A New Technique for Quantifying Pressure Interference in Fractured Horizontal Shale Wells

Abstract

Pressure communication is commonly observed in fractured horizontal shale wells, particularly at early times when wells are placed on production. This paper will present a new technique, based on the diffusion exponent from the power-law model, to quantify connectivity in multi-stage hydraulic fractured wells with complex fracture networks. In addition to explaining the theory and analysis techniques, we will present examples utilizing measured bottom-hole pressure (BHP) from the Permian Basin Wolfcamp Shale, which illustrate the utility of this technique to better understand the relationship between completion size, well spacing, and well performance. Chen and Raghavan (2015) recently developed a one-dimensional, fractional-order, transient diffusion equation to model fluid flow in complex geological media. They showed power-law behavior is the norm in unconventional reservoirs such as Permian Basin Wolfcamp Shale. Under the framework of power law behavior, we plot pressure interference test (PIT) data in terms of the Chow Pressure Group (CPG), which enables us to define an indicator of connectivity reflecting temporal and spatial effects. On each test, we derive a diffusion exponent reflective of the magnitude of pressure interference (MPI). We will show among other things that multiple PITs over time often indicate degrading connectivity between wells. From PIT analyses in Permian Basin Wolfcamp Shale, we were able to establish a relationship between MPI and well spacing. The first example demonstrates analyses of PITs between wells during the production phase and also shows how connectivity between wells diminishes over time. A second example applies the same analysis techniques to quantify inter-well connectivity during the post-stimulation phase by analyzing a pressure falloff (PFO) after communication with other wells. A third example illustrates an application of desuperposition to remove the effect of a power-law pressure trend on interference tests. Techniques to analyze PITs assuming radial or linear flow have been previously developed; however, Raghavan and Chen (2018) showed apparent radial or linear flow could exist under anomalous diffusion for heterogeneous reservoirs. In this work, we present a technique for analyzing power-law PIT data, which is typical of most horizontally fractured shale wells. This model is a unique approach to understanding flow behavior, quantifying well interference, and analyzing & predicting well performance in unconventional reservoirs. Our examples, which are based on high-quality BHP gauge data, show how this technique could shorten the cycle time for operators to determine the well spacing for a given completion design.

Investigation on Interference Test for Wells Connected by a Large Fracture

“…From Equations (35) and (40), it can be seen that the pressure conductivity coefficient for WsCLF differs from that for homogeneous reservoirs by a factor 2. The distance used in Equation 35is the distance along the fracture rather than the straight line distance.…”

“…Frequently, hydraulic fracturing causes pressure communication in adjacent horizontal wells [32][33][34]. Interference test wells are also used to test their connectivity [35]. The existing analysis models consider the flow of the entire reservoir and are generally solved through numerical or semi-numerical methods [36,37].…”

The Theis solution for subdiffusive flow in rocks

“…The concept of subdiffusion offers a viable option to evaluate well tests which display near power-law behaviors; as already mentioned, classical methods to address tests of the kind shown in Figure 6 require the conjuring up of counterfactual geological options or ignoring heterogeneity altogether. Models incorporating subdiffusive effects have been shown to be a promising alternative in explaining the performance of shale reservoirs; see Chu et al (2017Chu et al ( , 2018.…”

“…Other approaches that account for spatial variability have represented transient diffusion by representing the porous medium as a fractal object (Camacho-Velázquez et al, 2008;Chang and Yortsos, 1990;Raghavan, 2009a). This approach is particularly fruitful because it has been suggested (Kim et al, 2015;Raghavan, 2011) and shown (Benson et al, 2004;Chu et al, 2017Chu et al, , 2018 that there is an interdependence between the topological and geometric properties of the reservoir rock and the physics of fluid movement particulary if the geology is complex. This hypothesis leads to the consideration that diffusion is anomalous and a reconsideration of Darcy's law; see for example, Nigmatullin (1984Nigmatullin ( , 1986, Le Mẽhautẽ (1984), Dassas and Duby (1995), Henry et al (2010) to name a few of the many such citations.…”

An application of a multiindex, time-fractional differential equation to evaluate heterogeneous, fractured rocks

“…Time-Fractional Flow Equations (t-FFEs) are particularly useful in the evaluation of systems of complex geology to incorporate the internal architecture and internal imprint involving barriers, intercalations and the like Chu et al (2017Chu et al ( , 2018, Ingle et al (2020), Raghavan and Chen (2018). Such blockages result in interconnected highconductivity pathways interspersed with low permeability blockages.…”