A general photobioreactor microbial growth rate prediction model and method thereof

Abstract

A general photobioreactor microbial growth rate prediction model and method thereof, the prediction model comprising a pretreatment module, a fluid dynamics calculation module, a light transmission module and a microbial growth rate mechanism module; first, a physical model of the photobioreactor is obtained; second, according to the obtained physical model and the calculation region, mesh division is carried out to construct the pretreatment module; then, the initial value of the growth parameter of the microbial particles in the photobioreactor is calculated; finally, the microbial growth rate in the photobioreactor is calculated and predicted through a coupled model of computational fluid dynamics, light intensity transmission law and microbial growth mechanism; the present application is based on physical modeling, and the computational fluid dynamics, light intensity transmission and microbial growth mechanism are coupled, thereby expanding the generality of the growth rate prediction; and the model can more accurately predict the microbial growth rate in any photobioreactor.

Description

Technical Field

[0001] This invention relates to the field of photobioreactor technology for microbial culture, and in particular to a general model and method for predicting the growth rate of microorganisms in a photobioreactor. Background Technology

[0002] Microalgae are a type of autotrophic microorganism that absorbs carbon dioxide and releases oxygen, and can produce high-value products such as biodiesel and pigments. Due to their high metabolic flexibility, adaptability to various culture conditions, and extremely rapid growth rate, they are suitable for wastewater treatment and bioenergy production, and do not compete with crops for land. Therefore, increasing research is exploring their potential as a source of high-biological-value products.

[0003] The design and control methods of microalgal photobioreactors need to be flexibly selected based on specific circumstances to achieve optimal growth and product accumulation. However, the reality is that all design and control must be based on a thorough understanding of the bioreactor and the microalgal growth mechanism; otherwise, it becomes a chaotic, random, and coarse process. Furthermore, for large-scale reactors, flow mixing is a crucial issue that cannot be ignored, yet traditional microalgal growth mechanism influencing factors rarely address this. Flow conditions are also a major reason why various microalgal mechanism models are not universally applicable to reactors of different shapes and sizes. Therefore, constructing a comprehensive model coupling fluid dynamics with other influencing factors is of significant guiding importance for the design and control of large-scale photobioreactors. Existing design and manufacturing guidelines for photobioreactors have significant gaps and deficiencies, relying primarily on experience and experimentation. Moreover, existing microbial growth and metabolic mechanism models generally have poor applicability in large-scale reactors, and guidance on the control of various related parameters during the cultivation process is also lacking. Existing strategies are all coarse and result in significant energy dissipation. Therefore, scientifically guiding the expansion design of photobioreactors is a crucial step for the future large-scale utilization of microalgae. Furthermore, during the operation of the photobioreactor, matching and scientifically regulating the material flow (aeration concentration, liquid culture medium circulation) and energy flow (stirring, aeration, hydraulic residence time, light) to achieve the most efficient microalgae growth rate is also a key step for large-scale, low-cost applications.

[0004] The literature [Jin M, Xu Y, Chen J, et al. A comprehensive universal model framework of microalgae growth dynamics for photobioreactor scaling-up design and optimization[J]. Energy Conversion and Management, 2024, 299: 117832.] proposes a predictive model for the growth rate of microorganisms in a photobioreactor that couples computational fluid dynamics, light intensity transmission, and growth mechanism. However, the growth mechanism in this model adopts a steady-state assumption, that is, the growth of microorganisms changes rapidly during the process of being exposed to varying light intensity, without relaxation time. Therefore, it does not conform to the actual process, and does not consider the influence of light history and time on it. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to provide a universal model and method for predicting the growth rate of microorganisms in photobioreactors. Based on physical modeling, it couples computational fluid dynamics, light intensity transmission, and microbial growth mechanism, thereby expanding the universality of growth rate prediction. By coupling computational fluid dynamics, light intensity transmission, and a more complete growth mechanism (transient, considering light history and time), the model can more accurately predict the growth rate of microorganisms in any photobioreactor.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A general model for predicting microbial growth rates in photobioreactors includes:

[0008] Preprocessing module: Acquires the physical model of the photobioreactor, the fluid computation region, the initial value of the phase volume fraction, the initial value of the microbial concentration in the fluid, the light intensity boundary conditions, the aeration / stirring mixing conditions during the operation of the photobioreactor, and the mesh generation conditions, which are used to predict the growth rate of microorganisms in the photobioreactor.

[0009] Fluid dynamics calculation module: used to calculate the gas, liquid and solid three-phase flow distribution in the photobioreactor, thereby obtaining the accurate flow distribution of solid-phase microorganisms in the photobioreactor;

[0010] Light transmission module: used to quantitatively calculate the precise distribution of light intensity within the photobioreactor;

[0011] Microbial growth rate mechanism module: accurately calculates the growth rate of microorganisms by measuring the light intensity they receive;

[0012] By obtaining the precise flow distribution of solid-phase microorganisms in the photobioreactor through the fluid dynamics calculation module and the precise light intensity distribution in the photobioreactor through the light transmission module, the light intensity received by each solid-phase microorganism in the photobioreactor is obtained. Then, the precise microbial growth rate is calculated through the microbial growth rate mechanism module, and the average growth rate of all solid-phase microbial particles in the photobioreactor is taken to obtain the precise growth rate of all microorganisms in the photobioreactor.

[0013] A general method for predicting microbial growth rates in photobioreactors, comprising the following steps:

[0014] Step 1: Based on the shape and operating parameter information of any photobioreactor, obtain the physical model of the photobioreactor, the fluid calculation domain, the initial values ​​of velocity, pressure and phase volume fraction within the fluid calculation domain, the boundary values ​​of velocity, pressure and phase volume fraction at the boundary of the fluid calculation domain, the initial value of microbial concentration in the fluid, the light intensity boundary conditions, and the aeration / stirring mixing conditions during the operation of the photobioreactor.

[0015] Step 2: Based on the physical model and fluid computation region obtained in Step 1, perform mesh generation. On the basis of the mesh generation, and based on the mixing conditions of aeration / stirring during the operation of the photobioreactor obtained in Step 1, the initial values ​​of velocity, pressure, and phase volume fraction in the fluid computation region, the boundary values ​​of velocity, pressure, and phase volume fraction at the boundary of the fluid computation region, the initial value of microbial concentration in the fluid, and the light intensity boundary conditions, construct a preprocessing module for predicting the growth rate of microorganisms in the photobioreactor.

