Pressure/Pressure Convolution Analysis of Multiprobe and Packer-Probe Wireline Formation Tester Data
- Mustafa Onur (Istanbul Technical U.) | Peter S. Hegeman (Schlumberger) | Fikri J. Kuchuk (Schlumberger)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- October 2004
- Document Type
- Journal Paper
- 351 - 364
- 2004. Society of Petroleum Engineers
- 5.6.1 Open hole/cased hole log analysis, 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 5.5.11 Formation Testing (e.g., Wireline, LWD), 5.6.4 Drillstem/Well Testing, 5.1 Reservoir Characterisation, 4.3.4 Scale, 5.5.8 History Matching, 5.6.3 Pressure Transient Testing, 4.6 Natural Gas
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In cases in which flow-rate data are not reliable, the need for flow rate in estimating permeability from wireline formation tester multiprobe and packer-probe pressure-data sets can be eliminated by the use of the so-called pressure/pressure (p/p) convolution. The p/p convolution is based on the use of different pressure-data sets recorded at two different spatial locations and thus enables one to perform parameter estimation without flow rate. In this work, we present a detailed analysis of multiprobe and packer-probe pressure-transient tests by considering various p/p convolution options for both single-layer and multilayer systems. Approximate equations that apply during spherical and radial flow for a vertical well in a single-layer system for various p/p convolution options are derived. These equations indicate which parameters can be determined uniquely from p/p convolution. It is shown that p/p convolution analysis sometimes may not provide unique parameter estimates. Also, we provide a flow-rate-estimation method that proves useful to check the validity of parameter estimates obtained from p/p convolution analysis. Two example tests, a synthetic multiprobe test and a field packer-probe test, are given to illustrate the methodology and procedures developed in this work.
The multiprobe (Fig. 1) and packer-probe (Fig. 2) wireline formation testers 1-6 are used in the industry to conduct controlled local production and vertical interference tests. These tools provide valuable information on undisturbed formation pressure, formation fluid samples, and estimates of horizontal and vertical permeability and wellbore damage. Further details about wireline formation testers, combined with packers and multiple probes, can be found in Refs. 1 through 6.
Permeability estimation from pressure data acquired by multiprobe and packer-probe formation testers has been the subject of several studies1-14 in the literature. Goode and Thambynayagam 1 were the first to present comprehensive analytical models to study multiprobe formation tester pressure behaviors in single-layer anisotropic systems. They showed that if flow rate is known at the sink probe, it is possible to determine horizontal and vertical mobilities (k h/µ and k v/µ), as well as the porosity/compressibility product (fct), from pressure data recorded at the horizontal and vertical probes by using pressure/rate (p/r) convolution.
Fluid production at the sink probe or the packer module can be performed by using a sample chamber module, flow-control module, or pumpout module.1-6 In cases in which the flow-control and/or pumpout modules are used, reliable flow-rate data often can be determined from direct measurements of the piston displacement and tool characteristics.1-6 Sometimes, wireline formation testers have no direct flow-metering device; thus, flow rate vs. time data required in the analysis based on p/r convolution must be inferred from other measurements. Zimmerman et al.2 noted that flow-rate data also could be computed from sink-probe pressure data using a modified form of a technique described by Samso et al.7 In a later paper, Goode et al. 3 presented a similar flow-rate-estimation method based on the solution given by Moran and Finklea. 8 The flow-rate-estimation methods given in Refs. 2 and 3 assume that the flow pattern around the sink probe is reasonably well approximated by spherical flow, and they require an iterative procedure that adjusts a lumped parameter involving horizontal mobility until the predicted volume of fluid recovered matches the recovered sample chamber volume.
Pop et al.5 were the first to introduce vertical interference testing with a wireline-conveyed straddle-packer tool equipped with a vertical observation probe. They presented an interpretation technique to estimate mobility and permeability anisotropy from the interference-test pressure data. Their estimation technique uses nonlinear least-squares matching of vertical probe pressures based on the p/r convolution. The flow-rate data required in p/r convolution are computed from measured packer-interval pressures using an iterative procedure. Later, Kuchuk et al.6 presented an interpretation method based on the simultaneous nonlinear matching of packer-interval and vertical probe pressures to estimate formation parameters as well as flow rates. Recently, Onur and Kuchuk9 presented a computationally more efficient nonlinear least-squares optimization scheme that also allows simultaneous estimation of formation permeabilities and flow rates from pressure-transient data acquired from multiprobe and packer-probe tests. The pressure behaviors of multiprobe and packer-probe modules in crossflow-layered systems and horizontal wells were studied by Kuchuk.10-12
Although various flow-rate-estimation techniques exist, there is always a concern about the reliability of computed rates. During flow periods, the computed flow rates may be inaccurate because of factors such as changing fluid compressibility within the tool and friction. For the buildup period, flow rate rapidly becomes too small to be computed or measured accurately. By considering these problems, Goode et al.3 presented a formulation that combines the pressure data recorded at two different locations (horizontal and vertical probe pressures) to eliminate the need for flow-rate data. This formulation is known as p/p convolution. Because pressure measurements at the probes are acquired accurately with high-resolution quartz pressure gauges, the p/p convolution becomes quite attractive for model (flow-regime) identification and parameter estimation without flow-rate measurements. The applications of the p/p convolution and deconvolution to model identification and parameter estimation from multiprobe and packer-probe pressure data have been considered in some detail in several studies.3,5,13,14 The studies involving multiprobe tests only considered the p/p convolution based on the use of horizontal and vertical probe pressures, while the studies involving packer-probe tests only considered the p/p technique based on the use of packer-interval and single vertical probe pressures. Furthermore, these studies are limited to single-layer systems.
In this work, our objective is to provide a detailed investigation of the uniqueness of parameters estimated from various p/p convolution options in both single-layer and multilayer systems.
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