Microbial mineralization process regulation method, device, equipment and medium

Abstract

The present application relates to the technical field of bioinformatics, and discloses a microorganism mineralization process regulation method, device, equipment and medium. The present application constructs a MICP dynamic system model, abstracts a few key state variables from the complex MICP physical-biological-chemical process, establishes a set of ordinary differential equations describing the interaction relationship of the state variables, clearly demarcates the function life and function death boundaries of the MICP process, converts the mathematical inequality constraints in the model, divides the space spanned by the state variables into a feasible region and an infeasible region, identifies the successful or failed attractors and the key critical manifold in the space by using the dynamic system theory, and monitors the trajectory of the process state in the feasibility space in real time or offline. When the trajectory approaches the critical manifold, a warning is triggered, and the input regulation parameter is adjusted to make the state trajectory away from the failure manifold and guide to the successful attractor. The present application improves the mineralization accuracy.

Description

Technical Field

[0001] This invention belongs to the field of bioinformatics technology, specifically relating to a method, apparatus, equipment, and medium for regulating microbial mineralization processes. Background Technology

[0002] Microbial-induced calcium carbonate precipitation (MICP) is an environmental biotechnology with broad application prospects. By utilizing the metabolic activities of microorganisms (mainly urease-positive bacteria), urea is hydrolyzed and combined with calcium ions to generate calcium carbonate precipitate in porous media, thereby achieving engineering goals such as soil and rock reinforcement, crack repair, seepage prevention and plugging, and cultural relic protection.

[0003] While MICP technology has demonstrated its potential in laboratory and field trials, the core bottleneck in its transition from laboratory to large-scale, reliable engineering applications lies in the unpredictability and extensive control of the process. Current technologies for optimizing MICP strategies (such as bacterial concentration, cementing solution concentration, injection rate, and cycle intervals) primarily rely on numerous repetitive column experiments, employing a trial-and-error approach to observe the reinforcement effects (such as strength and uniformity) under different schemes. This is a "black box" or "grey box" operating mode. This method is costly and time-consuming. Furthermore, while the two main failure modes in MICP—"biological inactivation" and "premature pore blockage"—are widely recognized, our understanding of when and under what conditions they occur is qualitative and retrospective. Typically, failure is traced back to the source through profiling analysis after poor reinforcement results. For failure tracing, although some mathematical models for MICP have been developed, including detailed models based on reaction-transport equations, these models are mainly used for post-event explanation of phenomena or numerical simulations of complex scenarios. They are usually computationally expensive, have many parameters, and are highly complex. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this invention is to provide a method, apparatus, equipment and medium for regulating the microbial mineralization process.

[0005] According to one aspect of this application, a method for regulating a microbial mineralization process is disclosed, the method comprising: Identify several key state variables of the microorganisms to be mineralized; Construct the ordinary differential equations for the evolution of each key state variable over time to obtain the initial set of ordinary differential equations; The initial set of ordinary differential equations is simplified and preprocessed to obtain the target set of ordinary differential equations; By assigning fixed parameters and control parameters to the objective set of the ordinary differential equation system, a dynamic system model is constructed. Define microbial functional feasibility constraints, physical transport feasibility constraints, and chemical environment feasibility constraints for the dynamic system model; The intersection region of the microbial functional feasibility constraints, physical transport feasibility constraints, and chemical environment feasibility constraints in the multidimensional state space is determined as the mineralization feasibility region of the microorganism to be mineralized, wherein the multidimensional state space is determined based on the number of key state variables. Based on the dynamic system model and the mineralization feasibility region, the microorganisms to be mineralized are subjected to mineralization treatment in a porous medium, and at least one critical manifold in the multidimensional state space used to separate different process final states is identified during the mineralization process. Real-time monitoring data reflecting the key state variables during the mineralization process are acquired and mapped to the multidimensional state space to obtain real-time state points; A first control characterization value is determined for the boundary between the real-time state point and the critical manifold, and a second control characterization value is determined for the boundary between the real-time state point and the mineralization feasibility region. When either the first or the second control characterization value is less than its corresponding preset warning threshold, the control parameter is adjusted to adjust the mineralization process within the mineralization feasibility range.

[0006] In some embodiments, the key state variables include at least two of microbial activity, urea concentration, mineral deposition volume fraction, and ammonium ion concentration. The construction of ordinary differential equations (ODEs) for the time evolution of each key state variable to obtain an initial set of ODEs includes: We constructed ordinary differential equations for microbial activity, urea concentration, mineral sedimentation volume fraction, and ammonium ion concentration, respectively. The ordinary differential equation for microbial activity is as follows: ; In the formula, The maximum specific activity change rate The study simulated the self-sustaining and saturation effects of activity. It is a suppression function, for example ,in The suppression constant, The Hill coefficient characterizes the toxicity of ammonium ions; The deactivation rate constant is It is a stress function. Characterizing the coupling of calcite saturation index and other parameters; The ordinary differential equation for urea concentration is: ; In the formula, For the maximum reaction rate, Michaelis constant, reaction rate and microbial functional activity Proportional For the injection flow rate, The concentration of the injected solution, The current porosity, ; The ordinary differential equation for the volume fraction of mineral sediments is: ; In the formula, Let be the precipitation rate constant. This is a yield coefficient used to convert the number of moles of calcium carbonate produced per unit of urea consumed into a volume fraction. This is the empirical sedimentation rate formula. The saturation index of calcite. , It is 1 or 2. Let be a Heaviside function, indicating that only if Precipitation only occurs when the temperature is >1; The ordinary differential equation for ammonium ions is: ; In the formula, Urea hydrolysis produces ammonium ions; each mole of urea hydrolyzes to produce 2 moles of ammonium ions. This refers to the convective discharge term of ammonium ions carried out by the fluid. For the injection flow rate, The current porosity, .

[0007] In some embodiments, the simplification preprocessing of the initial set of ordinary differential equations to obtain the target set of ordinary differential equations includes: The terms in the ordinary differential equation that characterize the fluid diffusion gradient in the porous medium are represented as zero or equivalent dispersion coefficients. Coupling calcium ion concentration with urea concentration simplifies the calculation path for mineral precipitation kinetics. According to the target constraint requirements, the inhibition term corresponding to the target constraint requirements is characterized as zero, and the target constraint requirements represent the objective constraints that the mineralization process is required to achieve.

[0008] In some embodiments, the microbial functional feasibility constraint is In the formula, A represents microbial functional activity. The activity threshold is the limit value characterizing whether the microbial community can maintain a sufficient hydrolysis rate to drive effective mineralization; the physical transport feasibility constraint is... In the formula, The effective porosity of a porous medium. The initial porosity of the porous medium. The volume fraction of mineral sedimentation is denoted as . The porosity critical threshold characterizes the minimum permeability acceptable for mineralization engineering, with chemical environmental feasibility constraints as follows. ,as well as In the formula, This refers to the concentration of ammonium ions. This represents the maximum inhibition threshold for ammonium ions; Among them, effective porosity The determination method and effectiveness judgment include: effective porosity Defined as the ratio of the pore volume available for free fluid flow in a porous medium to the total volume, i.e. ,in The initial porosity of the porous medium. For mineral sediment volume fraction, when ≥ When the porous medium is determined to have effective transport capacity, the fluid permeability is not lower than the minimum acceptable threshold for engineering, reactants such as urea and calcium ions can be effectively transported to the reaction site, and the product ammonium ions can be discharged in a timely manner; when < At this point, the fluid permeability drops sharply, the mass transfer capacity is insufficient, and the constraint determining the feasibility of physical transport is violated. The porosity threshold can be determined in the following ways: based on seepage theory, the critical porosity threshold can be determined by experimental analysis of the relationship between soil permeability and porosity; or, based on engineering requirements, the porosity corresponding to the minimum acceptable permeability can be calculated by back-calculating the upper limit of the injection pressure; or, based on a pore network model, the porosity corresponding to the seepage threshold can be determined by numerical simulation.

[0009] In some embodiments, the mineralization feasibility zone is: .

[0010] In some embodiments, the mineralization treatment of the microorganisms to be mineralized in the porous medium based on the dynamic system model and the mineralization feasibility region, and the identification of at least one critical manifold in the multidimensional state space used to separate different process final states during the mineralization process, includes: In the multidimensional state space, the mineralization feasibility region is geometrically decomposed to distinguish the initial state leading to different process final states and their corresponding evolution paths. The initial state is the combination of values ​​of multiple key state variables at the start of the mineralization process, and the evolution path is the trajectory of each key state variable changing over time during the mineralization process. Based on the initial state and its corresponding evolution path, at least one system attractor of the dynamic system model is located in the multidimensional state space. The system attractor includes a successful attractor representing a successful mineralization steady state and a failure attractor representing process failure. In the multidimensional state space, at least one critical manifold is identified that separates the successful attractor from the failed attractor, or separates the trajectories leading to different attractors, wherein the critical manifold is at least one of a mortality manifold, an ordering manifold, or a collapse manifold.