[0016] Step 3: Based on the preprocessing module constructed in Step 2, calculate the initial values ​​of growth parameters of microbial particles in the photobioreactor;

[0017] Step 4: Based on the preprocessing module constructed in Step 2 and the initial values ​​of microbial particle growth parameters calculated in Step 3, the growth rate of microorganisms in the photobioreactor is calculated and predicted by a coupled model of computational fluid dynamics, light intensity transmission law and microbial growth mechanism.

[0018] The specific method for step 2 is as follows:

[0019] Step 2.1 Basic Mesh Construction

[0020] Based on the principle of optimal mesh generation, the physical model obtained in step 1 is meshed:

[0021] The physical model dimensions of the photobioreactor are calibrated based on grid size, grid skewness, grid aspect ratio, grid dynamic and static partitioning, boundary region and internal region. Based on the optimal grid division principle, the physical model of the photobioreactor is gridded. For grids with high skewness and aspect ratio (i.e., poor quality) and grid flow boundary regions, grid refinement and re-segmentation are performed to improve the grid division quality. Then, the node, boundary, size, volume and topological relationship information of the grid are extracted to obtain the physical grid information of the photobioreactor.

[0022] Step 2.2 Multiphase, Stirring Grid Supplementation

[0023] Based on the mesh defined in step 2.1, and using the aeration / stirring operation parameters of the photobioreactor obtained in step 1, the inlet boundary and / or stirring region of the photobioreactor are divided to obtain multiphase and / or dynamic mesh partitioning information. When stirring operation is present, the mesh needs to be divided into dynamic and static regions. The dynamic region includes the stirring component of the photobioreactor, while the static region consists of other regions. The dynamic and static regions are coupled at the contact interface. In subsequent calculations, the static region mesh remains stationary, while the dynamic region mesh actively rotates with the stirring component. When aeration is present, at the inlet and outlet boundaries, the corresponding regions are divided into gas inlet and outlet region boundaries according to the physical model obtained in step 1.

[0024] Step 2.3 Calculation of initial conditions for the light intensity field

[0025] Based on the initial values ​​of velocity, pressure, and phase volume fraction within the fluid computational region obtained in step 1, and the boundary values ​​of velocity, pressure, and phase volume fraction at the boundary of the fluid computational region, the parameters of the mesh boundary region and interior region are directly set; based on the initial concentration conditions and light intensity boundary conditions obtained in step 1, the initial light intensity field conditions within the photobioreactor are calculated as follows:

[0026]

[0027] Where A0 is absorbance, I0 is incident light intensity, I is local light intensity, K is a constant coefficient related to light wavelength, b is the distance from the light incident point to the local point, also known as the light path, and c is the concentration of the solution at which the light is incident; Equation (1) is the description equation of Beer Lambert's law, which describes the relationship between incident light intensity and outgoing light intensity under different concentrations and light paths. When there is no superposition between incident lights, that is, the incident light direction is parallel or the solution concentration is too high for the light to penetrate, Equation (1) is directly used to calculate the light intensity field distribution. When there is superposition of incident lights, the basic Beer Lambert's law is improved, and the light intensity field in the photobioreactor is calculated by the following discrete summation method:

[0028]

[0029] Among them, I j I represents the local light intensity at the j-th grid point, and n represents the total number of incident light points. i A represents the incident light intensity at the i-th incident point, A0 is the absorbance, and l is the distance from the i-th incident point to the j-th grid, i.e., the light path.

[0030] At this point, the preprocessing module is complete. The preprocessing module includes the grid information of the photobioreactor; initial values ​​of velocity, pressure, and phase volume fraction within the fluid computation region; and boundary values ​​of velocity, pressure, and phase volume fraction, as well as light intensity boundary conditions at the boundaries of the fluid computation region.

[0031] The specific steps of step 3 are as follows:

[0032] Step 3.1 Based on the preprocessing module constructed in Step 2, calculate the growth rate of microbial particles in the photobioreactor under the steady-state assumption: that is, couple computational fluid dynamics, light intensity transport law, and steady-state microbial growth mechanism as a coupled model. Based on the rotating mesh method in the dynamic mesh change, evolve the mesh: after each time step, the dynamic zone mesh rotates by a predetermined angle; that is, the mesh iterates at each time step iteration, changing the dynamic zone mesh while keeping the static zone mesh stationary. The connection surface between the dynamic and static zone meshes is coupled using an arbitrary mesh interface (AMI) surface to avoid mesh deformation; subsequently... The flow patterns of culture medium (liquid phase), gas (gas phase), and microorganisms (solid phase) in a photobioreactor were calculated using a three-phase model based on computational fluid dynamics. The gas and liquid phases were considered continuous phases, while the solid phase was a discrete phase. Based on the position of each microbial particle in the photobioreactor obtained from the fluid dynamics calculations, the light intensity at its local grid location was acquired. The growth rate of each microbial particle was then calculated using the steady-state growth rate formula. Finally, the average growth rate of all microbial particles in the reactor under the steady-state assumption was obtained by averaging their growth rates.

[0033] Step 3.2 Solve for the average growth parameter as the initial value for the transient solution.

[0034] The specific process of step 3.1 is as follows:

[0035] Step 3.1.1 Solve for the gas and liquid continuous phase flow using the Navier-Stokes equations to obtain the velocity and pressure flow information of the gas and liquid continuous phases:

[0036]

[0037] ρ=αρ1+(1-α)ρ2 (5)

[0038] μ m =αμ1+(1-α)μ2 (6)

[0039]

[0040] 0 < α < 1 (8)

[0041] in, ρ is the fluid velocity; ρ is the fluid density; ρ1 and ρ2 are the densities of each phase; p is the pressure; τ is the shear stress; g is gravity; f σ s is surface tension; s is the source term; μ m μ is the viscosity of the fluid; μ1 and μ2 are the viscosities of each phase; α is the volume fraction of one phase.

