A Practical and Rigorous Approach for Production Data Analysis in Unconventional Wells

Abstract

A new approach for production data analysis in unconventional reservoirs is presented. Unlike the existing decline-curve analysis methods, this approach is not empirical and it is theoretically rigorous. The basis of the approach is an anomalous diffusion model for the performance of fractured horizontal wells surrounded by a stimulated reservoir volume. In the anomalous diffusion model, instead of Darcy's Law, a more general constitutional relation is used to incorporate the non-local and hereditary nature of flow in highly heterogeneous nanoporous media. The sub-or super-diffusive state of flow can be deduced from the slope of the straight line on the log-log plot of rate vs. time. Nonnecessity of a detailed description of the intrinsic properties and spatial distribution of matrix and fracture constitutes the practical advantage of the model. The reduced number of parameters can be conveniently estimated from production data and used in the anomalous diffusion model to predict future production. In this paper, a one-dimensional numerical model is implemented and applied to two Barnett shale gas wells and compared to common empirical models. It is shown that, even with limited completion, reservoir, and production data, the anomalous diffusion model has the potential to capture the production characteristics. Moreover, the model can be used to run sensitivities on actual system variables such as hydraulic fracture length, height and spacing, as well as to account for changing operating conditions. Current approaches for analyzing well performances in tight-oil and shale-gas plays mostly use the dual-porosity idealization for the stimulated (naturally fractured) reservoir volume (SRV) between hydraulic fractures. In these approaches, fluid flow is described at two distinct scales: the low permeability, high storativity matrix, and the high permeability but low storativity fracture network. The matrix acts as a source term to the continuum-forming fracture network, which transports the fluids to the well. Average properties are assigned to both matrix and fractures and uniform spatial distributions are assumed. The flux equation describing flow in both media is the well-known Darcy's law, which relates the flux to an instantaneous and local pressure gradient and assumes that the fluid-particle displacement during flow can be modeled as Brownian motion with a Gaussian (normal) distribution. This approach is well suited for conventional naturally fractured reservoirs where the matrix permeabilities are reasonably high and both, matrix and fracture network, can be treated as relatively homogeneous.Tight, unconventional reservoirs, on the other hand, exhibit a multitude of different scales including nano-and micro-pores, microfractures within the matrix, disconnected natural fractures, and induced fractures. The absence of a clear scale separation in the petrophysical heterogeneity makes definitions of locally averaged flow properties inappropriate and dual-or multi-porosity idealizations inapplicable. Anomalous diff...

Rules for Flight Paths and Time of Flight for Flows in Porous Media with Heterogeneous Permeability and Porosity

“…On the microscopic scale, the fluid may perform as non-Darcy flow where classical Darcy's law will no longer stand. To better model non-Darcy flow, different tools and flow equations have been proposed to simulate the atomic level of the diffusion phenomena; for example, the fractional diffusion equations were proposed to replace the classical diffusion equation [27][28][29][30][31][32]. The fractional decline curve model was introduced for well rate analysis and production forecast [33,34].…”

Analytical Modeling of Flow in Highly Disordered, Fractured Nano-Porous Reservoirs

“…There have been several applications of fractional calculus to fluid flow in naturally fractured reservoirs in the literature (e.g., Chang and Yortsos 1990, Beier 1994, Flamenco-Lopez and Camacho-Velázquez 2003, Fuentes-Cruz et al 2010. In a recent study, Holy and Ozkan (2016) have demonstrated the potential of anomalous diffusion formulation for the analysis of production data of fractured horizontal wells in unconventional reservoirs. They presented a procedure to identify the diffusion type (super-or sub-diffusion) and to estimate the diffusion exponents.…”

“…Using the estimated diffusion exponents and an anomalous diffusion model, they history matched the data to estimate the phenomenological coefficient. Figure 7, taken from Holy and Ozkan (2016), shows the history match of gas production data for a Bakken horizontal well by using a numerical anomalous diffusion model, which is similar to the analytical model used in this work. The blue data points in Fig.…”

“…Field Applications fromHoly and Ozkan (2016) flexibility and additional utility. Verifications showed that that the solution reverts to the traditional DP solution under ND.…”

Physics-preserving averaging scheme based on Grünwald-Letnikov formula for gas flow in fractured media

“…Combining a collection of these properties, we end up with a Non-Newtonian Non-Darcy flow equations system (Amir and Sun, 2017). That system can easily be simplified into the typical Newtonian Darcy flow system through substituting each superscript and M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT by 1 (Amir and Sun, 2017) such that each possible range within the viscosity described using the "power-law" or "Ostwald de Waele" establishes some indications as follows: (1) < 1 → shearthinning fluid; (2) = 1 → Newtonian fluid; and (3) > 1 → shear-thickening fluid (Chhabra and Richardson, 2011) along with some other multi-scale heterogeneous-diffusion uncertainties (Albinali and Ozkan, 2016;Holy and Ozkan, 2016) that can be indicated by ranges within the temporal and spatial flux equations as follows: (1) < 1 → Anomalous Sub-Diffusion; (2) = 1 → Normal Diffusion; and (3) > 1 → Anomalous Super-Diffusion (Obembe et al, [2017a(Obembe et al, [ , 2017b(Obembe et al, [ , and 2017c; Chen, [2013 and).…”