[0011] In some embodiments, the real-time acquisition of monitoring data reflecting the key state variables during the mineralization process and mapping it to the multidimensional state space to obtain real-time state points includes: Real-time acquisition of monitoring data reflecting the key state variables during the mineralization process, the monitoring data including at least one or more combinations of pore fluid pH, conductivity, injection pressure, outlet flow rate, and urea and ammonium ion concentrations obtained through periodic sampling and analysis; Based on the dynamic system model, the monitoring data is input to the state observer for online estimation and data fusion to obtain real-time estimates of key state variables; The real-time estimated value is used as coordinates and mapped onto the multidimensional state space to form dynamically updated real-time state points.

[0012] According to another aspect of this application, a device for regulating a microbial mineralization process is also disclosed, the device comprising: The key state variable determination module is used to determine multiple key state variables of the microorganism to be mineralized; The module for determining the initial set of ordinary differential equations is used to construct the ordinary differential equations for the evolution of each key state variable over time, thereby obtaining the initial set of ordinary differential equations. The ordinary differential equation target set determination module is used to perform simplification preprocessing on the initial set of ordinary differential equations to obtain the ordinary differential equation target set; The dynamic system model construction module is used to assign fixed parameters and control parameters to the objective set of the ordinary differential equation system to construct the dynamic system model; The feasibility constraint definition module is used to define microbial functional feasibility constraints, physical transport feasibility constraints, and chemical environment feasibility constraints for the dynamic system model. The mineralization feasibility region determination module is used to determine the intersection region between the microbial functional feasibility constraints, physical transport feasibility constraints and chemical environment feasibility constraints in the multidimensional state space as the mineralization feasibility region of the microorganism to be mineralized, wherein the multidimensional state space is determined based on the number of key state variables. A critical manifold identification module is used to perform mineralization treatment on the microorganisms to be mineralized in a porous medium based on the dynamic system model and the mineralization feasibility region, and to identify at least one critical manifold in the multidimensional state space used to separate different process final states during the mineralization process. The real-time state point acquisition module is used to acquire monitoring data reflecting the key state variables during the mineralization process in real time, and map them into the multi-dimensional state space to obtain real-time state points. The regulation characterization value determination module is used to determine a first regulation characterization value of the boundary between the real-time state point and the critical manifold, and a second regulation characterization value of the boundary between the real-time state point and the mineralization feasibility region. The adjustment module is used to adjust the control parameters when either the first control characterization value or the second control characterization value is less than its corresponding preset warning threshold, so as to adjust the mineralization process within the mineralization feasibility area.

[0013] According to another aspect of this application, an electronic device is also disclosed, the electronic device including a memory and at least one processor, the memory storing instructions; the at least one processor invokes the instructions in the memory to cause the electronic device to perform various steps of the microbial mineralization process regulation method as described in any of the preceding claims.

[0014] According to another aspect of this application, a computer-readable storage medium is also disclosed, wherein instructions are stored on the computer-readable storage medium, which, when executed by a processor, implement the various steps of the microbial mineralization process regulation method as described in any of the preceding claims.

[0015] The present invention includes, but is not limited to, the following beneficial effects: (1) This scheme transforms the complex dynamics of bio-chemical-physical multi-field coupling in the process of microbial mineralization (MICP) into a low-dimensional, analytical, and easily controllable mathematical model through a progressive modeling process of key state variable screening → initial set of ordinary differential equations → simplified preprocessing → parameter assignment → dynamic system model. Compared with traditional empirical trial and error or high-dimensional black box models, this model retains the dynamic laws of the core processes (microbial activity, substrate concentration, mineral precipitation, environmental constraints) and significantly reduces the dimensionality and analysis difficulty, providing a clear mathematical basis for subsequent feasibility analysis, critical manifold identification, and real-time control; (2) This scheme defines the mineralization feasibility region, which includes the feasibility of microbial function (e.g., activity ≥ critical value), physical transport feasibility (e.g., pores not being blocked), and chemical environment feasibility (e.g., inhibitors ≤ tolerance limit). In the intersection region of the multidimensional state space, it is quantified as the safe operating area of ​​the system. This region clarifies the geometric boundary of the mineralization process, which can succeed or fail. This allows engineers to intuitively judge whether the current state is safe and whether the process has a risk of failure, thus solving the ambiguity problem of judging the safety margin based on experience in traditional methods. (3) This scheme finds the critical manifold that separates the successful final state and the failed final state in the state space. Combined with the dual threshold early warning mechanism and dynamic parameter adjustment, it realizes the process control from post-remediation to pre-warning + dynamic correction, which improves the reliability and economy of the project. (4) This scheme constructs a framework of state variables-constraints-model-control. It does not depend on specific microbial species, porous media types or mineralization targets. It can quickly adapt to different engineering needs by redefining key state variables, constraint thresholds and control parameters for specific scenarios. It has strong universality and scalability. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0017] Figure 1 This is a flowchart of the microbial mineralization process regulation method according to an embodiment of this application; Figure 2 This is a structural block diagram of the microbial mineralization process control device according to an embodiment of this application; Figure 3 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0018] The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0019] For ease of understanding, the specific process of the embodiments of the present invention will be described below. Figure 1 This is a flowchart of the microbial mineralization process control method according to an embodiment of this application. (See attached document.) Figure 1 It includes the following steps: S100: Determine several key state variables of the microorganisms to be mineralized.

[0020] Key state variables are the logical starting point and technical foundation for constructing a dynamic system model of the microbial-induced calcium carbonate precipitation (MICP) process. Their core objective is to abstract, from the complex bio-chemical-physical coupling process, the minimum set of variables that characterizes the core functional states of the system, determines the success or failure of the process, and can be mathematically described and monitored. These variables will serve as the coordinate axes of the state space, used for subsequent description, analysis, and control of the entire mineralization process.

[0021] For example, based on the reaction mechanism and main failure modes of MICP, this example selects the following 2 to 4 variables to form the state vector X. These variables constitute the minimum sufficient set for whether effective mineralization can continue and whether failure will occur.

[0022] Variable x1: Microbial functional activity (A), a core indicator characterizing the overall ability of urease-positive bacterial communities to catalyze urea hydrolysis. It is not directly equal to cell number, but rather reflects the effective working capacity of the cell population, integrating the effects of cell activity, enzyme activity, and environmental adaptability. It is a direct manifestation of the feasibility of biological function. Its value ranges from [0,1]. Specifically, A=1 represents the maximum hydrolytic activity achievable by the bacterial community under given conditions, while A=0 represents complete loss of bacterial function, rendering the community unable to drive the mineralization reaction.

[0023] Variable x2: Urea concentration ([U]) in the pore fluid, the core substrate concentration driving the entire MIP reaction chain. Its consumption rate directly determines the calcium carbonate formation potential, and its spatial distribution and supply affect the uniformity of mineralization. Units are mol / L or mM.

[0024] Variable x3: Mineral (calcium carbonate) sedimentary volume fraction ( This characterizes the proportion of pore space occupied by calcium carbonate precipitation in a porous medium. It reflects the reinforcement effect (strength, sealing performance) and the degree of change in the current pore structure, and is a related variable of "physical transport feasibility," with a value range of [0, ]. ],in The initial porosity of the porous medium.

[0025] Variable x4: Ammonium ion concentration ([NH4⁺]) in the pore fluid, a major byproduct of urea hydrolysis and a potential microbial inhibitor. Its accumulation leads to an increase in pH, which may be toxic to microbial activity and enzyme function. It is a key factor affecting chemical environmental feasibility, expressed in mol / L or mM.

[0026] S102. Construct the ordinary differential equations for the evolution of each key state variable over time to obtain the initial set of ordinary differential equations.

[0027] Specifically, taking at least two of the key state variables, including microbial activity, urea concentration, mineral sediment volume fraction, and ammonium ion concentration, as an example, we construct ordinary differential equations for the evolution of each key state variable over time. The initial set of ordinary differential equations can be constructed by separately constructing ordinary differential equations for microbial activity, urea concentration, mineral sediment volume fraction, and ammonium ion concentration, respectively. The ordinary differential equation for microbial activity is as follows: ; In the formula, The maximum specific activity change rate The study simulated the self-sustaining and saturation effects of activity. It is a suppression function, for example ,in The suppression constant, The Hill coefficient characterizes the toxicity of ammonium ions; The deactivation rate constant is It is a stress function. Characterizing the coupling of calcite saturation index and other parameters; The ordinary differential equation for urea concentration is: ; In the formula, For the maximum reaction rate, Michaelis constant, reaction rate and microbial functional activity Proportional For the injection flow rate, The concentration of the injected solution, The current porosity, ; The ordinary differential equation for the volume fraction of mineral sediments is: ; In the formula, Let be the precipitation rate constant. This is a yield coefficient used to convert the number of moles of calcium carbonate produced per unit of urea consumed into a volume fraction. This is the empirical sedimentation rate formula. The saturation index of calcite. , It is 1 or 2. Let be a Heaviside function, indicating that only if Precipitation only occurs when the temperature is >1; The ordinary differential equation for ammonium ions is: ; In the formula, The hydrolysis of urea produces ammonium ions, with 2 moles of ammonium ions produced per mole of urea hydrolysis. This refers to the convective discharge term of ammonium ions carried out by the fluid. For the injection flow rate, The current porosity, .