[0042] Step 3.1.2 After obtaining the velocity and pressure flow information of the gas and liquid continuous phases, the velocity of the discrete phase microbial particles is solved using Newton's second law:

[0043]

[0044] in, Where m is the particle velocity and m is the particle mass; It is the force exerted on the particles by the fluid; It is drag force; It is gravity; It is a pressure gradient; It is a virtual mass force; It is other forces;

[0045] Step 3.1.3 Obtain the light intensity field distribution calculated based on the law of light intensity transmission

[0046] After solving the velocity of the discrete phase microbial particles in step 3.1.2, the location of the discrete phase microbial particles is known. The local light intensity of each discrete phase microbial particle is obtained according to equation (2) and used to calculate the growth rate of each discrete phase microbial particle in the next step.

[0047] Step 3.1.4 Describe the steady-state microbial growth mechanism using photosynthetic factories (PSF) and calculate the local growth rate of each discrete phase microbial particle:

[0048] A photosynthetic factory (PSF) is the sum of a light-harvesting system, a reaction center, and related devices that produce corresponding photosynthetic products under a given light energy. PSF has three states: resting state, activated state, and inhibited state. The probabilities of PSF being in the resting state, activated state, and inhibited state are represented by growth mechanism parameters A, B, and C, respectively.

[0049] The steady-state microbial growth mechanism is derived by applying the steady-state assumption to the transient microbial growth mechanism, where the transient microbial growth mechanism equation is described as follows:

[0050]

[0051] A+B+C=1 (12)

[0052] μ=kγB-M (13)

[0053] Under the steady-state assumption, the microbial growth mechanism simultaneously satisfies this assumption:

[0054]

[0055] Substituting equation (14) into equations (10)-(13) yields the following control equation for the steady-state microbial growth mechanism. The growth rate of the particle at this point can be calculated based on the following equation:

[0056]

[0057] Where μ is the growth rate, α, β, δ, γ, k, M are all model parameters, I represents the light intensity received by the microorganisms, and the average growth rate of the photobioreactor is obtained by averaging all solid particles representing the microorganisms.

[0058] The specific process of step 3.2 is as follows:

[0059] Based on the average growth rate of all microorganisms in the photobioreactor Solving for mean growth parameters

[0060]

[0061] Subsequently, based on average growth parameters Solve for the average light intensity inside the reactor

[0062]

[0063] Equation (17) is about the independent variable The quadratic equation has two solutions. The average light intensity is constrained by the incident light boundary conditions. Then, another average growth parameter of the microorganism is calculated.

[0064]

[0065] The average value of the growth parameters obtained by the solution is used as the initial value of the transient growth parameters, thus obtaining the initial values ​​of the microbial growth mechanism parameters A and B in the photobioreactor.

[0066] The specific steps of step 4 are as follows:

[0067] Based on the coupled computational fluid dynamics, light intensity transport law, and steady-state microbial growth mechanism model described in step 3.1, and based on the historical growth characteristics of each microbial particle, i.e., the past growth mechanism parameters A, B, and C, and the light intensity value obtained in step 3.1.3, as well as the discrete time step set by the coupled model calculation, the growth parameters of each microbial particle are updated:

[0068]

[0069] A+B+C=1 (21)

[0070] μ=kγB-M (22)

[0071] Discretize it explicitly with respect to time:

[0072] A t+1 -A t =Δt(-αI t A t +γB t +δC t ) (twenty three)

[0073] B t+1 -B t =Δt(αI) t A t -γB t -βI t B t ) (twenty four)

[0074] C t+1 =1-A t -B t (25)

[0075] Among them, A, B, and C are stored separately with each microbial particle, indicated by superscript. t+1 and t Here, Δt represents the value at the current time step and the value at the previous time step, respectively, and Δt is the time step size. After updating the growth mechanism parameters A, B, and C at the current moment, the growth rate of the microbial particle can be expressed by the following formula:

[0076] μ t+1 =kγB t+1 -M (26)

[0077] After traversing all discrete-phase microbial particles in the photobioreactor, the overall growth rate of the microbial particles in the photobioreactor can be obtained by averaging the growth rates of all microbial particles.

[0078] Compared with the prior art, the beneficial effects of the present invention are:

[0079] This invention combines computational fluid dynamics, light intensity transmission, and microbial growth mechanisms, with these three elements working synergistically to enhance the model's versatility. The workflow of the coupled model of computational fluid dynamics, light intensity transmission laws, and microbial growth mechanisms can be summarized as follows:

[0080] The fluid dynamics calculation module uses a gas-liquid-solid three-phase model to calculate the flow of culture medium (liquid phase), gas (gas phase), and microorganisms (solid phase) in the photobioreactor, and implements stirring through dynamic changes in the grid.

[0081] The law of light intensity transport can be used to calculate the light intensity distribution in a photobioreactor, and an accurate solution for the high gradient distribution of light intensity in the photobioreactor can be obtained.

[0082] As the time step progresses, the transient growth mechanism parameters carried by each microbial particle are updated, and the growth rate is calculated based on the growth mechanism parameters. Since the particles store the growth parameters from the previous time step, this method specifically considers the influence of light history and light duration on growth.

[0083] The key technical point of this method lies in its modeling based on physical laws, coupling computational fluid dynamics, light intensity transmission, and microbial growth mechanisms. This results in strong versatility and expands the general applicability of growth rate prediction, enabling the model to more accurately predict the microbial growth rate in any photobioreactor. Specifically, the simulation method based on computational fluid dynamics, light intensity transmission, and microbial growth mechanisms has significant advantages and beneficial effects in the following aspects:

[0084] 1. High-precision and versatile predictive capability: By employing a modeling approach based on computational fluid dynamics, light intensity transmission, and microbial growth mechanisms, the model is derived entirely from a physical model, enabling more accurate and versatile prediction of microbial growth rates within photobioreactors. This is of great significance for the scale-up design of photobioreactors and the dynamic control of operating parameters during operation.

[0085] 2. Interpretability and Understandability: Compared to empirical coupling models and machine learning methods, this method based on physical laws can provide more interpretable results. It can reveal the relationship between microbial growth rate and factors such as shape, size, flow boundary conditions, and light intensity boundary conditions in photobioreactors, providing a deeper understanding of the scale-up design and dynamic control of operating parameters of photobioreactors.

[0086] 3. Low cost: Compared to traditional empirical coupling models, where model parameters need to be experimentally measured for different reactors and under reactors of the same size and shape, this method only needs to obtain microbial growth mechanism parameters to predict the growth rate of photobioreactors of any size, under any light conditions, and under any flow conditions. This significantly reduces experimental costs.

