Numerical Sensitivity Studies for the Joint Inversion of Pressure and DC Resistivity Measurements Acquired with In-Situ Permanent Sensors

Abstract

Abstract In-situ permanent sensors allow the possibility of monitoring in real time dynamic changes in formation properties due to primary or enhanced hydrocarbon recovery. A feedback loop can be enforced in response to in-situ permanent sensor data to optimally control the recovery of hydrocarbon assets. Prototypes of in-situ permanent sensors include pressure gauges, acoustic geophones, and direct-current (DC) resistivity electrodes. In the past, quantitative studies have been performed to assess the value of in-situ permanent pressure data to mapping permeability variations in close proximity to the sensor deployment1. Malinverno and Torres-VerdÍn2 on the other hand, have described a procedure to estimate water invasion profiles using in-situ DC resistivity sensors. However, to date little is known about the possibility of estimating petrophysical variables that jointly honor pressure and DC resistivity data acquired with in-situ permanent sensors. The two types of data sense different and complementary components of the underlying petrophysical model, and it seems appropriate to develop a quantitative estimation procedure that can assimilate the best elements of the two types of measurements. In this paper, we develop a methodology to jointly invert pressure and DC resistivity data acquired with in-situ permanent sensors in a hypothetical water injection experiment. Time-variable flow rates are enforced while injecting water into the surrounding rock formations, hence producing a sequence of repeated pressure pulses. The objective of the experiment is to estimate permeabilities, porosities, and fluid distributions that honor (a) sensor data acquired during a single pressure pulse, and (b) a more complete time record of pressure data acquired starting from the early stages of water injection. Our inversion results shed new light to the independent and joint sensitivity of noisy pressure and DC resistivity data to detecting dynamic perturbations of petrophysical properties. Examples of inversion are used to assess the relative benefits of different types of sensor deployments. Introduction Inversion of pressure transient data into spatial distributions of permeability has traditionally been a central element of the characterization and evaluation of hydrocarbon reservoirs. Data for this type of inversion consists of time records of fluid production and pressure. Examples of nonlinear inversion problems arising in the context of reservoir characterization can be found in Chen et al.3, Chavent et al.4, He et al.5, Wu et al.6, Wu7, and Wu and Datta-Gupta8. More recently, the availability of permanently installed downhole sensors has created a renewed interest in the solution of complex inverse problems in hydrocarbon reservoir characterization. A continuous space and time-domain data-stream is now available to conduct real-time monitoring of the variation of fluid flow parameters resulting from production (or injection) schedules. Prototypes of permanent sensors have also been constructed for behind-casing deployment9. When commercially available, in-situ sensors will offer the means of delivering real-time images of the spatial distribution of petrophysical properties not only in the proximity of a well but also between existing wells. These sensors will eventually serve as tools for real-time formation evaluation as well as for reactive reservoir management. The petrophysical information inferred through the interpretation of in-situ sensor data could be utilized in applications such as opening or closing of production intervals in response to the breakthrough of unwanted fluids, or in the early detection of an advancing water front prior to breakthrough. Permanently deployed resistivity arrays have been successfully tested to monitor fluid movement at the near and far-field reservoir scale9.