# A Data assimilation framework for EGS thermal perdiction

**Introduction**

Predicting the thermal performance of enhanced geothermal systems (EGS) requires a comprehensive characterization of the underlying fracture flow patterns from practically available data such as tracer testing data. However, due to the inherent complexities of subsurface fractures and the generally insufficient geological/geophysical data, interpreting tracer data for fracture flow characterization and thermal prediction remains a challenging task. We tackle the challenge by leveraging a data assimilation method to maximize the utilization of information inherently contained in tracer data, and meanwhile maintain the flexibility to handle various uncertainties. More details can be found in the following manuscript:

**Methodology**

We propose a tracer data interpretation framework to first invert for fracture aperture distribution through ensemble smoother with multiple data assimilation (ES-MDA), and then predict thermal performance based on the inversion results. The following three components are integrated to achieve effective fracture characterization and accurate performance prediction:

- We use principal component analysis (PCA) to reduce the dimensionality of model parameter space and overcome the data scarcity challenge.
- We use ensemble smoother with multiple data assimilation (ES-MDA) to invert for fracture aperture/flow fields and obtain posterior model ensembles for uncertainty quantification purpose. Various data types are assimilated jointly to improve the prediction capability of the posterior ensemble.
- The inverted fracture aperture fields are then incorporated into reservoir models to predict thermal performance.

**Application to a field-scale EGS example**

We use a field-scale EGS model to illustrate the proposed method (Fig. 2). Three vertical wells are connected to a horizontal fracture with highly heterogenous aperture following a multimodal distribution (non-Gaussian). We intentionally use such an irregular aperture distribution to examine the robustness and effectiveness of the proposed method. We first generate synthetic tracer data by injecting conservative/sorptive tracers into the fracture through well 1 and monitoring tracer breakthrough curves (TBCs, dots in Fig. 3) at wells 2 and 3.

The first step of data assimilation is generating a prior ensemble consisting of stochastic model realizations (heterogeneous aperture distributions, 800 in this example). These prior realizations can be viewed as blind guesses based on our prior knowledge. In this synthetic case, we assume that the aperture distribution follows a log-normal distribution, which is a commonly used prior constraint for subsurface fractures. Note that the true aperture distribution is not within the parameter space implied by the ensemble.

As expected, simulated tracer responses for the 800 prior realizations vary tremendously, and are overall very different from the synthetic tracer data (first row in Fig. 3). We then use ES-MDA to drive these realizations iteratively to match the tracer data, and thereby obtain a posterior ensemble in which the 800 model realizations yield an overall reasonable match to the data (second row in Fig. 3). By comparing the true model, a randomly picked prior realization and the corresponding posterior realization (Fig. 4), we find that the posterior realization resolves the flow pattern reasonably well.