[0087] 4. Flexibility and scalability: This invention consists of three independent modules that are interconnected. Therefore, replacing or adding a new module will not affect the overall feasibility of the model, and it is very simple and convenient. For example, the traditional Beer-Lambert law can be improved to create a more advanced and comprehensive light intensity transmission model, or the growth mechanism can be further improved from a single-factor transient mechanism of light intensity to a two-factor model, or it can be modified to a single-factor model influenced by other factors as needed.

[0088] In summary, the simulation method based on computational fluid dynamics, light intensity transfer, and microbial growth mechanisms can effectively provide important data support, theoretical guidance, and decision-making basis for the scale-up design, operation parameter control prediction, and growth rate prediction of photobioreactors. Attached Figure Description

[0089] Figure 1 This is the overall flowchart of the algorithm of this invention.

[0090] Figure 2 This is the core flowchart of the algorithm of this invention.

[0091] Figure 3 This is an example of a physical reactor selected for this invention.

[0092] Figure 4 This is the physical model corresponding to the physical diagram of the present invention.

[0093] Figure 5 This is the mesh corresponding to the physical model of this invention. Detailed Implementation

[0094] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0095] A general model for predicting microbial growth rates in photobioreactors includes:

[0096] Preprocessing module: Acquires the physical model of the photobioreactor, the fluid computation region, the initial value of the phase volume fraction, the initial value of the microbial concentration in the fluid, the light intensity boundary conditions, the aeration / stirring mixing conditions during the operation of the photobioreactor, and the mesh generation conditions, which are used to predict the growth rate of microorganisms in the photobioreactor.

[0097] Fluid dynamics calculation module: used to calculate the gas, liquid and solid three-phase flow distribution in the photobioreactor, thereby obtaining the accurate flow distribution of solid-phase microorganisms in the photobioreactor;

[0098] Light transmission module: used to quantitatively calculate the precise distribution of light intensity within the photobioreactor;

[0099] Microbial growth rate mechanism module: accurately calculates the growth rate of microorganisms by measuring the light intensity they receive;

[0100] By obtaining the precise flow distribution of solid-phase microorganisms in the photobioreactor through the fluid dynamics calculation module and the precise light intensity distribution in the photobioreactor through the light transmission module, the light intensity received by each solid-phase microorganism in the photobioreactor is obtained. Then, the precise microbial growth rate is calculated through the microbial growth rate mechanism module, and the average growth rate of all solid-phase microbial particles in the photobioreactor is taken to obtain the precise growth rate of all microorganisms in the photobioreactor.

[0101] A general method for predicting microbial growth rates in photobioreactors, comprising the following steps:

[0102] Step 1: Based on the shape and operating parameter information of any photobioreactor, obtain the physical model of the photobioreactor; the fluid computation domain; the initial values ​​of velocity, pressure, and phase volume fraction within the fluid computation domain; the boundary values ​​of velocity, pressure, and phase volume fraction at the boundary of the fluid computation domain; the initial value of the microbial concentration in the fluid; the light intensity boundary conditions; and the aeration / stirring mixing conditions during the operation of the photobioreactor.

[0103] Step 2: Based on the physical model and computational domain obtained in Step 1, perform mesh generation. On the basis of the mesh generation, and based on the aeration / stirring mixing conditions, velocity, pressure, initial and boundary values ​​of phase volume fraction, initial conditions of microbial concentration in the fluid, and light intensity boundary conditions of the photobioreactor obtained in Step 1, construct a preprocessing module for predicting the microbial growth rate in the photobioreactor.

[0104] Step 3: Based on the preprocessing module constructed in Step 2, calculate the initial values ​​of growth parameters of microbial particles in the photobioreactor;

[0105] Step 4: Based on the preprocessing module constructed in Step 2 and the initial values ​​of microbial particle growth parameters calculated in Step 3, the growth rate of microorganisms in the photobioreactor is calculated and predicted by a coupled model of computational fluid dynamics, light intensity transmission law and microbial growth mechanism.

[0106] Furthermore, the specific method for step 2 is as follows:

[0107] 2.1 Basic Mesh Construction

[0108] Based on the principle of optimal mesh generation, the physical model obtained in step 1 is meshed:

[0109] Based on the grid size, grid skewness, grid aspect ratio, grid dynamic and static partitioning, boundary region and internal region, the physical model size and shape information of the photobioreactor is analyzed and calibrated using a grid generation platform or grid generation software. Based on the optimal grid generation principle, the physical model of the photobioreactor is gridded. For grids with high skewness and aspect ratio (i.e., poor quality) and grid flow boundary layer regions, grid refinement and re-segmentation are performed to improve the grid quality. When the automatic grid generation quality cannot be improved by the software, manual grid generation is performed. Then, the grid node, boundary, size, volume and topological relationship information are extracted to obtain the physical grid information of the photobioreactor.

[0110] 2.2 Multiphase, Stirring Grid Supplement

[0111] Based on the grid defined in step 2.1, and using the obtained aeration / stirring operation parameters of the photobioreactor, the inlet boundary or stirring region of the photobioreactor is divided to obtain multiphase or dynamic grid partitioning information. When stirring operation is present, the grid needs to be divided into dynamic and static regions. The dynamic region needs to include the reactor components that actively cause stirring behavior, while the static region is other regions. The dynamic and static regions are coupled at the contact interface. In subsequent calculation steps 3 and 4, the static region grid remains stationary, while the dynamic region grid rotates actively with the stirring device. When aeration conditions are present, at the boundary inlet and outlet, the corresponding regions are divided into gas inlet and outlet region boundaries according to the physical model obtained in step 1.