[0028] S104. Simplify and preprocess the initial set of ordinary differential equations to obtain the target set of ordinary differential equations.

[0029] Understandably, the bio-induced calcium carbonate precipitation (MICP) process involves multi-field coupling of biological (microbial metabolism), chemical (urea hydrolysis, calcium carbonate precipitation), and physical (pore fluid diffusion, media mass transfer) fields. Its original mathematical model (initial set of ordinary differential equations) typically contains numerous complex terms (such as fluid diffusion gradient terms, independent computational paths for mineral precipitation kinetics, and chemical inhibition terms). These terms increase the model's dimensionality and analytical complexity, hindering subsequent feasibility space decomposition, critical manifold identification, real-time state mapping, and control strategy design. Through targeted simplification, retaining terms that are crucial to the feasibility and achievement of the mineralization process while eliminating redundant or secondary terms, we obtain a lower-dimensional, more physically meaningful, and easier-to-analyze set of ordinary differential equations, laying the foundation for constructing a low-dimensional dynamic system model.

[0030] Specifically, simplified preprocessing can involve characterizing the term in the ordinary differential equation that represents the fluid diffusion gradient in the porous medium as zero or an equivalent dispersion coefficient; coupling calcium ion concentration with urea concentration to simplify the independent calculation path of mineral precipitation kinetics; and characterizing the inhibition term corresponding to the target constraint as zero according to the target constraint requirements, which are determined based on any one of the microbial functional feasibility constraints, physical transport feasibility constraints, and chemical environment feasibility constraints.

[0031] For example, for the simplification of (1) the fluid diffusion gradient term: In the original ordinary differential equation, the term characterizing the fluid diffusion gradient in the porous medium (such as the diffusion term based on Fick's law or Darcy's law, in the form of...) Where D is the diffusion coefficient and C is the solute concentration, it can be simplified in the following two scenarios: Scenario 1: Homogeneous porous medium and diffusion-dominated mass transfer: If the porous medium has a homogeneous pore structure and the fluid flow is dominated by molecular diffusion (rather than convection), the diffusion gradient term can be characterized as an equivalent dispersion coefficient (i.e., a dispersion coefficient calculated empirically / theoretically). Replacing the complex gradient term, the equation can be simplified to .

[0032] Scenario 2: Negligible diffusion effect (convection-dominated or rapid response): If the fluid flow is dominated by convection (e.g., high-velocity injection), or the solute reaction rate is extremely fast (e.g., urea diffuses instantaneously and uniformly in the pores), the diffusion gradient term can be characterized as zero (i.e., assuming the solute concentration is spatially uniformly distributed). At this point, the contribution of the diffusion term to the concentration change is negligible.

[0033] For (2) the coupling simplification of mineral precipitation kinetics: In the original model, calcium ions ( ) concentration and urea Precipitation kinetics at different concentrations can be calculated using independent pathways (e.g., calculating calcium ions separately). The diffusion / reaction of urea, the diffusion / reaction of urea, and then coupling through mass conservation. To simplify calculations and align with the core reaction logic of MICP (urea hydrolysis to produce alkali → increase pH → promote...), and The two need to be coupled to simplify the independent computation path: Based on the reaction mechanism of MICP (urea formation) ,and Combined generation ),Will The ordinary differential equations for concentration and urea concentration share key intermediate variables (such as pH value and carbonate concentration), or are directly derived from the stoichiometric ratio of the reaction. : =1:1 generated The rates of change of the two are correlated to form a coupled ordinary differential equation.

[0034] Regarding the elimination of suppression terms in (3): The original model may contain terms that inhibit the mineralization process (such as high concentrations of ammonium ions NH4). + (Inhibition terms on microbial activity, mass transfer limitations due to pore blockage, etc.). If maximizing mineralization efficiency is required, such as achieving the target precipitation amount in the shortest possible time, then terms related to inhibition efficiency, such as ammonium ion inhibition terms, need to be characterized as zero. If ensuring process robustness is required, such as allowing fluctuations in ammonium ion concentration but avoiding inhibition, then inhibition terms are retained.

[0035] S106. Assign fixed parameters and control parameters to the objective set of the ordinary differential equation system to construct the dynamic system model.

[0036] Specifically, the fixed parameters are constants determined by the inherent properties of the microbial species, the physicochemical characteristics of the porous media, and the intrinsic kinetics of the reaction; these are inherent properties of the model. The controllable parameters are external operational variables that can be actively adjusted in engineering practice; these represent the interaction between the model and the external world.

[0037] For example, fixed parameters may include microbial physiological and enzymatic parameters, which are determined by the selected microbial species. These microbial physiological and enzymatic parameters may include the maximum specific growth / activity change rate (SCR). This refers to the maximum potential growth rate of microbial activity per unit time. It can be obtained by fitting the activity growth curve of microorganisms under optimal conditions through batch culture experiments. It may also include the maximum reaction rate (…). ) and Michaelis constant ( The urease inhibition constant (UHEC) is a core parameter used to describe the kinetics of urease-catalyzed urea hydrolysis. It can be obtained by measuring the initial hydrolysis rate at different urea concentrations and fitting a Michaelis-Menten kinetic curve. It may also include the product inhibition constant. ) and Hill coefficient ( ), which is used to describe ammonium ions ( The degree of inhibition of microbial activity is a parameter. Inhibition models (such as ammonium ion concentration) can be fitted by measuring the specific growth rate or urease activity of microorganisms at different ammonium ion concentrations. get.

[0038] Fixed parameters may also include mineral chemistry and precipitation kinetic parameters, such as the precipitation rate constant ( ) and experience index ( The solubility product constant (Ω) is a parameter used to describe the relationship between the precipitation rate of calcium carbonate and the saturation index of calcite. It can be obtained through experiments monitoring the precipitation kinetics of calcite in supersaturated solutions. Another example is the solubility product constant (Ω). The solubility product of calcium carbonate (calcite) is a key thermodynamic constant for calculating the calcite saturation index Ω, and is a standard physicochemical data point. Another example is the yield coefficient (Y), which describes the volume fraction of calcium carbonate precipitate produced per unit mole of urea consumed. Determined by reactosmosis and mineral density, it can be obtained through theoretical calculations combined with experimental verification.

[0039] Furthermore, the fixed parameters may also include porous media characteristic parameters, such as initial porosity ( The pore volume fraction (V / V) is the pore volume fraction of the porous medium before treatment. It can be obtained through geotechnical testing methods such as the hydrometer bottle method and the water saturation method. Another example is the equivalent dispersion coefficient (EMC). This parameter characterizes the overall mass transfer capacity in porous media. It can be obtained through data inversion from tracer penetration experiments (such as NaCl tracers).

[0040] Control parameters are externally input operational variables whose values ​​can be adjusted in real time or in stages according to the control objective. Control parameters may include the concentration of the injected solution, such as the urea injection concentration. This refers to the molar concentration of urea in the cementing solution. It is a core regulatory parameter controlling the reaction driving force and precipitation rate. Another example is the calcium ion implantation concentration (…). This refers to the molar concentration of calcium ions in the cementitious solution. It is usually related to... It can be prepared according to a specific stoichiometric ratio (e.g., 1:1), but can also be adjusted independently to achieve specific goals (e.g., controlling the precipitation morphology). Further control parameters may include injection strategy parameters, such as injection flow rate ( This refers to the volume of fluid injected into the porous medium per unit time. Controlling the reactant supply rate and the fluid shear force within the pores affects mixing, transport, and potential microbial scouring. Other important discrete control parameters include the number of injection rounds and intervals; for multi-round injection strategies, the duration of each round and the settling time between rounds are also crucial. Control parameters can also include other environmental control parameters, such as the pH and temperature of the injected solution.

[0041] S108. Define the feasibility constraints for microbial function, physical transport, and chemical environment for the dynamic system model.

[0042] Specifically, the functional feasibility constraints of microorganisms are as follows: In the formula, A represents the functional activity of the microorganism. The activity threshold is the limit value at which the microbial community can maintain a sufficient hydrolysis rate to drive effective mineralization; the physical transport feasibility constraint is... In the formula, The effective porosity of a porous medium. The initial porosity of the porous medium. This represents the volume fraction of mineral sedimentation. The critical porosity threshold is defined as , the minimum permeability acceptable for mineralization engineering is defined as , and the chemical environment feasibility constraint is defined as . ,as well as In the formula, This refers to the concentration of ammonium ions. This represents the maximum inhibition threshold for ammonium ions.

