}_{G}^{\prime}$

**versus**Re plot for 41.05% by vol. W/O emulsion flow in a 8.89 mm diameter pipeline.

**Figure 9.**Influence of dispersed-phase volume fraction of emulsion on the ratio of entropy production rate in emulsion flow to entropy production rate in single-phase Newtonian flow with the same properties (viscosity and density).

**Figure 11.**Influence of pipe diameter on entropy production rate in 38.14% by vol. W/O emulsion flow.

**Figure 12.**Influence of pipe diameter on entropy production rate in 41.05% by vol. W/O emulsion flow.

Pipe inside diameter (mm) | Entrance length (m) | Length of test section (m) | Exit length (m) |
---|---|---|---|

8.89 | 0.89 | 3.35 | 0.48 |

12.60 | 1.19 | 2.74 | 0.53 |

15.8 | 1.65 | 2.59 | 0.56 |

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**MDPI and ACS Style**

Pal, R.
Entropy Production in Pipeline Flow of Dispersions of Water in Oil. *Entropy* **2014**, *16*, 4648-4661.
https://doi.org/10.3390/e16084648

**AMA Style**

Pal R.
Entropy Production in Pipeline Flow of Dispersions of Water in Oil. *Entropy*. 2014; 16(8):4648-4661.
https://doi.org/10.3390/e16084648

**Chicago/Turabian Style**

Pal, Rajinder.
2014. "Entropy Production in Pipeline Flow of Dispersions of Water in Oil" *Entropy* 16, no. 8: 4648-4661.
https://doi.org/10.3390/e16084648