[0112] 2.3 Calculation of initial conditions for light intensity field

[0113] Based on the initial values ​​of velocity, pressure, and phase volume fraction within the fluid computational region obtained in step 1, and the boundary values ​​of velocity, pressure, and phase volume fraction at the boundary of the fluid computational region, the parameters of the mesh boundary region and the internal region are directly set. Based on the initial concentration conditions and light intensity boundary conditions obtained in step 1, the initial light intensity field conditions within the photobioreactor are calculated as follows:

[0114]

[0115] Where A0 is absorbance, I0 is incident light intensity, I is local light intensity, K is a constant coefficient related to light wavelength, b is the distance from the light incident point to the local point, also known as the light path, and c is the concentration of the solution at which the light is incident; Equation (1) is the description equation of Beer Lambert's law, which describes the relationship between incident light intensity and outgoing light intensity under different concentrations and light paths. When there is no superposition between incident lights, that is, the incident light direction is parallel or the solution concentration is too high for the light to penetrate, Equation (1) is directly used to calculate the light intensity field distribution. When there is superposition of incident lights, the basic Beer Lambert's law is improved, and the light intensity field in the photobioreactor is calculated by the following discrete summation method:

[0116]

[0117] Among them, I j I represents the local light intensity at the j-th grid point, and n represents the total number of incident light points. i A represents the incident light intensity at the i-th incident point, A0 is the absorbance, and l is the distance from the i-th incident point to the j-th grid, i.e., the light path.

[0118] At this point, the preprocessing module is complete. The preprocessing module includes the grid information of the photobioreactor, the initial values ​​of the model, and the boundary conditions (including velocity, pressure, concentration, and light intensity).

[0119] Furthermore, the specific steps of step 3 are as follows:

[0120] 3.1 Based on the preprocessing module constructed in step 2, the growth rate of microbial particles in the photobioreactor under the steady-state assumption is calculated. That is, computational fluid dynamics, light intensity transport law, and steady-state microbial growth mechanism are coupled as a coupled model. The grid is evolved according to the rotating grid method in the dynamic grid change: after each time step, the dynamic zone grid will rotate by a predetermined angle. That is, the grid is iterated at each time step iteration to change the dynamic zone grid and avoid grid deformation. Subsequently, the flow of culture medium (liquid phase), gas (gas phase), and microorganisms (solid phase) in the photobioreactor is calculated by the gas-liquid-solid three-phase model in computational fluid dynamics. Among them, the gas phase and liquid phase are continuous phases, and the solid phase is a discrete phase. According to the calculated position of each microorganism in the photobioreactor, the light intensity at its local grid is obtained, and the growth rate of each microorganism is calculated according to the steady-state growth rate calculation formula. By averaging the growth rates of all microorganisms in the reactor, the average growth rate of microorganisms in the reactor under the steady-state assumption can be obtained.

[0121] Since the stirred tank is a rotating vessel, the rotating mesh method iterates the mesh at each time step, changing the mesh in the active agitator region to achieve an accurate transient solution for each time step. The sliding mesh model is theoretically the most accurate method for simulating rotating flow, correctly describing the entire transient start-up process. It generates two separate mesh regions: the first is a cylindrical mesh containing the rotating components (inner region), and the second is the rest of the mesh (outer region). Each mesh region is defined by an interface connecting the opposing mesh regions. These two mesh regions slide relative to each other along the mesh interface in discrete steps. The arbitrary mesh interface (AMI) operates by projecting the geometry of one interface onto the other. The two mesh regions are geometrically separate but numerically connected by the AMI, ensuring that the general field value is the same on both sides of the interface. The outer mesh does not move during the calculation, while the inner mesh rotates during the simulation. After each time step, the inner mesh rotates by a predetermined angle, thus correctly reproducing the motion of the gear face. The advantage of the rotating mesh method is that it ensures optimal accuracy while avoiding mesh distortion.

[0122] The specific steps are as follows:

[0123] 3.1.1 Solve for the gas-liquid continuous phase flow using the Navier-Stokes equations. Taking the gas-liquid two-phase model described by the VOF method as an example, obtain the velocity and pressure flow information of the gas-liquid continuous phases:

[0124]

[0125] ρ=αρ1+(1-α)ρ2#(5)

[0126] μ m =αμ1+(1-α)μ2#(6)

[0127]

[0128] 0 < α < 1#(8)

[0129] in, ρ is the fluid velocity; ρ is the fluid density; ρ1 and ρ2 are the densities of each phase; p is the pressure; τ is the shear stress; g is gravity; f σ s is surface tension; s is the source term; μ m μ is the viscosity of the fluid; μ1 and μ2 are the viscosities of each phase; α is the volume fraction of one phase.

[0130] 3.1.2 After obtaining the velocity and pressure flow information of the gas and liquid continuous phases, the velocity of the discrete phase microorganisms (solid phase) is solved using Newton's second law:

[0131]

[0132] in, Where m is the particle velocity and m is the particle mass; It is the force exerted on the particles by the fluid; It is drag force; It is gravity; It is a pressure gradient; It is a virtual mass force; It is other forces;

[0133] 3.1.3 Obtaining the light intensity field distribution calculated based on the law of light intensity transmission

[0134] After solving the velocity of the discrete phase microbial particles in step 3.1.2, the location of the discrete phase microbial particles is known. The local light intensity of each discrete phase microbial particle is obtained according to equation (2) and used to calculate the growth rate of each discrete phase microbial particle in the next step.

[0135] 3.1.4 Describing the steady-state microbial growth mechanism using photosynthetic factories (PSFs) and calculating the local growth rate of each discrete-phase microbial particle:

[0136] A photosynthetic factory (PSF) is the sum of a light-harvesting system, a reaction center, and related devices that produce corresponding photosynthetic products under a given light energy. PSF has three states: resting state, activated state, and inhibited state. The probabilities of PSF being in the resting state, activated state, and inhibited state are represented by growth mechanism parameters A, B, and C, respectively.

[0137] The steady-state microbial growth mechanism is derived by applying the steady-state assumption to the transient microbial growth mechanism, where the transient microbial growth mechanism equation is described as follows:

[0138]

[0139] A+B+C=1 (12)

[0140] μ=kγB-M (13)

[0141] A quiescent PSF can be stimulated and transitioned to an activated state by capturing a photon. An activated PSF has two possible paths: either it receives another photon to be inhibited, or it transfers the acquired energy to a receptor to initiate photosynthesis and then returns to the quiescent state. Meanwhile, an inhibited PSF can recover to the quiescent state. Since nutrient saturation is guaranteed, light is the only variable. The reaction rate involved in each photon transition (i.e., A→B and B→C) is assumed to be a first-order function of the photon flux density. The other two processes are assumed to be zero-order.

