Geocritical Reservoir Flow Simulation and Display Using Open Porous Medium (opm) Code

Spatial fluctuations for in situ flow structures tend to be spatially highly erratic and to scale with physical dimension. Such reservoir flow spatial fluctuation properties are reflected in the lognormal distributions of well productivities in some oil/gas and geothermal fields. Ability to efficiently recognize and manage large-scale spatially erratic flow structures when they are present is thus key to cost-effective reservoir operation. The Open Porous Medium (OPM) consortium provides industry-compatible open-source finite-element flow simulation code with robust handling of spatially complex flow distributions. For situations where the flow is dominated by fractures, 3 empirical rules be stated: (i) power-law-scaling fracture density fluctuations exist over cm-km scale lengths; (ii) changes in permeability δκ are proportional to the product of permeability κ and changes in porosity δφ, δκ ∝ κ δφ; and (iii) κ is lognormally distributed, κ ∝ exp(αφ), α >> 1. OPM can be adapted to systematic modelling of this type of heterogeneity, which we show can be detected by new methods in seismic emission tomography. We exhibit here the aptitude of OPM code for simulating and displaying spatially complex, single-phase flow distributions. We show that it can be efficient and accurate used for modeling of reservoir where significant flow heterogeneity is responsible for lognormal distributions of well productivity. 1. GEOCRITICALITY: THE THREE RULES Out of computational necessity some past geothermal reservoir observations and concepts have been fit to earth models comprising a small range of geologically identified formations (e.g., Grindley 1965 MDW 1977; DSIR 1981; Wood 1992; Allis 2000; White et al 2005; Bignal & Milicich 2012). These formations are generally assumed to have essentially uniform physical properties (e.g., Theis 1935, 1952; Biot, 1941; Horner 1951; Freeze 1975; Earlougher 1977; Kitanidis 1990; Horne 1995; Mannington et al 2004; Ingebritsen et al 2010; Gudmundsdottir 2012; Ricard et al 2012). In some cases non-uniformity in physical properties has been limited to adding various mechanically discontinuous fault structures as needed to adjust flow models to observed pressure and flow data. In situations where reservoir properties are highly heterogeneous, the limitations of such reservoir modeling assumptions have long been recognised (Warren & Skiba 1964; Freeze 1975; Smith & Freeze 1979; Dagan 1981, 1982; Desbarats 1987; Kitanidis 1990). For example, because of pervious computational limitations, it has been practically difficult to use them to forecast new well productivity, along with well-core permeability, and trace element and ore grade distributions. In many instances these properties are found to follow lognormal distributions (Law 1944; Warren & Skiba 1964; Jensen, Hinkley & Lake 1987; Limpert, Stahel & Abbt, 2001; Leary & Al Kindy 2002; US Energy Information Administration 2011; Grant 2009; Leary, Pogacnik & Malin 2012; Leary et al 2013a,c). One modeling approach for dealing with these observations is to include multiple layers with multiple properties, the net distribution of which approach lognormality (M. O’Sullivan, personal communication, 2013). Quantitatively, such distributions imply at there exists large scale features that span the sample volume (e.g. Mitzenmacher, 2004), thereby helping account for many of the observed features of the flow field. To understand the effects of introducing more and more heterogeneity into a flow model consider first a simple system of geologically-recognized layers. If we log a well drilled through a reservoir model composed of a few laterally uniform layers, we record a series of step-functions in logged properties at their boundaries. As discussed in Appendix A, the Fourier spectrum of such a numerical log has a specific property explicitly associated with step functions: