There are several mathematical algorithms that can be used to estimate the flow of influent and effluent for anaerobic digestion and struvite precipitation processes. Some commonly used methods include mass balance equations, dynamic modeling, and process simulation.

One way to estimate the flow of influent and effluent for anaerobic digestion is to use mass balance equations. This involves determining the amount of organic matter entering and leaving the system, as well as the amount of biogas produced. This can be done by measuring the chemical oxygen demand (COD) or total solids (TS) of the influent and effluent, and using those values to calculate the mass balance.

Another approach is to use dynamic modeling, which involves creating a mathematical model of the system that can predict the behavior of the process over time. This can be done using software such as Aspen Plus or SuperPro Designer, which can simulate the process and predict the flow of influent and effluent.

Simulation is also another approach that can be used to estimate the flow of influent and effluent. This method involves creating a computer model of the system that can simulate the process and predict the flow of influent and effluent. This can be done using software such as MATLAB or Simulink, which can simulate the process and predict the flow of influent and effluent.

Ultimately, the specific algorithm or method that is chosen will depend on the available data, the specific requirements of the system, and the level of accuracy and precision desired.

Mass balance algorithms are mathematical methods used to calculate the balance of a system, usually in terms of inputs and outputs of a material or energy. To use mass balance algorithms, you typically need to follow these steps:

Define the system and its boundaries: Determine what the system is and what inputs and outputs are included in the calculation.

Identify the inputs and outputs: List all the inputs (e.g., inputs of material, energy, etc.) and outputs (e.g., outputs of material, energy, etc.) of the system.

Choose the appropriate algorithm: Select an appropriate mass balance algorithm based on the type of system and the information available.

Gather data: Collect data on inputs, outputs, and any other relevant parameters.

Perform the calculation: Use the chosen algorithm to perform the calculation and determine the balance of the system.

Analyze the results: Evaluate the results of the calculation to determine if the system is in balance, and if not, identify where the imbalance is and what steps can be taken to correct it.

It's important to note that the specific steps and algorithms used may vary depending on the type of system and the information available, but these steps provide a general framework for using mass balance algorithms.