[0142] Under the steady-state assumption, the microbial growth mechanism simultaneously satisfies this assumption:

[0143]

[0144] Substituting equation (14) into equation 10-13 yields the following control equation for the steady-state microbial growth mechanism. The growth rate of the particle at this point can be calculated based on the following equation:

[0145]

[0146] Where μ is the growth rate, α, β, δ, γ, k, and M are model parameters that are related to the species of microorganisms and all external environments except light intensity during their growth process, and I represents the light intensity received by the microorganisms. The average growth rate of the photobioreactor is obtained by averaging the solid particles representing all microorganisms.

[0147] 3.2 Solve for the average growth parameter as the initial value for the transient solution:

[0148] Based on the average growth rate of all microorganisms in the photobioreactor Solving for mean growth parameters

[0149]

[0150] Subsequently, based on average growth parameters Solve for the average light intensity inside the reactor

[0151]

[0152] Equation (17) is about the independent variable The quadratic equation has two solutions. The average light intensity is constrained by the incident light boundary conditions. Then, another average growth parameter of the microorganism is calculated.

[0153]

[0154] The average value of the growth parameters obtained by the solution is used as the initial value of the transient growth parameters, thus obtaining the values ​​of the initial values ​​of microbial growth parameters A and B in the reactor.

[0155] Furthermore, the specific steps of step 4 are as follows:

[0156] Based on the coupled computational fluid dynamics, light intensity transport law, and steady-state microbial growth mechanism model described in step 3.1, and based on the historical growth characteristics of each microbial particle, i.e., the past growth mechanism parameters A, B, and C, and the light intensity value obtained in step 3.1.3, as well as the discrete time step set by the coupled model calculation, the growth parameters of each microbial particle are updated:

[0157]

[0158] A+B+C=1 (21)

[0159] μ=kγB-M (22)

[0160] Explicitly discretizing it with respect to time yields the following equation:

[0161] A t+1 -A t =Δt(-αI t A t +γB t +δC t ) (twenty three)

[0162] B t+1 -B t =Δt(αI) t A t -γB t -βI t B t ) (twenty four)

[0163] C t+1 =1-A t -B t (25)

[0164] Where A, B, and C represent the probabilities of each of the three stages describing the growth mechanism of a single microorganism, and are stored separately with each particle. (Superscript) t+1 and t Here, Δt represents the value at the current time step and the value at the previous time step, respectively, and Δt is the time step size. After updating the growth parameters A, B, and C at the current moment, the growth rate of the particle can be expressed by the following formula:

[0165] μ t+1 =kγB t+1 -M (26)

[0166] After traversing all discrete phase particles in the photobioreactor, the overall growth rate of the photobioreactor can be obtained by averaging the growth rates of all particles.

[0167] The overall process framework of this invention is as follows: Figure 1As shown, the core algorithm flow is as follows: Figure 2 As shown.

[0168] Firstly, for any photobioreactor, this example uses, as follows: Figure 3 The physical model of the photobioreactor shown is extracted as follows: Figure 4 The mesh generation results are as follows Figure 5 As shown in the figure, we selected the gas-liquid fluid region inside the reactor as the computational domain, and its physical dimensions and shape were obtained through measurement. Simultaneously, a stirring impeller is located at the center of the reactor, along with a gas-liquid interface. First, we meshed the entire fluid region. After obtaining a high-quality mesh, we supplemented the multiphase inlet / outlet regions and the stirring mesh. The top of the computational domain, i.e., the top of the reactor, was designated as the gas outlet region. Since no aeration was used in this example, no inlet setting was implemented. Regarding the supplementation of the stirring mesh, we first defined a cylindrical region outside the impeller, ensuring that this region completely enclosed the stirring device. This region was designated as the moving region of the mesh, and the remaining region was designated as the static region. The connection surface between the two regions was then coupled using an AMI surface.

[0169] Secondly, based on the physical conditions and operating conditions, the actual initial and boundary conditions are obtained. Since the reactor has no inlet setting, the inlet, including the wall surface, is set to a no-slip boundary condition; the outlet is set to a pressure outlet boundary condition; the dynamic-static mesh coupling boundary is set to a sliding mesh velocity boundary condition; the agitator is set to a moving wall velocity boundary condition, with the value matching the rotational speed of the moving mesh; and the agitator shaft is set to a rotating wall velocity boundary condition, with its angular velocity matching the rotational speed of the moving mesh. Simultaneously, the phase volume fraction is set according to the inoculated liquid level height: areas below the liquid level are designated as the liquid phase, and areas above the liquid level are designated as the gas phase.

[0170] The initial concentration value was selected from the concentration value after inoculation on day zero of the experiment. The light intensity boundary condition was the value obtained from the experimental light intensity measurement. Subsequently, the light intensity distribution within the photobioreactor was calculated based on the multi-light source method.

[0171]

[0172] Since this case uses a circular lighting method, the above formula can be simplified to:

[0173]

[0174] in, I0 is the incident light intensity, I(r) is the local light intensity at a distance r from the center of the cylinder, A0 is the absorbance, l(r,θ) is the light path from any incident point to a distance r from the center of the cylinder, and θ is the angle between the line of the light path and the diameter of the local point. Based on this, the light intensity field distribution inside the reactor can be solved. This completes the preprocessing module for the model.

[0175] After obtaining the model preprocessing module, it is necessary to solve for the initial conditions of microbial particle growth parameters. Here, the steady-state growth rate of the model needs to be solved first. The velocity distribution of the gas-liquid continuous phase fluid is solved by the following set of equations:

[0176]

[0177] ρ=αρ 1 +(1-α)ρ2#

[0178] μ m =αμ1+(1-α)μ2#

[0179]

[0180] 0 < α < 1#

[0181] After obtaining the velocity distribution of the continuous phase fluid, the velocity and position distribution of the discrete phase particles are calculated using the following equations:

[0182]

[0183] After calculating the flow characteristics such as velocity and position of discrete-phase microorganisms (solid phase) using computational fluid dynamics, the local light intensity of each discrete-phase microbial particle is obtained. Based on the local light intensity of the grid where all particles are located at different times, the growth rate of each particle is solved.

[0184]

[0185] The average of all growth rates is then calculated, and the value at the steady-state stage is selected as the steady-state growth rate of the reactor. The initial value of the growth parameter B is then calculated using the following formula:

[0186]

[0187] After obtaining the initial value of B, the characteristic light intensity is solved using the following formula:

[0188]

[0189] The two light intensity values ​​obtained are constrained based on the surface light intensity, and a characteristic light intensity value that conforms to the actual value is selected. Then, the growth characteristic parameter A is solved using the selected characteristic light intensity.

