A Data assimilation framework for EGS thermal perdiction

From Open Energy Information

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:

Manuscript.pdf


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:

  1. We use principal component analysis (PCA) to reduce the dimensionality of model parameter space and overcome the data scarcity challenge.
  2. 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.
  3. The inverted fracture aperture fields are then incorporated into reservoir models to predict thermal performance.
Fig. 1 Workflow of the tracer data interpretation framework. Aperture distribution is shown as 2D spatially correlated fields. PCA stands for principal component analysis.


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.

Fig. 2 A field-scale EGS model to demonstrate the proposed method for aperture and flow field inference. Left: a 3D view of a square area of a fracture and its relationship with three wells. Right: Aperture distribution.
Fig. 3 Tracer simulations (grey curves) from prior (upper row) and posterior ensembles (lower row). Colored dots are “true” tracer breakthrough curves (TBCs) simulated on the fracture shown in Fig. 2. Four TBCs are matched in the process: recovery at the two producers X two tracer types. The green shadings are the 90% credible intervals of the simulation results from 800 stochastic realizations that constitute the ensemble. The posterior ensemble matches the true curves reasonably well. Cons. = Conservative; Sorp. = Sorptive.
Fig. 4 Comparison of aperture distribution, flow field and fracture temperature evolution among the true model (first row), a prior realization (second row) and the corresponding posterior realization (third row).
Fig. 5 Prediction of production temperature (flow rate averaged) from prior and posterior ensembles. The solid black line is the true thermal breakthrough curve. The olive (left) and red (right) lines are results for 50 selected realizations from the prior and posterior ensembles, respectively.