59th Annual Report on Research 2014

Fracture Characterization Method:

We have adapted the EnKF and examined its performance for monitoring data integration in hydraulic fracturing. The EnKF consists of a forecast step to predict the measured data using an appropriate forward model of the process, and the update step that integrates the predictions from the forecast step with observed responses from the field to improve the fracture models and the production predictions.

Forward Models for Forecast Step: We have used several forward models to represent the individual multiphysic processes in hydraulic fracturing. For microseismic data, we have implemented a simple representation of rock failure using the pore pressure relaxation theory [Shapiro, 2008; Tarrahi, 2012]. This model assumes that at any location in the reservoir whenever the pore pressure exceeds a measure of rock strength (rock criticality), the rock failure occurs and fractures are developed. This pore pressure diffusion equation and the standard flow and transport governing equations are solved using a commercial reservoir simulator [i.e., Eclipse, 2011]. The goal of the forward model is to establish a relation between model parameters (fractures properties) and the observed monitoring data (through predictive analytics). In our future work, we plan to use a coupled flow and geomechanics forward model.    

The EnKF Update Step: The EnKF is derived from the classical linear Kalman filter [Kalman, 1960] for non-linear problems [Evensen, 2007]. The forecast and update steps of the EnKF can be summarized as

(forecast)	(1)
(update)	(2)
	(3)

where the notations are defined in Appendix 1. For parameter estimation, we define the state vector to contain the parameters and the predicted measurements, that is . For assimilating discrete microseismic events, we first transform the data to a continuous dataset using Kernel density estimation techniques [Tarrahi et al., 2013]. Furthermore, for high dimensional correlated data such as microseismic, we project the data onto a reduced subspace defined by the left singular vectors of the perturbed observation matrix. This reduced-rank projection decorrelates the data and alleviates the variance underestimation that can occur in processing large correlated datasets with the EnKF.

Numerical Experiments and Discussion:

Numerical Experiments: To investigate the data integration formulation, we have considered several numerical experiments for both planar fracture models and fracture network models [Crockett, 1989; Xu, 2009a; Xu, 2009b; Cipolla, 2010]. For brevity, we only present a few sample numerical experiments in this report.

Experiment 1: Planar Fractures. In this experiment we consider planar fracture models and infer the fracture geometry (length-scales) from microseismic data. The fractures are approximated by regular cells with much higher permeability than the matrix. While we have considered both pixel-based and parametric description of planar fractures, we only show the results obtained for the parametric description where fractures are represented with oval-shaped planes with their minor and major principal axes (fracture length and height) as the parameters to be estimated. We consider N_e=100 sample realizations of the prior fracture models in the reservoir with lengths and heights randomly distributed within the [140, 595] (ft) and [30,175] (ft) intervals, respectively. Figure 1 shows the reservoir configuration with 7 fracturing stages of different geometric properties. A summary of the reservoir properties provided in Table 1. The EnKF is applied to update the ensemble of models with the uncertain fracture lengths and heights (estimating two parameters per fracture stage). The estimation results are summarized in Figure 2. To test the validity of our results, we repeated the experiment multiple times for different range of fracture parameters, all indicating that the estimated parameter ensembles move closer to the reference values.

Experiment 2: Stochastic Fracture Networks. In this experiment, we consider characterization of complex fracture networks using the microseismic response data. Given the stochastic nature of these models, our parameter estimation is focused on constraining the stochastic parameters that control the ratio of propped to non-propped fractures, which is directly related to the stimulated reservoir volume (SRV). Figure 3 shows a naturally fractured formation and the resulting microseismic events distribution, indicating that the data cannot distinguish between conductive (brown) and non-conductive (green) fractures. Here, we use the microseismic data to estimate the ratio (P) of propped to non-propped fractures. The parameter P provides a measure of propped fracture density that can be used for stochastic prediction of production volume and the extent of refracturing needed. Figure 4 shows the estimation results for this example and the production forecast with 100 realizations before and after updating this parameter. The microseismic data is able to constrain this parameter and improve the production predictions. However, additional constraining may be achieved from flow and transport data, a topic that is currently under investigation.

Ongoing and Future Work:

Since microseismic data alone does not reveal information about fracture conductivity, we plan to incorporate flow and transport data types to retrieve fracture and matrix hydraulic properties. Our ongoing work is focused on estimating fracture conductivity and length scale from pressure, flowrate, and tracer concentration (during flowback) data. Our future goal is to combine all these data types into a unified joint inversion framework for estimating fracture geometric and hydraulic properties from multiphysics data by using more rigorous coupled flow and geomechanical models.