[0190]

[0191] At this point, all initial values ​​for growth characteristic parameters are obtained. These values ​​are then assigned to the growth characteristic parameters of all discrete phase particles representing microorganisms in the reactor, and the transient growth rate prediction calculation begins. The calculation process is as follows: Figure 2 As shown, the PIMPLE velocity-pressure iterative algorithm is first used to solve the Navier-Stokes equations. The inner loop includes dynamic feature evolution of the mesh, changing the mesh topology and shape, followed by calculating the phase volume fractions of the gas and liquid phases. Then, the velocity and pressure fields of the continuous phase are iteratively solved, and the inner loop ends. Next, the force on each particle is calculated based on its mesh location. After obtaining the force, the particle acceleration is calculated, and the velocity and coordinates are updated. Combined with the time each particle spends under its specified light intensity, the growth parameters of the particle are updated using the following formula:

[0192] A t+1 -A t =Δt(-αI t A t +γB t +δC t )

[0193] B t+1 -B t =Δt(αI) t A t -γB t -βI t B t )

[0194] C t+1 =1-A t -B t

[0195] The growth rate is calculated using the updated parameters according to the following formula:

[0196] μ t+1 =kγB t+1 -M

[0197] The dynamically stable value was selected as the growth rate value under each condition.

[0198] The following table compares the model's predicted values ​​with the experimental values ​​and the aforementioned steady-state values:

[0199] growth rate OD = 0.1 OD = 0.5 OD = 1.0 OD = 1.5 This model 1.95e-5 7.0e-6 2.0e-6 -5.0e-7 steady-state model 1.82e-5 3e-6 -0.5e-6 -1.7e-6 Experimental values 1.99e-5 6.85e-6 2.10e-6 <0

[0200] The comparison shows that the growth rate predictions of this transient model at the four characteristic concentrations selected throughout the experimental growth process are close to the experimentally measured growth rates, especially at medium to high concentrations (OD = 0.5, 1.0), where the model prediction error is significantly reduced compared to the steady-state model. This also verifies the limitations of the aforementioned steady-state assumption, namely that when microorganisms are exposed to varying light intensities, they can instantly transform into steady-state growth characteristics under those light intensities. This is only applicable to low-concentration conditions with relatively uniform light intensity distribution. For medium to high concentrations, the model's prediction accuracy is greatly reduced due to the strong non-uniformity of light intensity distribution. Our model, by eliminating the steady-state assumption and calculating based on the entire transient growth mechanism, significantly improves the accuracy of model predictions.

Claims

1. A universal method for predicting microbial growth rate in a photobioreactor, characterized in that, The specific steps are as follows: Step 1: Based on the shape and operating parameter information of any photobioreactor, obtain the physical model of the photobioreactor; the fluid computation domain; the initial values ​​of velocity, pressure, and phase volume fraction within the fluid computation domain; the boundary values ​​of velocity, pressure, and phase volume fraction at the boundary of the fluid computation domain; the initial value of the microbial concentration in the fluid; the light intensity boundary conditions; and the aeration / stirring mixing conditions during the operation of the photobioreactor. Step 2: Based on the physical model and fluid computation region obtained in Step 1, perform mesh generation. On the basis of the mesh generation, and based on the mixing conditions of aeration / stirring during the operation of the photobioreactor obtained in Step 1, the initial values ​​of velocity, pressure, and phase volume fraction in the fluid computation region, the boundary values ​​of velocity, pressure, and phase volume fraction at the boundary of the fluid computation region, the initial value of microbial concentration in the fluid, and the light intensity boundary conditions, construct a preprocessing module for predicting the growth rate of microorganisms in the photobioreactor. Step 3: Based on the preprocessing module constructed in Step 2, calculate the initial values ​​of growth parameters of microbial particles in the photobioreactor; Step 4: Based on the preprocessing module constructed in Step 2 and the initial values ​​of microbial particle growth parameters calculated in Step 3, the microbial growth rate in the photobioreactor is calculated and predicted using a coupled model of computational fluid dynamics, light intensity transport law, and microbial growth mechanism. Based on the historical growth characteristics of each microbial particle (i.e., the past growth mechanism parameters A, B, and C), the light intensity value calculated in Step 3, and the discrete time step set by the coupled model, the growth parameters of each microbial particle are updated. （19） （20） （21） （22） Discretize it explicitly with respect to time: （23） （24） （25） Among them, A, B, and C are stored separately with each particle, indicated by superscript. t+1 and t These are the values ​​at the current time step and the previous time step, respectively. Let A be the time step; after updating the growth mechanism parameters A, B, and C at the current moment, the growth rate of the particle can be expressed by the following formula: （26） After traversing all discrete phase particles in the photobioreactor, the overall growth rate of the photobioreactor can be obtained by averaging the growth rates of all particles.

