Probabilistic Decline Curve Analysis in the Permian Basin using Bayesian and Approximate Bayesian Inference

Summary In this work, a probabilistic methodology for decline curve analysis (DCA) in unconventional reservoirs is presented using several Bayesian model-fitting algorithms and deterministic models. The deterministic models considered are the power law exponential (PLE) model, the stretched exponential production decline (SEPD) model, Duong’s model, and the logistic growth analysis (LGA) model. Accurate production forecasting and uncertainty quantification were the primary objectives of this study. The Bayesian inferencing techniques described in this work utilize three sampling vehicles, namely the Gibbs sampling (implemented in OpenBUGS, an open-source software), the Metropolis-Hastings (MH) algorithm, and approximate Bayesian computation (ABC) to sample parameter values from their posterior distributions. These different sampling algorithms are applied in conjunction with DCA models to estimate DCA parameter prediction intervals. Using these prediction levels, production is forecasted, and uncertainty bounds are established. To examine its reliability, the methodology was tested on over 74 oil and gas wells located in the three main subplays of the Permian Basin, namely, the Delaware play, the Central Basin Platform, and the Midland play. Results show that the examined DCA-Bayesian models are well calibrated, result in low production errors, and narrow uncertainty bounds for the production history data sets. Also, the LGA model is best in terms of prediction errors for all algorithms except MH. The Gibbs algorithm is nearly the best algorithm in terms of prediction error for all DCA models except the Arps model. Prediction errors are the highest in the Central Basin Platform. The methodology was also successfully applied to unconventional reservoirs with as low as six months of available production history. Depending on the amount of production history data available, the probabilistic model that provides the best fit can vary. It is therefore recommended that all possible combinations of the deterministic and Bayesian model-fitting algorithms be applied to the available production history. This is to obtain more confidence in the conclusions related to the production forecasts, reserves estimate, and uncertainty bounds. The novelty of this methodology relies on using multiple combinations of DCA-Bayesian models to achieve accurate reserves estimates and narrow uncertainty bounds. This paper can help assess shale plays because some of the shale plays are in the early stages of development when productivity estimations are carried out.

Techniques and best practices in multiattribute display

All color monitors display images by mixing red, green, and blue (RGB) components. These RGB components can be defined mathematically in terms of hue, lightness, and saturation (HLS) components. A fourth alpha-blending (also called opacity) component provides a means to corender multiple images. Most, but not all, modern commercial interpretation workstation software vendors provide multiattribute display tools using an opacity model. A smaller subset of vendors provide tools to interactively display two or three attributes using HLS, CMY, and RGB color models. I evaluated a technique (or trick) to simulate the HLS color model using monochromatic color bars and only opacity. This same trick only approximates true color blending of RGB or CMY components. There are three basic objectives in choosing which attributes to display together. The first objective is to understand the correlation of one attribute to another, and most commonly, of a given attribute to the original seismic amplitude data. The second objective is to visualize the confidence or relevance of a given attribute by modulating it with a second attribute. The third objective is to provide a more integrated image of the seismic data volume by choosing attributes that are mathematically independent but correlated through the underlying geology. I developed the interpretation value of the HLS display technique on a 3D data volume acquired over the Central Basin Platform of west Texas exhibiting faults, fractures, folds, channels, pinch outs, and karst features. To be a useful “technique,” I need to demonstrate these workflows within a specific package. Although I implemented the workflow in Petrel 2014, similar images can be generated using any software with flexible opacity capabilities. I also developed a short list of attribute combinations that are particularly amenable to corendering in HLS.

Eustatic controls on stratigraphy, chemostratigraphy, and water mass evolution preserved in a Lower Permian mudrock succession, Delaware Basin, west Texas, USA

Bone Spring (Leonardian) mudrock successions in Delaware Basin vary between silica- and carbonate-rich facies marking depositional responses to sea-level changes. Increased Mo, [Formula: see text], and total organic carbon (TOC) record reduced oxygenation during sea-level lowstands. In a 91.4-m (300 ft) core from Sun No. 1 Houssels well and a 39.6-m (130 ft) core from Shell No. 1 Marsden well (Reeves Co., Texas), lower Bone Spring cycles comprised siliceous-calcareous mudrock couplets. The Marsden core was correlative to the upper part of the Houssels core. Cyclicity was interpreted from mineralogical calculations at numerous core horizons using energy-dispersive X-ray fluorescence (ED-XRF) measurements of elemental content. Elemental abundances enabled predicting mineralogy based on the stoichiometric relationships between elements and dominant minerals (calcite and quartz), and from average values of Si and K in published illite analyses. The average sample spacing for ED-XRF measurements was 0.24 m (0.8 ft) for the Houssels core and 0.15 m (0.5 ft) for the Marsden core. The measurements and interpretations provided: (1) information regarding comparisons in stratigraphic and geographic development of facies over the 10-km (6.2-mi) distance between wells and (2) guidance for petrographic, scanning electron micrograph, and organic matter analyses that address processes that produced different facies. Greater carbonate abundance in the Houssels core reflected the proximity to carbonate shelves on the Central Basin Platform (CBP); the greater siliciclastic abundance in the Marsden core was thought to reflect the greater distance from the CBP. Redox element (S and Mo) and TOC concentrations were greater, and [Formula: see text] values were higher in some siliciclastic-dominated intervals, suggesting that anoxia characterized sea-level lowstands when normal marine water flowing from the Panthalassa Ocean was inhibited through narrow interbasin channels or over sills. Carbon isotope ([Formula: see text]) variations suggested changes in organic matter characteristics, whereby greater [Formula: see text]-depleted organic matter was deposited during sea-level lowstands, marking: (1) reduction of shallow-marine sources or (2) increased terrigenous organic carbon contributions.

Instantaneous spectral attributes to detect channels

Channels filled with porous rock and encased in a nonporous matrix constitute one of the more important stratigraphic exploration plays. Although attributes such as coherence can be used to map channel width, they are relatively insensitive to channel thickness. In contrast, spectral decomposition can be used to map subtle changes in channel thickness. The peak spectral frequency derived by using the short-window, discrete Fourier transform (SWDFT) is an excellent tool for mapping such changes along an interpreted horizon. We show that by use of instantaneous spectral attributes, we can generate equivalent maps for complete seismic volumes. Because we are often interested in mapping high-reflectivity channels encased in a lower-reflectivity matrix, we find that a composite plot of the peak frequency and the above-average peak amplitude accentuates highly tuned channels. Finally, by generating a composite volume using peak frequency, peak amplitude, and coherence, we can establish not only the channel thickness, but also its width. We demonstrate the value of such 3D volumetric estimates through application to (1) a marine survey acquired over Tertiary channels from the Gulf of Mexico and (2) a land data survey acquired over Paleozoic channels from the Central Basin Platform, west Texas, United States. The channels in both marine and land surveys can be highlighted through composite-volume analysis.