[0043] Among them, effective porosity The determination method and effectiveness judgment include: effective porosity φ is defined as the ratio of the pore volume available for free fluid flow in the porous medium to the total volume, i.e. ,in The initial porosity of the porous medium. This represents the volume fraction of mineral sedimentation. When... At this point, the porous medium is considered to have effective transport capacity. The fluid permeability is not lower than the minimum acceptable threshold for engineering applications, reactants (urea, calcium ions) can be effectively transported to the reaction site, and products (ammonium ions) can be discharged promptly. At that time, the fluid permeability dropped sharply, and the mass transfer capacity was insufficient, indicating that the physical transport feasibility constraint was violated. The porosity threshold can be determined in the following ways: ① Based on seepage theory, the critical porosity threshold is determined by experimental analysis of the relationship between soil permeability and porosity; ② Based on engineering requirements, the porosity corresponding to the minimum acceptable permeability is calculated by back-calculating the upper limit of the injection pressure; ③ Based on the pore network model, the porosity corresponding to the seepage threshold is determined by numerical simulation.

[0044] S110. The intersection region of the functional feasibility constraints, physical transport feasibility constraints, and chemical environment feasibility constraints in the multidimensional state space is determined as the mineralization feasibility region of the microorganism to be mineralized.

[0045] Specifically, the areas with mineralization feasibility are: .

[0046] S112. Based on the dynamic system model and the mineralization feasibility region, mineralize the microorganisms to be mineralized in the porous medium, and identify at least one critical manifold in the multidimensional state space used to separate the different process final states during the mineralization process.

[0047] Specifically, the steps include: 1) In the multidimensional state space, the mineralization feasibility region is geometrically decomposed to distinguish the initial state leading to different process final states and their corresponding evolution paths. The initial state is the combination of values ​​of multiple key state variables at the beginning of the mineralization process, and the evolution path is the trajectory of each key state variable changing over time during the mineralization process.

[0048] Specifically, due to the complete composition of all state variables (such as activity A, urea concentration [U], deposition amount) The multidimensional state space spanned by ammonium concentration [NH4⁺] is difficult to visualize intuitively. Visual analysis can be performed in a 2D or 3D subplane by projection or selection of key state variable pairs. Exemplary combinations include: Active-mineral deposition plane ( This plane directly illustrates the competitive relationship between the two core constraints: the feasibility of biological function and the feasibility of physical transport. The feasibility region on this plane is represented by a straight line... and A rectangle (or an infinitely extending strip) that is enclosed.

[0049] Urea-ammonium ion concentration plane ([U]-[ This plane illustrates the chemical balance between substrate-driven and product-inhibited processes.

[0050] Active-ammonium ion concentration plane (A-[ This plane directly shows the biological tolerance boundary.

[0051] Within this selected subplane, the boundary of the mineralization feasibility zone is plotted, and based on the dynamic system model, the vector field (i.e., arrows indicating the direction and rate of state change) at each point on this plane is calculated and plotted. This vector field visually illustrates how the system state will evolve over time.

[0052] Within this selected subplane, the boundary of the mineralization feasibility zone is plotted, and based on the dynamic system model, the vector field (i.e., arrows indicating the direction and rate of state change) at each point on this plane is calculated and plotted. This vector field visually illustrates how the system state will evolve over time.

[0053] 2) Based on the initial state and its corresponding evolution path, locate at least one system attractor of the dynamic system model in the multidimensional state space. The system attractor includes a successful attractor representing the steady state of successful mineralization and a failure attractor representing the failure of the process.

[0054] Specifically, on the visualization plane, the dynamic system equations dX / dt=0 corresponding to the dynamic system model are solved using numerical methods (such as the Newton-Raphson iteration method) to find the steady-state points of the system (i.e., points where the arrow length in the vector field is zero). These points may include: A successful attractor (S) corresponds to a healthy steady state with high microbial activity, moderate mineral deposition, and a reaction that is nearing completion (e.g., [U] approaches zero), representing a successful mineralization consolidation outcome.

[0055] Failure attractor: The biological inactivation attractor (F1) corresponds to a steady state where microbial activity is zero (A=0) and the reaction has completely stopped.

[0056] Physical blockage attractor (F2), corresponding to pores completely filled by minerals ( ≈ ), the steady state of fluid transport termination.

[0057] Unstable equilibrium points (such as saddle points).

[0058] 3) In a multidimensional state space, identify at least one critical manifold that separates successful attractors from failed attractors, or separates attractors that lead to different attractor trajectories, wherein the critical manifold is at least one of a mortality manifold, an ordering manifold, or a collapse manifold.

[0059] Specifically, within the context of vector fields and feasible regions, the system systematically seeks geometric structures that separate initial state regions leading to different final states. Identifying mortality manifolds is the core of this process. Focus on critical boundaries: Pay special attention to feasibility boundaries directly related to failure, such as the feasibility boundaries of biological functions. .

[0060] Analyze the boundary dynamics: Examine the direction of the vector field at each point on the boundary. If at some point on the boundary, the vector points into the feasible region (dA / dt>0), it means that the state may recover from that point; if the vector points outward (dA / dt<0), it means that once this boundary is reached, the state will irreversibly slide towards failure.

[0061] Locate the exit point: Find the point on the boundary where the vector field is exactly tangent to the boundary.

[0062] Constructing a manifold through inverse integration: Starting from these key exit or entry points, integrate the dynamical system equations in reverse along time. The resulting inverse integration trajectory will sweep out a surface (in three-dimensional space) or curve (in two-dimensional plane) within the feasible region. This surface / curve is the mortality manifold.

[0063] Furthermore, this includes the ordering manifold, which, when considering spatial heterogeneity (such as the entrance and depth), determines which spatial location will fail first (either deactivate or become blocked), and is used to predict the propagation order and spatial patterns of failures. It also includes the collapse manifold, used to analyze whether a failure event (such as local blockage) will trigger a chain reaction (domino effect) leading to overall system collapse.

[0064] S114. Real-time acquisition of monitoring data reflecting key state variables during the mineralization process, and mapping to a multi-dimensional state space to obtain real-time state points.

[0065] Specifically, this step includes: Real-time acquisition of monitoring data reflecting key state variables during the mineralization process. The monitoring data includes at least one or more combinations of pore fluid pH, conductivity, injection pressure, outlet flow rate, and urea and ammonium ion concentrations obtained through periodic sampling and analysis. Based on the dynamic system model, monitoring data is input into the state observer for online estimation and data fusion to obtain real-time estimates of key state variables.

[0066] The real-time estimated values ​​are used as coordinates and mapped onto a multi-dimensional state space to form dynamically updated real-time state points.

[0067] S116. Determine the first control characterization value of the boundary between the real-time state point and the critical manifold, and the second control characterization value of the boundary between the real-time state point and the mineralization feasibility region.

[0068] S118. When either the first or second control characterization value is less than its corresponding preset warning threshold, the control parameters are adjusted to keep the mineralization process within the mineralization feasibility zone.

[0069] Furthermore, to facilitate understanding of the overall solution above, the following detailed description is provided in the form of specific implementation methods: Step 1: Constructing a dynamic system model of the MICP process This step aims to abstract the complex, multi-scale MICP physical-biological-chemical processes into a low-dimensional deterministic dynamical system that can be analyzed using mathematical tools. Its core idea is to grasp the key variables that dominate the process's fate while ignoring secondary details, thereby preserving the system's essential behavior while remaining computable.

[0070] Step 1.1: Determine the key state variables Select a few key macroscopic variables that can characterize the health status and failure risk of the MICP system. For a typical, spatially homogenized reaction unit (such as a representative pore volume), select the following 2-4 state variables to form the state vector X: x1: Microbial functional activity (A). Characterizes the overall ability of the microbial community to catalyze the hydrolysis of urea. It is a dimensionless quantity ranging from [0,1]. A=1 represents maximum activity, and A=0 represents complete loss of function. It reflects the feasibility of the biological function.

[0071] x2: Urea concentration ([U]) in the pore fluid. Units can be mol / L or mM. It is the core substrate, and its dynamic changes directly drive the entire reaction chain.

[0072] x3: Mineral (calcium carbonate) sediment volume fraction ( Characterizes the proportion of pore space occupied by minerals, ranging from [0, 0, 1]. It is a related variable for the feasibility of physical transmission.

[0073] (Optional) x4: Ammonium ion concentration ([NH4⁺]) in the pore fluid. Units can be mol / L or mM. As a major byproduct and potential inhibitor, it is a key factor influencing chemical environmental feasibility.

[0074] Selection criteria: These variables represent the minimum sufficient set to determine whether mineralization can continue effectively or will fail. Activity (A) and mineral deposition volume fraction ( These directly correspond to the two main failure modes; urea and ammonium concentrations are the chemical driving forces for the processes of driving and inhibiting them.

[0075] Step 1.2: Establish the ordinary differential equation Based on mass conservation, reaction kinetics, and inhibition effects, ordinary differential equations (ODEs) are established for each state variable.

[0076] 1. Ordinary differential equation for microbial activity (A): ; First item (growth / maintenance): This represents the maximum specific activity change rate. The term simulates the self-sustaining and saturation effects of activity (similar to logical growth). It is a suppression function, for example ,in The suppression constant, The Hill coefficient characterizes the toxicity of ammonium ions; this function may also include the reduction in activity due to mineral inclusions, such as... .

[0077] The second item (attenuation / deactivation): This is the deactivation rate constant. It is a stress function that may be related to environmental stress. For example, when the calcite saturation index Ω is extremely high, it may accelerate cell inactivation.

[0078] 2. Ordinary differential equation for urea concentration ([U]): ; First item The term for hydrolysis consumption is: the Michaelis-Menten equation is used to describe the enzyme-catalyzed reaction. For the maximum reaction rate, This is the Michaelis constant. The reaction rate is directly proportional to the microbial activity A.

[0079] The second term (convective transport term): describes the changes in urea caused by fluid injection. For the injection flow rate, The concentration of the injected solution, The current porosity ( This directly couples the model with external operating conditions (injection strategy).

[0080] 3. Mineral sediment volume fraction ( The ordinary differential equation of ) ; Precipitation rate term: is the precipitation rate constant. Y is the yield coefficient, which converts the number of moles of calcium carbonate produced per unit of urea consumed into a volume fraction. This is an empirical precipitation rate formula, where Ω is the calcite saturation index ( p is usually 1 or 2. H(Ω-1) is the Heaviside function, which means that precipitation only occurs when Ω>1 (supersaturation).

[0081] Key coupling: Ω itself is a function of [U], [NH4⁺] (hydrolysis affects pH and CO3²⁻ concentration), and [Ca²⁺]. It is typically assumed that [Ca²⁺] and [U] are injected in a fixed stoichiometric ratio, therefore Ω can be expressed as a function of [U] and pH (related to [NH4⁺]). This establishes a closed loop in the chemical-mineral deposition process.

[0082] Step 1.3: Model Simplification and Parameter Determination To make the model usable for feasibility space analysis, it needs to be reasonably simplified and its parameters assigned.

[0083] 1. Model simplification: Assuming good mixing of fluids in porous media, the diffusion gradient is ignored (or an equivalent dispersion coefficient is introduced into the transport term).

[0084] By coupling calcium ion concentration with urea concentration, the calculation of Ω is simplified.

[0085] Depending on the specific application scenario, certain suppression terms may be ignored (e.g. (Ammonium inhibition or mineral encapsulation inhibition in the middle) to first analyze the most important failure mechanism.

[0086] 2. Parameter Determination and Classification: Fixed parameters: determined by the strain and mineral chemistry, such as , , Y can be obtained through independent batch experiments or literature values.

[0087] Adjustable parameters: characterize environmental stress and operating conditions, such as , (Suppression constant), and external input and These are the levers for regulation.

[0088] State initialization: Initial state This corresponds to the system state before the injection begins.

[0089] Parameter acquisition path: Some parameters can be determined by inversion through curve fitting with small column experiments or literature data.

[0090] Thus, a low-dimensional dynamical system model describing the MICP process, consisting of a set of coupled ordinary differential equations (ODEs), has been obtained. This system model will serve as the mathematical foundation for subsequent construction and analysis of the "feasibility space." The next step will be to define explicit survival and death boundaries for this model.

[0091] Step 2: Define the feasibility constraints of the MICP process The core of this step is to establish clear and quantitative "survival" and "death" boundaries for the dynamic system model constructed in Step One. These boundaries divide the state space into a "functionally feasible region" (within which the MICP process can self-sustain and achieve engineering goals) and a "functionally failed region" (once entered, the process will irreversibly stall or fail). Three interrelated but fundamentally different types of feasibility constraints are defined, corresponding to the three main failure modes of MICP.

[0092] Step 2.1: Define the "biological functional feasibility" constraint This constraint ensures that the microbial catalyst itself does not lose its core function (urease activity).

[0093] Constraint: Microbial functional activity A must be above a critical threshold. .

[0094] Mathematical expression: .

[0095] Physical / biological significance: When activity A is lower than At this point, it was believed that the microbial community was no longer able to maintain a sufficient hydrolysis rate to drive effective mineralization. This could be due to the following reasons: substrate starvation: prolonged urea deficiency leads to metabolic stagnation.

[0096] a. Product inhibition / toxicity: Cytotoxicity or enzyme inactivation caused by high concentrations of ammonium ions (NH4⁺) or high pH.

[0097] b. Physical encapsulation / burial: Calcium carbonate deposits too quickly on the cell surface or inside the colony, physically blocking the transport of substrates and products.

[0098] c. Environmental stress: Osmotic pressure, ionic strength, etc. exceed the tolerance range.

[0099] threshold The determination of this value: This value is not fixed at 0, but is a small value greater than 0 (e.g., =0.1~0.3). It can be determined experimentally, for example, by measuring the critical cellular activity that causes the mineralization rate to drop sharply or stop (characterized by ATP content, dehydrogenase activity or direct hydrolysis rate measurements).

[0100] Step 2.2: Define the "Physical Transmission Feasibility" constraint This constraint ensures the efficient transport of reactants (urea, calcium ions) and products (ammonium ions) within the porous medium to continuously supply the reaction and remove inhibitors. Specifically, the constraint requires that the effective porosity φ of the porous medium must exceed a critical threshold. Mathematical expression: or equivalent to (in ) Specifically, This corresponds to the porosity at the seepage threshold or the minimum acceptable permeability in engineering. When the porosity is below this value, the fluid flow resistance increases sharply, leading to: a surge in injection pressure, making it impractical in actual engineering; or a shift from convection-dominated to diffusion-dominated transport, where the reactant supply rate cannot meet the upstream hydrolysis requirements, resulting in process self-limitation; or the formation of a surface sealing layer that prevents subsequent slurry from entering the material interior, causing uneven reinforcement.

[0101] Specifically, the threshold can be obtained through geotechnical mechanics experiments (such as permeability-porosity relationship determination) or theoretical calculations based on pore network models. It is a parameter closely related to the initial pore structure of the medium.

[0102] Step 2.3: Define the "Chemical Environmental Feasibility" constraint This constraint ensures that the chemical environment of the pore fluid is within a range that is tolerable to microorganisms and allows for the effective functioning of enzymes.

[0103] Constraint 1 (Ammonium ion toxicity): The concentration of ammonium ions in the pore fluid [ It must be below a suppression threshold. .

[0104] Mathematical expression: Constraint 2 (pH tolerance): The pH value of the pore fluid must be within a suitable range. Internal. Due to pH and [ This constraint is often indirectly related to hydrolysis reactions and chemical equilibrium. Constraints are used to embody or supplement this. The mathematical expression is: Understandably, excessively high... Extreme pH levels can disrupt cell membrane potential and inhibit enzyme activity centers, leading to irreversible damage to biological functions.

[0105] The pH range can be obtained through microbial physiological experiments, such as measuring the bacterial specific growth rate or urease activity at different ammonium concentrations and pH levels, and using the value corresponding to an activity decrease to 50% or lower as the critical threshold.

[0106] Step 2.4: Comprehensive Feasibility Area Ultimately, the comprehensive feasibility region (V) of the MICP process is an intersection region defined by all the above constraints in the state space. For example, ... An example of the constructed state space, which can be represented as: .

[0107] This region is a multidimensional box or polyhedron. Its boundary is the hyperplane defined by the equality of the above inequalities (a plane in three dimensions and a line in two dimensions). The system's state trajectory must always remain inside V; once it touches or crosses its boundary, the corresponding mode fails, and the entire process will fail to achieve the intended goal.

[0108] Thus, a clear survival rule has been established for the MICP dynamical system model. The next step will be to analyze the system's dynamic behavior within this constrained state space and to identify the key geometric structures—critical manifolds—that determine different trajectories.

[0109] Step 3: Construct the feasibility space of the MICP process and perform geometric decomposition. This step is the core of this invention, moving from theoretical modeling to analytical insight. The dynamic system model established in step one is placed within the feasibility constraints defined in step two. Within the geometric framework of state space, the global fate of the MICP process is systematically decomposed. The goal is to identify the critical geometric structures—i.e., manifolds—that separate different outcomes (such as successful hardening versus biological inactivation, uniform deposition versus premature blockage).

[0110] Step 3.1: Visualize the feasible region in the state subspace Since the complete state space may have high dimensions (such as 4-dimensional), we first use projection or slicing to visually represent the shape of the feasible region and its relationship with dynamics in a 2-dimensional or 3-dimensional subspace.

[0111] First, select a pair or set of state variables that best reflect the core contradiction for visual analysis. The most typical and physically meaningful combinations include: Plane P1: [Activity (A) Comparison of mineral deposition (A)] This plane directly illustrates the competitive relationship between the two major failure modes: biological function and physical obstruction. The feasible region is represented as a rectangle on this plane. and .

[0112] Plane P2: [Urea concentration ([U]) compared to ammonium ion concentration ( This plane illustrates the chemical equilibrium between substrate-driven and product-inhibited processes. The feasible region is affected by... constraint.