2. The method for predicting the growth rate of microorganisms in a photobioreactor according to claim 1, characterized in that, The specific method for step 2 is as follows: Step 2.1 Basic Mesh Construction Based on the principle of optimal mesh generation, the physical model obtained in step 1 is meshed: The physical model dimensions of the photobioreactor are calibrated based on grid size, grid skewness, grid aspect ratio, grid dynamic and static partitioning, boundary region and internal region. Based on the optimal grid division principle, the physical model of the photobioreactor is gridded. For grids with high skewness and aspect ratio (i.e., poor quality) and grid flow boundary regions, grid refinement and re-segmentation are performed to improve the grid division quality. Then, the node, boundary, size, volume and topological relationship information of the grid are extracted to obtain the physical grid information of the photobioreactor. Step 2.2 Multiphase, Stirred Grid Supplementation Based on the mesh defined in step 2.1, and using the aeration / stirring operation parameters of the photobioreactor obtained in step 1, the inlet boundary and / or stirring region of the photobioreactor are divided to obtain multiphase and / or dynamic mesh partitioning information. When stirring operation is present, the mesh needs to be divided into dynamic and static regions. The dynamic region includes the stirring component of the photobioreactor, while the static region consists of other regions. The dynamic and static regions are coupled at the contact interface. In subsequent calculations, the static region mesh remains stationary, while the dynamic region mesh actively rotates with the stirring component. When aeration is present, at the inlet and outlet boundaries, the corresponding regions are divided into gas inlet and outlet region boundaries according to the physical model obtained in step 1. Step 2.3 Calculation of initial conditions for the light intensity field Based on the initial values ​​of velocity, pressure, and phase volume fraction within the fluid computational region obtained in step 1, and the boundary values ​​of velocity, pressure, and phase volume fraction at the boundary of the fluid computational region, the parameters of the mesh boundary region and interior region are directly set; based on the initial concentration conditions and light intensity boundary conditions obtained in step 1, the initial light intensity field conditions within the photobioreactor are calculated as follows: （1） in, It is absorbance. It is the intensity of the incident light. It is the local light intensity. It is a constant coefficient related to the wavelength of light. It is the distance from the point of light incidence to the local point, also known as the optical path. It is the concentration of the solution at which light is incident; Equation (1) is the describing equation of Beer Lambert's law, which describes the relationship between the incident light intensity and the outgoing light intensity under different concentrations and light paths. When there is no superposition between incident lights, that is, the incident light direction is parallel or the solution concentration is too high for light to penetrate, Equation (1) is directly used to calculate the light intensity field distribution. When there is superposition of incident lights, the basic Beer Lambert's law is improved, and the light intensity field in the photobioreactor is calculated by the following discrete summation method: in, represents the local light intensity at the j-th grid point, and n represents the total number of incident light points. Representing the The intensity of incident light at each incident point It is absorbance. It is the first From the first incident point to the second The distance between each grid point, i.e., the optical path; At this point, the preprocessing module is complete. The preprocessing module includes the grid information of the photobioreactor; initial values ​​of velocity, pressure, and phase volume fraction within the fluid computation region; and boundary values ​​of velocity, pressure, and phase volume fraction, as well as light intensity boundary conditions at the boundaries of the fluid computation region.

3. The method for predicting the growth rate of microorganisms in a photobioreactor according to claim 1, characterized in that, The specific steps of step 3 are as follows: Step 3.1 Based on the preprocessing module constructed in Step 2, calculate the growth rate of microbial particles in the photobioreactor under the steady-state assumption: that is, couple computational fluid dynamics, light intensity transmission law and steady-state microbial growth mechanism as a coupling model, and evolve the mesh according to the rotating mesh method in the dynamic mesh change: after each time step, the dynamic zone mesh will rotate at a predetermined angle, that is, the mesh is iterated at each time step iteration, changing the dynamic zone mesh while the static zone mesh remains unchanged, and the connection surface between the dynamic zone mesh and the static zone mesh is coupled with the arbitrary mesh interface (AMI) surface to avoid mesh deformation; Subsequently, the flow of culture medium (liquid phase), gas (gas phase), and microorganisms (solid phase) in the photobioreactor was calculated using a three-phase model in computational fluid dynamics. The gas and liquid phases were considered continuous phases, while the solid phase was a discrete phase. Based on the position of each microbial particle in the photobioreactor obtained from the fluid dynamics calculations, the light intensity at its local grid location was acquired. The growth rate of each microbial particle was then calculated using the steady-state growth rate formula. By averaging the growth rates of all microbial particles in the reactor, the average growth rate of the microbial particles in the reactor under the steady-state assumption was obtained. Step 3.2 Solve for the average growth parameter as the initial value for the transient solution.

4. The method for predicting the growth rate of microorganisms in a photobioreactor according to claim 3, characterized in that, The specific process of step 3.1 is as follows: Step 3.1.1 Solve for the gas and liquid continuous phase flow using the Navier-Stokes equations to obtain the velocity and pressure flow information of the gas and liquid continuous phases: in, It is the velocity of the fluid; It is the density of the fluid; , It is the density of each phase; It is pressure; It is shear stress; It is gravity; It is surface tension; It is the source term; It is the viscosity of the fluid; , It is the viscosity of each phase; It is the volume fraction of one of the phases; Step 3.1.2 After obtaining the velocity and pressure flow information of the gas and liquid continuous phases, the velocity of the discrete phase microbial particles is solved using Newton's second law: in, It's particle velocity. It refers to particle mass; It is the force exerted on the particles by the fluid; It is drag force; It is gravity; It is a pressure gradient; It is a virtual mass force; It is other forces; Step 3.1.3 Obtain the light intensity field distribution calculated based on the law of light intensity transmission After solving the velocity of the discrete phase microbial particles in step 3.1.2, the location of the discrete phase microbial particles is known. The local light intensity of each discrete phase microbial particle is obtained according to equation (2) and used to calculate the growth rate of each discrete phase microbial particle in the next step. Step 3.1.4 Describe the steady-state microbial growth mechanism using photosynthetic factories (PSF) and calculate the local growth rate of each discrete phase microbial particle: A photosynthetic factory (PSF) is the sum of a light-harvesting system, a reaction center, and related devices that produce corresponding photosynthetic products under a given light energy. PSF has three states: resting state, activated state, and inhibited state. The probabilities of PSF being in the resting state, activated state, and inhibited state are represented by growth mechanism parameters A, B, and C, respectively. The steady-state microbial growth mechanism is derived by applying the steady-state assumption to the transient microbial growth mechanism, where the transient microbial growth mechanism equation is described as follows: （10） （11） （12） （13） Under the steady-state assumption, the microbial growth mechanism simultaneously satisfies this assumption: Substituting equation (14) into equations (10)-(13) yields the following steady-state microbial growth mechanism control equation. The growth rate of the particle at this time can be calculated based on the following equation: in, For growth rate, All of these are model parameters. The average growth rate of the photobioreactor is obtained by averaging the light intensity received by all solid particles representing microorganisms.

5. The method for predicting the growth rate of microorganisms in a photobioreactor according to claim 3, characterized in that, The specific process of step 3.2 is as follows: Based on the average growth rate of all microorganisms in the photobioreactor Solving for mean growth parameters : （16） Subsequently, based on average growth parameters Solve for the average light intensity inside the reactor : （17） Wherein, equation (17) is about the independent variable The quadratic equation has two solutions. The average light intensity is constrained by the incident light boundary conditions. Then, another average growth parameter of the microorganism is calculated. : （18） The average value of the growth parameters obtained by the solution is used as the initial value of the transient growth parameters, thus obtaining the initial values ​​of the microbial growth mechanism parameters A and B in the photobioreactor.

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