Long‐range, critical‐point dynamics in oil field flow rate data

Abstract

[1] Earthquake triggering data exhibit long-range spatiotemporal correlations of the power-law form C(l ) $ l À and anomalously-slow temporal diffusion of the mean triggering distance of the form: hli $ t H , with H < 0.5. We examine spatio-temporal correlations in subsurface effective stress state caused by fluid injection and extraction at well sites in a hydrocarbon reservoir using a multivariate statistical regression model, and observe long-range correlations in flow rate that cannot be caused by Darcy flow alone. Significantly-correlated well pairs align with the directions of incipient horizontal-displacement tensile and shear failure in the present-day stress field, while the contours of the first principal component of the regression matrix closely follow the macroscopic fault pattern in the main producing horizon. The correlation function for well pairs has a power-law form with % 0.5, and the mean correlation distance increases with H % 0.33, implying a similar critical-point response to perturbations in effective stress as the earthquake data.

Analysis of GPS Measurements in Eastern Canada Using Principal Component Analysis

“…The EOF analysis is often used to filter data through the identification of those modes associated with large percentages of unwanted covariance or those lower modes accounting for random noise (PREISENDORFER 1988;PENLAND 1989;DONG et al 2006). Others have applied the KLE technique to investigate spatiotemporally correlated geophysical signals in the position time series (SAVAGE 1988;POSADAS et al 1993;TIAMPO et al 2002;MAIN et al 2006;SMITH et al 2007), such as mass loading caused by seasonal deformation (TIAMPO et al 2004). For example, DONG et al (2002) and KEDAR et al (2003) demonstrated that some seasonal effects are due to systematic errors in the daily CGPS time series.…”

“…It has been applied to a number of complex nonlinear systems over the last 50 years, including the ocean-atmosphere interface, turbulence, meteorology, biometrics, statistics, and geophysics (HOTELLING 1933;FUKUNAGA 1970;AUBREY and EMERY 1983;PREISENDORFER 1988;SAVAGE 1988;PENLAND 1989;VAUTARD and GHIL 1989;POSADAS et al 1993;PENLAND and SARD-ESHMUKH 1995;HOLMES et al 1996;MOGHADDAM et al 1998;TIAMPO et al 2002;DONG et al 2006;MAIN et al 2006;SMALL and ISLAM 2007;SMITH et al 2007). In one of the first successful geodetic Vol.…”

The challenges and impact of compartmentalization in reservoir appraisal and development

“…As soon as the first well is drilled, the mechanical equilibrium of the field is disturbed. Once water or gases are introduced into a reservoir, as part of a secondary recovery processes to boost oil or gas recovery, their introduction can lead to changes in the permeability field and the physical properties of the reservoir (Jansen & Kelkar 1997;Pizarro & Lake 2001;Rutledge et al 2004;Main et al 2006).…”

“…We are now beginning to place a greater emphasis on capturing appropriate ranges of geological scenarios and associated uncertainty ranges, with the incorporation of dynamic signals from production data (Bentley & Smith 2008;Smalley et al 2008). Evidence is also mounting that as fields deplete under production they evolve mechanically: leading to changes in injectorproducer well communication; fault seal integrity; fault zone conductivity; fracture permeability; near and far-field stress configurations and orientations; and reservoir permeability heterogeneity (Heffer et al 1995;Heffer 2002;Main et al 2006;Zhang et al 2007). These effects are commonly not predicted at the early stages of field development.…”

Geomechanical mechanisms involving faults and fractures for observed correlations between fluctuations in flowrates at wells in North Sea oilfields

“…Heffer et al (1995) employed standard measures of correlation between flowrate series, especially the Spearman rank correlation coefficient. Main et al (2006Main et al ( , 2007 analysed flowrate fluctuations through the Statistical Reservoir Model (SRM), which produces a parsimonious linear relationship between flowrate fluctuations at different wells by a twostage process of eliminating correlations that are not statistically significant. In these analyses the histories of flowrates at each well can be displaced in time relative to each other; for example, the flowrate at one well can depend not only on the current flowrates at other wells but also on flowrates at previous times, offset by a 'time-lag'.…”