Research paperConditioning 3D object-based models to dense well data
Introduction
Object-based modeling (OBM) involves the following processes: parameterizing architectural objects, inferring distributions and other constraints on these parameters, sequentially drawing from these distributions to simulate and place objects into a reservoir model initialized with one background facies until some criteria, such as target global proportion and data conditioning are met (Pyrcz and Deutsch, 2014). Fluvial reservoir modeling is one area in which OBM is widely applied. The fluvial model is built from different types of fluvial sedimentary objects known as architectural elements. In the fluvial depositional setting there is a wealth of information on architectural elements, with 16 different types of rivers and associated reservoirs being described (Miall, 1996), each one defined by a particular association of architectural elements. Previous object-based modeling approaches considered objects such as channels (Labourdette, 2008; Ruiu et al., 2016), levees, crevasses (Deutsch and Wang, 1996), sand lenses, point bars (Hassanpour et al., 2013; Pyrcz and Deutsch, 2005) and oxbow mud fills (Pyrcz et al., 2009).
The most challenging aspect of OBM is data conditioning. Data conditioning is defined as architectural elements in wells intersected by the correct associated objects with the correct position and length of intersection. Furthermore, locations along wells interpreted as overbank are not intersected by any object. There are various data conditioning methods available for object-based models. Conditioning through pixel-based erosion and dilatation is not guaranteed to preserve geometry (Henrion et al., 2010). Viseur et al. (1998) and Shmaryan and Deutsch (1999) propose conditioning through direct object placement in a 1D simulation of the channel centerline simulation. Pyrcz and Deutsch (2005) present conditioning through simulation of many channel centerline candidates and rejection sampling along with local morphing for precise conditioning. Simulated annealing (Deutsch and Wang, 1996) and Metropolis-Hastings algorithms (Holden et al., 1998; Oliver, 2002) have been effective with limited data conditioning. However, these methods are computationally expensive, challenging to set up and have no guarantee of convergence. Rongier et al. (2017a, b) simulated stacked channels with nicely preserved morphology and some extent of data conditioning but additional work is needed for improving conditioning. Bertoncello et al. (2013), Boisvert and Pyrcz (2014) and Wingate et al. (2016) explore the application of new optimization techniques on OBM conditioning problems.
Regarding existing methods for channel conditioning, there are opportunities for improvement. Some methods build an initial unconditional object model by sampling randomly from the parameter distributions (Deutsch and Wang, 1996). Conditioning is achieved by perturbing the objects resulting in high computation cost. Other methods directly initialize objects to condition to well data (Viseur et al., 1998; Shmaryan and Deutsch, 1999), which significantly improves efficiency, but dramatically restricts the channel paths; as a result, the uncertainty space explored by these stochastic simulations may be limited. Methods that initialize objects randomly from a distribution and rely on rejection sampling and local morphing may still have a very low acceptance rate (Holden et al., 1998; Pyrcz and Deutsch, 2005). Given the recent rapid increases in computational power, there are new opportunities to improve OBM conditioning. The proposed methodology applies an optimization algorithm to candidate objects to effectively build a better conditioned population of objects. Implicit filtering (Kelley, 2011) is adapted to build large libraries of conditioned objects. These objects are locally optimized for conditioning, which means their shapes and location are adjusted according to the local conditioning data. After this local optimization, a subset of the locally conditioned objects is retained for the final realization. Bertoncello et al. (2013), Boisvert and Pyrcz (2014) and Wingate et al. (2016) showed the potential of optimization techniques to build conditioned object-based models. This paper demonstrates the ability of the optimization-simulation workflow with more versatile and complicated objects and encourages the use of modern optimization techniques in object-based modeling.
Case studies conditioning fluvial objects are presented with channels, levees, crevasse splays and oxbow lake architectural objects; this association of architectural elements is typical of low-energy rivers with highly sinuous channels. With more and more data emerging, especially seismic data, new interpretations regarding the origin, evolution and architecture of channel-levees (McHargue et al., 2011; Alpak et al., 2013; Deptuck et al., 2003; Sylvester et al., 2011; Babonneau et al., 2010; Abreu et al., 2003; Posamentier, 2003; Macauley and Hubbard, 2013; Deptuck et al., 2007) and crevasse splays (Ford and Pyles, 2014; Stouthamer, 2001; Li and Bristow, 2015) have been developed. This information may be adapted into the objects parameterization to ensure that the model is geologically realistic for improved prediction away from wells and forecasts of production rates.
In Section 2, the proposed optimization method for conditioning objects to local data is described through an example considering simplified channel objects. Then, a number of conditioned candidate objects are built and simulations of a full domain of objects are constructed by selecting from these objects. Procedures and results of channel-only simulations are presented in Section 4. The optimization-simulation workflow can be easily applied to other types of objects. In Section 3, geology and parameterization of several types of objects from a fluvial system are presented. The objects are optimized using the same methodology from Section 2 before they are selected for realizations. Finally, Section 5 demonstrates an approach based on combining all types of objects into realizations. Concluding remarks follow in Section 6.
Section snippets
Optimization methodology
In this section, the optimization methodology to build conditioned objects is presented through a simplified example. The general procedure is:
- 1.
Initialize an object with a set of parameters (x1, x2, …, xn) which fully define the initial state of the object.
- 2.
Define an objective function to minimize based on data conditioning and geological realism.
- 3.
Apply implicit filtering (Kelley, 2011) to adjust the initial parameters. The only inputs are the object generating function (step 1) and the objective
Fluvial objects
The conditioning of OBM is illustrated through objects from a fluvial depositional setting (Fig. 4), although the method can be used on any type of object.
Realization construction
The optimization method (Section 2) only conditions individual objects and nearby well data. A realization is created by combining locally optimized objects to match all available well data. In the first case study, only channels are considered. For the simulation of one stratigraphic unit of channel objects, the main procedure is:
- 1.
Build an object database with many optimized objects.
- 2.
Check match performance and whether every well with channel facies has been conditioned by at least one object
Conditioned realization with multiple objects
Additional objects besides channels are considered. Generally speaking, channels and levees are the main objects. They are optimized first using implicit filtering. After the optimization, the algorithm attaches crevasse splays and oxbow lakes to the channels. Each attached-object has an anchor point so that the relative positions of objects are constrained. The optimization for attached-objects begins with the anchored models.
Fig. 13 depicts each of the modeling steps for five types of
Discussion and conclusion
Prevalent optimization workflows for object based modeling tend to define an optimization hierarchy (Hauge et al., 2017), which requires ordering the parameters to optimize. The values of those parameters change according to tailored steps. The tailored optimization workflow can improve conditioning to some extent but is very time consuming in terms of designing programs. On the other hand, this paper leaves the optimization task to general optimization algorithms. Preferred features and
Unlisted references
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- 1
Formally Chevron Energy Technology Company.
- 2
Center for Computational Geostatistics, Department of Civil and Environmental Engineering, University of Alberta.