生物膜的Steady-state

2021-02-24 本文已影响0人代号北极能

在生物膜中存在着如下几个重要的过程。

1. 基质的扩散过程

$J=\frac{D}{L}(S-S_0)=D_f\frac{dS_f}{dz}|_{z=0}=D_f\frac{dS}{dz}|_{z=0}$

2.生物膜中基质利用方程

$0=D_f\frac{d^2S_f}{dz^2}-\frac{qX_fS_f}{K+S_f}$

3.生物膜中的活性生物组分变化

$0=YJ-bX_fS_f$

对于平衡状态下的生物膜应当同时满足以上三个方程。

解以上方程的前提是合理的选取下列参数。

$\hat{q}$

$D_f$

$X_f$

上图可以得到Steady-state的五个重要的趋势。

1. Steady-state状态下的生物膜损失速率biofilm loss rate等于生物膜的污泥龄SRT。对于以某一个biofilm loss rate运行的系统来说，存在最低的基质浓度Sbmin，可以通过下式计算

$S_{bmin}=K\frac{b}{Y\hat{q}-b}=K\frac{b+b_{det}}{Y\hat{q}-(b+b_{det})}$

对于CSTR来说，这个操作的基质浓度是维持生物膜SRT的最低基质浓度。因此这里的 $S_{min}$ 与 $S_{bmin}$ 用不同的notation。如果 $b_{det}=0$ , $S_{min}=S_{bmin}$ 。With a CSTR, the effluent S value is the same at a given $\theta_x$ regardless of the influent substrate concentration. In contrast with a biofilm reactor, increasing the influent substrate concentration causes the effluent value for S to increase over $S_{bmin}$ The difference comes about because, in a CSTR, all microorganisms are exposed to the same S, while the concentration decreases with depth into a biofilm. As with any steady-state completely mixed biological process, having S lower than this critical level gives a negative growth rate and no possibility for sustaining steady-state biomass. Thus, $S_{bmin}$ remains a very key factor for the design and operation of both systems.

2. J and $X_fL_f$ increase very sharply (on the logarithmic scale) as S increases slightly above $S_{bmin}$ . This rapid escalation occurs because J and $X_fL_f$ increases together. A small increase to S allows greater J, which allows greater $X_fL_f$ , however, greater $X_fL_f$ also increases J. Thus, the positive feedback among S, J, and $X_fL_f$ , allows a very rapid increase in J for S slightly above $S_{bmin}$ .

3. At some value of S > $S_{bmin}$ , the slope of J versus S declines from near infinity and approaches 1.0. This occurs at approximately S = 0.07 mg/ cm3 for the example in Figure 7.3.

4. For S large enough, the flux becomes equal to that of a deep biofilm. The concentration $S_{deep}$ signifies the spot, which is S approximately equal to 0.11 mg/cm3 in Figure 7.3. For all $S\geq S_{deep}$ the steady-state biofilm is deep, or St approaches zero before the attachment surface. The practical significance of having a deep biofilm is that J no longer depends on $X_fL_f$ because additional biomass does not increase the reaction rate (for the same S) when all of the added thickness has s1 = 0. On the other hand, J and Xf, increase for larger S, because the substrate concentrations inside the biofilm rise in response to a higher S.

5. For very large S, the slope of J versus S declines gradually and eventually reaches the limiting case of one-half-order kinetics, or $J=k_{1/2}*S^{1/2}$ • Half-order kinetics is a well-known special case for deep biofilms; it is discussed later in this chapter. The practical impact of a reaction order less than one is that increases in S give less than proportional increases in J, and marginal increases in substrate removal go down when the system is operated well into the deep region.

生物膜的Steady-state

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