[0113] Plane P3: [Activity (A) vs. Ammonium Ion Concentration () This plane directly displays the biological tolerance boundary.

[0114] Furthermore, within the selected subplane, the boundaries of the comprehensive feasibility region V defined in step 2.4 are drawn. For example, in the P1 plane, two straight lines are drawn: (Horizontal line) and (Vertical lines), the rectangle (or infinitely extending strip) enclosed by them and the coordinate axes is the feasible region projection on the plane.

[0115] Step 3.2: Calculate the vector field and locate the system attractor. Within the selected subplane, analyze the dynamic trajectory of the system.

[0116] First, for each point on the subplane mesh, calculate the direction of change of the state variable at that point (derivative dA / dt) according to the dynamic equations from step one. (etc.) and magnitude, represented by arrows. The vector field formed by these arrows visually illustrates how the system state will evolve. Further, the steady-state point of the system is found by solving the equation system dX / dt=0 using numerical methods (such as the Newton-Raphson method). These points may include: successful attractors (S): typically corresponding to a highly active ( ), moderate mineral sedimentation ( ), reaction complete ( A healthy steady state represents a successful mineralization consolidation outcome. It may also include a failure attractor (F1): corresponding to a biologically inactive steady state where activity is zero (A=0) and the reaction ceases. It may also include a failure attractor (F2): corresponding to complete pore blockage (…). This includes the physical blockage steady state at which transmission terminates. It may also include unstable equilibrium points, such as saddle points, which are crucial for defining the watershed between different outcomes.

[0117] Step 3.3: Identify key critical manifolds In the context of vector fields and feasible regions, we seek geometric structures that separate the initial states that lead to different final states (attractors).

[0118] For the identification of the mortality manifold, specifically, the mortality manifold is the initial state within the feasible region V that eventually reaches the successful attractor S and the state that eventually violates a certain feasible constraint (such as A decreasing). The following) and the boundary separated by the initial state of failure.

[0119] During the identification process, the primary focus is on the biological functional feasibility boundary A= Examine the direction of the vector field at each point on the boundary. If the vector points into the feasible region (dA / dt>0), the state starting from that point has a chance of survival; if it points outward (dA / dt<0), it indicates death. Further search for points on the boundary where the vector field is exactly tangent to the boundary (i.e., exit or entry points). Starting from these key tangent points, integrate the dynamic equations in reverse time; the resulting trajectory will sweep out a surface (or curve) within the feasible region V. This surface is the mortality manifold. It is understandable that the mortality rate manifold... This is a risk warning line for biological inactivation failure modes. If the system state point is located at... The side closest to the failure boundary, even if the current activity is still acceptable, is destined to slide into inactivation.

[0120] For the identification of an ordering manifold, specifically, when considering the coupling of two or more spatial locations (such as the pore inlet and depth), the ordering manifold determines which location will fail first (e.g., deactivation or blockage). The identification process first constructs an extended state space containing the state variables of all spatial locations. Then, it seeks the joint failure boundary, i.e., the set where multiple locations simultaneously meet their respective feasibility constraints. Further, starting from points on this joint boundary, it performs inverse integration, and the resulting trajectory forms the ordering manifold. It can be understood that the ordering manifold... This study reveals the propagation sequence and spatial patterns of failures in non-uniform MICP processes, which are crucial for predicting clogging locations or designing gradient injection strategies.

[0121] For the identification of collapse manifolds, specifically, after a failure event (such as blockage at a location) occurs, the collapse manifold determines the subsequent fate of the remaining system (e.g., whether it stops entirely or continues mineralization in other areas). During the identification process, system dynamics are activated by a constraint (such as... After a sudden change (alteration of model structure) occurs (reaching a critical value), the boundary lines separating different attractors are sought in the state space of the new dynamical system, and then mapped back to the original state space. This is understandable in the context of a collapsing manifold. Used to analyze the risk of domino-like cascading failures and to assess whether local failures will lead to the failure of the overall objective.

[0122] At this point, the geometric dissection of the MICP process feasibility space is complete. Step three yields a map indicating the safe feasible region and the hazardous constraint boundaries, including the critical manifold ( , , The next step will be to use this map to establish rules for real-time early warning and precise control.

[0123] Step 4: Early Warning and Control Methods Based on Feasibility Space Analysis This step transforms the feasible region, attractor, and critical manifold obtained in step three into a monitoring-early warning-control operation process that can be executed in real time or offline. The core logic of this method is to track the real-time position of the system on the map, predict its trajectory, and proactively intervene before it approaches the failure boundary to guide it back to a safe path.

[0124] Step 4.1: Real-time state mapping and trajectory tracking First, state monitoring and estimation are conducted. Specifically, in actual MICP engineering sites or experimental setups, sensors are deployed or periodic sampling is performed to obtain indirect or direct data reflecting key state variables. For example, pore fluid is monitored using pH electrodes and conductivity meters, and combined with chemical equilibrium models, urea concentration [U] and ammonium ion concentration [NH4⁺] are estimated in real time. Microbial activity A is indirectly assessed using bioimpedance spectroscopy or specific metabolite sensors. The amount of mineral deposits in the pores is inverted using ultrasonic probes, resistivity tomography (ERT), or pressure-flow rate relationships. Or effective permeability / porosity. The monitoring data stream is input into a state observer (such as a Kalman filter), which operates based on the kinetic model from step one. This observer fuses multi-source data, filters noise, and outputs a complete state vector for the current state. The best estimate.

[0125] Further, state mapping and trajectory drawing are performed; specifically, the estimated states are... This is mapped onto the feasibility space constructed in step three (specifically, the selected key 2D / 3D subplanes), becoming a dynamically updated state point. Furthermore, the changes of this state point over time are recorded, forming a real-time trajectory within the feasibility space. .

[0126] Step 4.2: Proximity Calculation and Failure Early Warning First, the distance to the critical manifold is calculated. Specifically, the system calculates the current state point in real time. To each key critical manifold (especially the mortality manifold) The geometric or dynamical distance to the constraint boundary (and the Euclidean distance). This can be achieved by projecting the Euclidean distance onto the subplane, or by calculating the estimated time-to-failure (TTF) required to reach the manifold or boundary along the current vector field direction. It is calculated only when the derivative is negative (towards the boundary).

[0127] Furthermore, a tiered early warning triggering system can be implemented. Specifically, two or three levels of warning thresholds can be set. For example, a level of concern (yellow warning) can be triggered when the TTF or geometric distance is less than a preset threshold L1, or when the state point trajectory is clearly moving towards a critical manifold. This alerts the operator that the system is entering a risk zone. An action level (red warning) can be triggered when the TTF or geometric distance is less than a smaller threshold L2, or when the state point is very close (e.g., within one numerical integration step) to the critical manifold. The system automatically prepares for or suggests implementing regulatory intervention.

[0128] Step 4.3: Derive the optimal control strategy in reverse. When an early warning is triggered (especially an action-level warning), the system automatically or assistedly generates a control strategy to determine where the system state needs to be guided. Typically, this involves moving away from the critical manifold with the greatest current threat and towards a safer region within the feasible zone, with the ultimate goal of converging the trajectory to the successful attractor S. Furthermore, it identifies externally adjustable operating parameters that appear directly in the input terms of the kinetic equations, primarily including the urea concentration of the injected fluid. Injection flow rate (Optional) Calcium ion concentration Suspend the injection, flush with clean water, etc.

[0129] Furthermore, the control quantity is calculated (inverse solution), specifically based on the current state. Based on the dynamic model, the system undergoes rapid forward simulation or optimization calculations. This can be achieved using the following methods: Method 1: Try a set of discrete control schemes (such as...) Reduced by 20%, Method 1: Increase by 50%), simulate the state evolution over short time intervals (e.g., the next few time steps), and select the solution that allows the state point to move away from the critical manifold as quickly as possible or increases the TTF the most. Method 2: Establish a simple optimization problem: Objective function: Maximize TTF (or minimize the distance to the critical manifold), decision variables: , (Within the upper and lower limits of operation), constraints: dynamic model (as a predictive constraint), solution: online solution using fast optimization algorithms (such as gradient descent, simplex method) to obtain the optimal combination of control parameters.

[0130] Step 4.4: Form a closed loop of monitoring, early warning, and regulation. First, the calculated optimal control parameters are sent to the injection system (such as a peristaltic pump or solution preparation unit) for automatic execution, or recommended for manual execution by the operator. Further, after the control is executed, the system continues with steps 4.1 and 4.2, monitoring the state trajectory's response to the control. It verifies whether the state point deviates from the critical manifold as expected. If not, a new round of control calculation based on the new state is triggered. Further, iterative optimization and learning are performed; understandably, the monitoring data, early warning records, and control effects throughout the process are recorded in a database. This data can be used to periodically update and calibrate the model parameters from step one (such as...). , This allows the entire system to become increasingly accurate as the project progresses, enabling it to learn on its own.

