Desenho Elétrico Técnico Perspectivas 3 D

MASS TRANSFER OZONE-BLOOD – ADAPTED MATHEMATICAL MODEL

H.C. Carvalho1,2, C.J. de Lima2,3, A.B. Fernandes2,3, L.P. Alves2,3, L.H. Moreira2,3 and R.A. Zângaro2,3

1. Universidade Tecnológica Federal do Paraná (UTFPR), CEP 87301-006, Campo Mourão/PR, Brazil
2. Center of Innovation, Technology and Education (CITÉ), CEP 12247-016, São José dos Campos/SP, Brazil
3. Biomedical Engineering Center, Anhembi Morumbi University (UAM), CEP 04546-001, São Paulo/SP, Brazil

Abstract—  Ozone therapy is a powerful technique applied for several purposes in healthcare. One modality of this therapy is through blood ozonation, a moderate immunomodulatory process that must consider the integrity of the blood components. In this work a mathematical model for waste-water ozone system was adapted for the mass-transfer ozone-blood. Our results demonstrated that the mathematical model proved to be well adapted for the ozone-blood mass transfer for rates of ozone decomposition and reaction, demonstrating that the application is appropriate for the studied process, decay rates, and reactivity of ozone.

Keywords— Ozone; blood; mass transfer; mathematical model; water.

1. INTRODUCTION

A knowledge about the efficient and behaviour of mass transfer is important to perform an effective evaluation of ozone effects on blood to guarantee safety and efficiency to those using ozone for therapeutic purposes. In this study, we present an adapted mathematical model for the ozone-blood mass transfer.

1. MATERIALS AND METHODS

The kinetic mathematical model developed by Farooq & Ahmed [1], as shown in Equation (1), for an ozone-wastewater system was adapted for use in a blood ozonation system. To adapt the equation for the blood ozonation, we recalculated some of the original values and parameters used, which are also in Table 1.

Table 1: Parameters of the mathematical model for ozone-blood.

Parameters	Value	Reference
CL = ozone concentration in liquid phase (mg/L)	?	-
gin = ozone supply rate (mg/min)	33 - 62	Proposed
G = gas flow rate (L/min)	0.125	Proposed
H = Henry’s constant (atm/mol fraction)	3188	[2]
kLa = overall mass transfer coeff. in the liquid phase (min-1)	0.09	Proposed
k1 = rate constant of ozone decomposition (min-1)	0 to 1	Proposed
k2 = rate constant for ozone reaction (L/mg1/2 min-1)	0 to 1	Proposed
n = order of the reactions	0.99	[1]
m = order of the reactions	0.53	[1]
p = order of the reactions	1.07	[1]
Q = liquid flow rate (L/min)	0.09	Proposed
V = volume of reactor (liters)	0.075	Proposed
S = remaining concentration of organic matter (COD) (mg/L)	1	Proposed

        (1)[pic 1]

1. RESULTS AND DISCUSSION

Figure 1-A/B chart the non-linear variation of the residual ozone CL for a given ozone input gin (33 and 62mg/L) with function of k1 (decomposition) and k2 (reaction), respectively, with Q, G, and H remaining constant. For the curve fitting, adjusted one-phase exponential decay function was employed with r2= 0.99 for k1 and r2= 0.98 for k2. For initial CL conditions of the k1 and k2 (CL = 6.5mg/L to gin = 33mg/L and CL = 12.2mg/L to gin = 62mg/L), considering the same gin, the value of CL decrease, respectively, to 7.1 and 3.8mg/L for k1 and 1.3 and 0.7mg/L for k2, due to decomposition (k1) and reaction (k2) of ozone in model-based referenced. The remaining concentration of organic matter (COD) (mg/L) of blood was proposed as 1 (S = 1), and the 7 model-dots shown in Figures 1 and 2 represent the proposed k1-k2 values: 0, 0.05, 0.1, 0.2, 0.4, 0.8 until 1.

[pic 2][pic 3][pic 4][pic 5]

Fig. 1: Relationship of ozone concentration in blood (CL) versus constant rate for ozone decomposition (k1) (1A), and for ozone reaction (k2) (1B) in a specific ozone input (gin).

The use of ozone in medical applications depends on the efficiency of liquid-gas mass transfer. Plasma constitutes approximately 55% of the blood volume, and contains 90% of water with small portion of inorganic materials corresponding to only 0.9% of its composition [3] thus, we decided to use an ozone-water model [1], taking into account the high blood water content. Moreover, the original model was applied to wastewater, which contains a high concentration of organic material (similar to blood). Despite these similarities and unlike the wastewater model, we are not interested in eliminating the organic materials. Our goal is to obtain high ozone mass transfer to the blood and estimate the ozone concentration, under the influence of decomposition and reactions, to provide benefits to the biological system without alterations to the blood cells. Unlike wastewater ozonation processes, the blood ozonation process seeks to activate the antioxidant hematological system with a control and modulation of oxidative stress, while maintaining vital characteristics of the fluid. This condition can be modeled mathematically by verifying the behavior of the decomposition rate k1 (min-1) and reactivity rate k2 (L/mg1/2 min-1), which in turn determines the decay of the remaining ozone concentration (CL) in the blood after the ozonation process. The higher CL decay ensures the integrity of most of the organic matter in blood, thus ensuring the purpose of blood ozonation and its desirable biological effects. The adopted mathematical model also verified that at the concentration of 33mg/L, a fast decay-reaction of CL occurs, evidencing that the residual ozone should not be able to damage the blood after 60s of the ozonation process.

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