# Software for Estimation of Stochastic Model Parameters for a Compacting Reservoir
## 1 Introduction  
The compaction of porous geological layers in oil, gas or groundwater extraction sites leads to the formation of a subsidence trough on the land surface. Among the best-known examples of such phenomena are large areas in The Netherlands, e.g., the Groningen gas field [1], Mexico, e.g., Mexico City [2; 3], or Italy, e.g., Venice [4]. Land subsidence due to compaction has also been observed in mining drainage sites and is mainly reported in deep, solid, mineral mine sites [5; 6; 7]. Changes on the surface may be registered with leveling surveys, GNSS, or InSAR [4; 8]. Analysis of measurement results indirectly describes the properties of reservoir rocks [9; 10; 11]. By comparing such data with rock mass geology, a connection may be found between the cause of the movement and its outcomes on the surface [12; 13; 14]. The parameters can be determined with a selected mathematical model, and a tool for predicting the future consequences of mining activity may be developed. Appropriately performed subsidence modeling will provide safer engineering structures [15] and surface infrastructure [16]. The compaction phenomenon may be described with a poro-elasticity model which establishes correlations between the reservoir skeleton and pressure changes in the fluid [17; 18]. This results in a deformation field on the land surface in the form of a subsidence trough. Various groups of mathematical models (empirical, analytical or theoretical) may be used to predict compaction and surface subsidence [8; 9; 10; 11; 19], but they differ in computational complexity, the number of the required parameters, and the time necessary to make a rock mass model [20]. Analytical models use a limited number of parameters which each have a physical interpretation and may be seen as a compromisewith the theoretical models [13; 20; 21] that have been described in our research. Analytical methods may potentially serve as a useful tool, particularly in the case of operating mines. Additionally, these methods have shown that the results of analytical models may indicate a similar land subsidence prediction accuracy as the results of numerical modeling. One of these analytical methods is called a stochastic model or an influence function model [13; 22; 23; 24; 25]. Models of this type first appeared in mathematical applications, statistics and applied research decades ago, but they are widely recognized today due to their relatively small number of parameters and high reliability. However, like all prediction models, they require the definition of parameters which control the calculation process. Researchers who model compaction-induced surface movements agree that evaluation of model parameters is very important for the accuracy and reliability of forecasts [10; 11; 26; 27; 28]. Frequently, the parameters cannot be acquired directly from in-situ tests or sampling, while at other times the density of samples is insufficient [29]. In such a situation, the presented model and parametrization method may be an alternative to existing solutions. This is the research gap that is filled by this study.  
The objectives comprise the following:  
* verify the efficacy of a parameter estimation method based on a stochastic model;
* implement an algorithm in open-source software;
* model subsidence due to dewatering in an underground coal mine.  
The article is structured as follows: The model parameters were established based on the influence function model (Section 2). The proposed software was tested in an underground coal mine where the compaction effect due to the pumping of water and its outcome in the form of extensive subsidence due to the drainage trough have been observed (Section 3). This example formed the basis of the discussion concerning the operation of the software (Section 4). The obtained results are discussed in the last chapter and show the applicability of this tool in areas where other raw materials are extracted, e.g., oil, gas or water (Section 5).