[0131] Thus, this invention achieves a complete closed loop from theoretical modeling to online intelligent control. It transforms MICP from open-loop empirical operation to closed-loop, precise process control based on model prediction and state feedback. The next step is to construct a concrete implementation system.

[0132] Step 5: Method Validation and Implementation System This step aims to transform the aforementioned theoretical framework (steps one through four) into a proven, operable, and integrable technical solution. It addresses the two key issues of how to prove the method's effectiveness and how to apply it in practice, representing the core step in moving this invention from theory to engineering application.

[0133] Step 5.1: Verify the effectiveness of the method through numerical simulation. Before conducting costly physical experiments, the rationality and value of the entire logical chain of this method are first verified in a virtual environment through comprehensive numerical simulation. Specifically, a benchmark simulation case is first constructed: for example, a set of model parameters that conform to typical engineering scenarios (such as those for specific bacterial species) are set. , Initial porosity of sandy soil Furthermore, a set of conventional injection strategies (such as fixed concentration) are defined. and flow rate ) and a set of risk injection strategies (such as higher concentrations) This could lead to excessive precipitation or inhibition. Further, perform fate prediction, including prior to injection, based on the method in step three, in key sub-planes (such as...). On a plane, pre-draw the feasible region, vector field, attractor, and critical manifold (such as the mortality manifold). Based on the initial state point ( , Relative to The position predicts that the conventional strategy will lead to a successful attractor S, while the trajectory of the risky strategy will cross... And it reaches the failure boundary. Further execution process simulation and early warning verification are carried out, including dynamic process numerical simulation (solving ODE) for the two strategies, such as observing whether the simulated trajectory is consistent with the map prediction in step 3, and in the simulation of the risk strategy, when the system state point ( , )near Record the moment when (e.g., when the distance is less than a preset threshold ε). This will prove the foresight of the early warning system—the failure actually occurs in the future. ,and Furthermore, perform regulatory simulations, including simulating risk strategies. At that time, the control mechanism is virtually triggered, and according to step 4.3, the control strategy is calculated and applied (such as adjusting the injection concentration). Downgraded to The simulation was continued to observe whether the regulated trajectory deviated from the original failed path, instead bypassing it and eventually converging to the successful attractor S. This proves the effectiveness of the regulation strategy.

[0134] Step 5.2: Design experiments for empirical calibration Numerical simulations are based on model assumptions and require physical experiments to calibrate key parameters and verify core predictions. The first step is to design parameter inversion experiments, including a series of small-scale, controlled MIP column experiments or batch experiments to measure key response data, such as changes in urea / ammonia ion concentration, pH, and permeability at different times, and the final mineralization amount determined by microbial activity. The experimental data are then fitted to the model simulation results, and the most accurate set of model parameters (e.g., ...) is derived through optimization algorithms. , , Suppression constant These parameters enable the model to reproduce the experiment. Further, empirical testing of the map is conducted, including designing several groups with different initial conditions (e.g., different initial activities). For experiments involving different injection concentrations, before the experiment, a calibrated model is used to generate a specific "feasibility space and critical manifold" prediction map for each group of experiments. The experiment is conducted, and key states are monitored in real time or in stages (e.g., indirectly assessing A through sampling, assessing A through CT scans). The distribution of the experimental results was examined, and it was also checked whether the final outcome (success / failure) of the experiment was consistent with the prediction of the region where the initial point was located in the prediction graph. At the same time, it was checked whether the evolution trajectory of the state points during the experiment was consistent with the trend revealed by the manifold structure in the prediction graph.

[0135] Step 5.3: Integrated software or hardware implementation system concept To facilitate engineering applications of this method, the following integrated system concept is proposed, which can be protected as a patented device or software product. First, the overall system architecture is introduced, including an input module for receiving initial parameters (medium characteristics, microbial information, engineering objectives) and real-time monitoring data (injection pressure, effluent pH, conductivity, and possible in-situ optical or acoustic sensor data) from the field or laboratory; a model library for storing pre-calibrated or adaptively learnable dynamic system models of different types of MIP processes (such as different microbial-soil combinations); and a real-time computing unit for estimating the current system state online based on the input data. And in the background, the geometric analysis from step three continues to run, updating the map, and generating early warning and decision units for calculation. To the nearest critical manifold (e.g.) The distance d(t) is calculated. When d(t) < ε, an early warning is issued. Simultaneously, based on the algorithm in step 4.3, optimized control parameters (such as a new injection concentration) are automatically generated and recommended. The output and execution module (including suggested pause times, etc.) is used to visually display the real-time "fate map," current status point trajectory, early warning information, and control suggestions to the operator on the human-machine interface. It is connected to the injection pump, valve, and other actuators through the automatic control interface to realize automatic feedback control based on the control suggestions, forming a closed loop.

[0136] Workflow examples include: Once the project is launched and basic site parameters are input, the system loads the corresponding model, injection begins, and the system receives real-time sensor data. The core engine continuously estimates the state and determines its proximity to the critical manifold. When approaching a risk area, the system issues an early warning and highlights the risk area on the interface, while simultaneously providing an instruction to "reduce the urea concentration by XX%". The operator confirms and executes the instruction, or the system directly adjusts the injection parameters through the automatic control interface. Alternatively, the system continues monitoring to confirm that the state point is far away from the risk area, and the process returns to normal.

[0137] Thus far, this invention has completed a comprehensive exposition from theoretical modeling, geometric analysis, early warning and control to experimental verification and system integration. This methodology transforms MICP technology from an empirical art into a predictable and quantitatively controllable precision engineering science, providing a revolutionary tool for its reliable and efficient application in fields such as soil and rock reinforcement and ecological restoration.

[0138] Furthermore, Figure 2 This is a structural block diagram of the microbial mineralization process control device according to an embodiment of the application, such as... Figure 2 As shown, the device includes: The key state variable determination module is used to determine multiple key state variables of the microorganism to be mineralized; The module for determining the initial set of ordinary differential equations is used to construct the ordinary differential equations for the evolution of each key state variable over time, thereby obtaining the initial set of ordinary differential equations. The ordinary differential equation target set determination module is used to simplify and preprocess the initial set of ordinary differential equations to obtain the target set of ordinary differential equations; The dynamic system model construction module is used to assign fixed parameters and control parameters to the objective set of the ordinary differential equation system to construct the dynamic system model; The feasibility constraint definition module is used to define feasibility constraints for microbial function, physical transport, and chemical environment for dynamic system models. The mineralization feasibility region determination module is used to determine the mineralization feasibility region of the microorganism to be mineralized by the intersection of the microbial functional feasibility constraints, physical transport feasibility constraints and chemical environment feasibility constraints in the multidimensional state space. The multidimensional state space is determined based on the number of key state variables. A critical manifold identification module is used to identify at least one critical manifold in the multidimensional state space that separates different final states of the mineralization process based on a dynamic system model and a mineralization feasibility region for the mineralization treatment of microorganisms to be mineralized in a porous medium. The real-time state point acquisition module is used to acquire monitoring data reflecting key state variables during the mineralization process in real time and map them into a multi-dimensional state space to obtain real-time state points. The regulation characterization value determination module is used to determine the first regulation characterization value of the boundary between the real-time state point and the critical manifold, and the second regulation characterization value of the boundary between the real-time state point and the mineralization feasibility region. The adjustment module is used to adjust the control parameters when either the first control characterization value or the second control characterization value is less than its corresponding preset warning threshold, so as to adjust the mineralization process within the mineralization feasibility area.

[0139] The application of the relevant modules of the device in this example can be referred to the relevant introduction of the method principle above, and will not be repeated here.

[0140] above Figure 2 The microbial mineralization process control device in the embodiments of the present invention will be described in detail from the perspective of modular functional entities. The electronic device in the embodiments of the present invention will be described in detail from the perspective of hardware processing.

[0141] Figure 3This is a schematic diagram of the structure of an electronic device 300 provided in an embodiment of the present invention. The electronic device 300 can vary significantly due to different configurations or performance characteristics. It may include one or more central processing units (CPUs) 310 (e.g., one or more processors) and a memory 320, and one or more storage media 330 (e.g., one or more mass storage devices) for storing application programs 333 or data 332. The memory 320 and storage media 330 can be temporary or persistent storage. The program stored in the storage media 330 may include one or more modules (not shown in the diagram), each module including a series of instruction operations on the electronic device 300. Furthermore, the processor 310 may be configured to communicate with the storage media 330 and execute the series of instruction operations in the storage media 330 on the electronic device 300.

[0142] Electronic device 300 may also include one or more power supplies 340, one or more wired or wireless network interfaces 350, one or more input / output interfaces 360, and / or one or more operating systems 331, such as Windows Server, MacOSX, Unix, Linux, FreeBSD, etc. Those skilled in the art will understand that... Figure 3 The illustrated electronic device structure does not constitute a limitation on electronic devices and may include more or fewer components than illustrated, or combine certain components, or have different component arrangements.

[0143] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when executed on a computer, cause the computer to perform the steps of any of the above-described methods for regulating the microbial mineralization process.

[0144] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system, device, or unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0145] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0146] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for regulating microbial mineralization processes, characterized in that, The method includes: Identify several key state variables of the microorganisms to be mineralized; Construct the ordinary differential equations for the evolution of each key state variable over time to obtain the initial set of ordinary differential equations; The initial set of ordinary differential equations is simplified and preprocessed to obtain the target set of ordinary differential equations; By assigning fixed parameters and control parameters to the objective set of the ordinary differential equation system, a dynamic system model is constructed. Define microbial functional feasibility constraints, physical transport feasibility constraints, and chemical environment feasibility constraints for the dynamic system model; The intersection region of the microbial functional feasibility constraints, physical transport feasibility constraints, and chemical environment feasibility constraints in the multidimensional state space is determined as the mineralization feasibility region of the microorganism to be mineralized, wherein the multidimensional state space is determined based on the number of key state variables. Based on the dynamic system model and the mineralization feasibility region, the microorganisms to be mineralized are subjected to mineralization treatment in a porous medium, and at least one critical manifold in the multidimensional state space used to separate different process final states is identified during the mineralization process. Real-time monitoring data reflecting the key state variables during the mineralization process are acquired and mapped to the multidimensional state space to obtain real-time state points; A first control characterization value is determined for the boundary between the real-time state point and the critical manifold, and a second control characterization value is determined for the boundary between the real-time state point and the mineralization feasibility region. When either the first or the second control characterization value is less than its corresponding preset warning threshold, the control parameter is adjusted to adjust the mineralization process within the mineralization feasibility range.

2. The method for regulating the microbial mineralization process according to claim 1, characterized in that, The key state variables include at least two of the following: microbial activity, urea concentration, mineral sediment volume fraction, and ammonium ion concentration. The construction of ordinary differential equations for the evolution of each key state variable over time yields an initial set of ordinary differential equations, including: We constructed ordinary differential equations for microbial activity, urea concentration, mineral sedimentation volume fraction, and ammonium ion concentration, respectively. The ordinary differential equation for microbial activity is as follows: ； In the formula, The maximum specific activity change rate The self-sustaining and saturation effects of simulated activity It is a suppression function. ,in The suppression constant, The Hill coefficient characterizes the toxicity of ammonium ions; The deactivation rate constant is It is a stress function. Characterizing the coupling of calcite saturation index and other parameters; The ordinary differential equation for urea concentration is: ； In the formula, For the maximum reaction rate, The Michaelis constant is given; the reaction rate is directly proportional to the microbial functional activity A. For the injection flow rate, The concentration of the injected solution, The current porosity, ; The ordinary differential equation for mineral sediment volume fraction is: ； In the formula, Let be the precipitation rate constant. This is a yield coefficient used to convert the number of moles of calcium carbonate produced per unit of urea consumed into a volume fraction. This is an empirical formula for the precipitation rate, where Ω is the calcite saturation index. , It is 1 or 2. The Heaviside function indicates that precipitation occurs only when Ω > 1; The ordinary differential equation for ammonium ions is: ； In the formula, The hydrolysis of urea produces ammonium ions, with 2 moles of ammonium ions produced per mole of urea hydrolysis. This refers to the convective discharge term of ammonium ions carried out by the fluid. For the injection flow rate, The current porosity, .

3. The method for regulating the microbial mineralization process according to claim 1, characterized in that, The simplification and preprocessing of the initial set of ordinary differential equations to obtain the target set of ordinary differential equations includes: The terms in the ordinary differential equation that characterize the fluid diffusion gradient in the porous medium are represented as zero or equivalent dispersion coefficients. Coupling calcium ion concentration with urea concentration simplifies the calculation path for mineral precipitation kinetics. According to the target constraint requirements, the inhibition term corresponding to the target constraint requirements is characterized as zero, and the target constraint requirements are used to characterize the objective constraints that the mineralization process is required to achieve.

4. The method for regulating the microbial mineralization process according to claim 1, characterized in that, The functional feasibility constraints of the microorganisms are In the formula, A represents microbial functional activity. The activity threshold is the limit value characterizing whether the microbial community can maintain a sufficient hydrolysis rate to drive effective mineralization; the physical transport feasibility constraint is... In the formula, The effective porosity of a porous medium. The initial porosity of the porous medium. This represents the volume fraction of mineral sedimentation. The porosity critical threshold characterizes the minimum permeability acceptable for mineralization engineering, with chemical environmental feasibility constraints as follows. ,as well as In the formula, This refers to the concentration of ammonium ions. This represents the maximum inhibition threshold for ammonium ions; Among them, effective porosity The determination method and effectiveness judgment include: effective porosity Defined as the ratio of the pore volume available for free fluid flow in a porous medium to the total volume, i.e. ,in The initial porosity of the porous medium. For mineral sediment volume fraction, when ≥ When it is determined that the porous medium has effective transport capacity, < At that time, the constraint that determines the feasibility of physical transmission was violated.

5. The method for regulating the microbial mineralization process according to claim 1, characterized in that, The area where mineralization is feasible is: 。 6. The method for regulating microbial mineralization process according to claim 1, characterized in that, The mineralization treatment of the microorganisms to be mineralized in the porous medium based on the dynamic system model and the mineralization feasibility region, and the identification of at least one critical manifold in the multidimensional state space used to separate different process final states during the mineralization process, include: In the multidimensional state space, the mineralization feasibility region is geometrically decomposed to distinguish the initial state leading to different process final states and their corresponding evolution paths. The initial state is the combination of values ​​of multiple key state variables at the start of the mineralization process, and the evolution path is the trajectory of each key state variable changing over time during the mineralization process. Based on the initial state and its corresponding evolution path, at least one system attractor of the dynamic system model is located in the multidimensional state space. The system attractor includes a successful attractor representing a successful mineralization steady state and a failure attractor representing process failure. In the multidimensional state space, at least one critical manifold is identified that separates the successful attractor from the failed attractor, or separates the trajectories leading to different attractors, wherein the critical manifold is at least one of a mortality manifold, an ordering manifold, or a collapse manifold.

7. The method for regulating microbial mineralization process according to claim 1, characterized in that, The real-time acquisition of monitoring data reflecting the key state variables during the mineralization process, and mapping it to the multi-dimensional state space to obtain real-time state points, includes: Real-time acquisition of monitoring data reflecting the key state variables during the mineralization process, the monitoring data including at least one or more combinations of pore fluid pH, conductivity, injection pressure, outlet flow rate, and urea and ammonium ion concentrations obtained through periodic sampling and analysis; Based on the dynamic system model, the monitoring data is input to the state observer for online estimation and data fusion to obtain real-time estimates of key state variables; The real-time estimated value is used as coordinates and mapped onto the multidimensional state space to form dynamically updated real-time state points.

8. A device for regulating a microbial mineralization process, characterized in that, The device includes: The key state variable determination module is used to determine multiple key state variables of the microorganism to be mineralized; The module for determining the initial set of ordinary differential equations is used to construct the ordinary differential equations for the evolution of each key state variable over time, thereby obtaining the initial set of ordinary differential equations. The ordinary differential equation target set determination module is used to perform simplification preprocessing on the initial set of ordinary differential equations to obtain the ordinary differential equation target set; The dynamic system model construction module is used to assign fixed parameters and control parameters to the objective set of the ordinary differential equation system to construct the dynamic system model; The feasibility constraint definition module is used to define microbial functional feasibility constraints, physical transport feasibility constraints, and chemical environment feasibility constraints for the dynamic system model. The mineralization feasibility region determination module is used to determine the intersection region between the microbial functional feasibility constraints, physical transport feasibility constraints and chemical environment feasibility constraints in the multidimensional state space as the mineralization feasibility region of the microorganism to be mineralized, wherein the multidimensional state space is determined based on the number of key state variables. A critical manifold identification module is used to perform mineralization treatment on the microorganisms to be mineralized in a porous medium based on the dynamic system model and the mineralization feasibility region, and to identify at least one critical manifold in the multidimensional state space used to separate different process final states during the mineralization process. The real-time state point acquisition module is used to acquire monitoring data reflecting the key state variables during the mineralization process in real time, and map them into the multi-dimensional state space to obtain real-time state points. The regulation characterization value determination module is used to determine a first regulation characterization value of the boundary between the real-time state point and the critical manifold, and a second regulation characterization value of the boundary between the real-time state point and the mineralization feasibility region. The adjustment module is used to adjust the control parameters when either the first control characterization value or the second control characterization value is less than its corresponding preset warning threshold, so as to adjust the mineralization process within the mineralization feasibility area.

9. An electronic device, characterized in that, The electronic device includes a memory and at least one processor, the memory storing instructions; the at least one processor invokes the instructions in the memory to cause the electronic device to perform the steps of the microbial mineralization process regulation method as described in any one of claims 1-7.

10. A computer-readable storage medium storing instructions thereon, characterized in that, When the instructions are executed by the processor, they implement the various steps of the microbial mineralization process regulation method as described in any one of claims 1-7.

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