See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/238447419 Compositional Modeling of Oil-Based-Mud- Filtrate Cleanup During Wireline Formation Tester Sampling ARTICLE in SPE RESERVOIR EVALUATION & ENGINEERING · APRIL 2008 Impact Factor: 0.99 · DOI: 10.2118/100393-PA CITATIONS 12 READS 53 4 AUTHORS: Faruk Omer Alpak Shell International Exploration and Producti… 60 PUBLICATIONS 275 CITATIONS SEE PROFILE Hani Elshahawi Shell Exploration and Production Company 77 PUBLICATIONS 226 CITATIONS SEE PROFILE Mohamed Hashem Cairo University 38 PUBLICATIONS 130 CITATIONS SEE PROFILE Oliver C Mullins Schlumberger Limited 245 PUBLICATIONS 6,003 CITATIONS SEE PROFILE Available from: Oliver C Mullins Retrieved on: 04 February 2016
Copyright 2006, Society of Petroleum Engineers This paper was prepared for presentation at the 2006 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, U.S.A., 24–27 September 2006. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract Miscible oil-based mud (OBM) filtrate contamination poses a major challenge to the acquisition of representative fluid samples using wireline formation testers (WFTs). A sound understanding of the physics of OBM filtrate clean-up and identification of first-order impact parameters is of paramount importance for the design of new generation WFT probes that can operate in OBM filtrate environments with enhanced efficiency.
Analytical as well as numerical models reported in the formation testing literature rely predominantly on simplifying assumptions in terms of the compositions of flowing fluid phases. These models characteristically assume single-component phases in the case of two-phase immiscible formulation, or a two-/three-component hydrocarbon phase in cases of black-oil/extended black-oil formulations. In turn, compositional interactions are entirely neglected or represented through simplistic empirical correlations. Such conventional models are deemed sufficient for pre-job planning and interpretation of measurements acquired in formations subject to water-base mud (WBM) filtrate contamination. Dynamics of flow in OBM filtrate contaminated formations is significantly more complex. A time-dependent coupling between fluid dynamics and phase behavior constitutes the governing physics of OBM filtrate clean-up process. Therefore, for OBM filtrate environments, accuracy of conventional formulations in representing the actual physics of flow is limited.
We have constructed a numerical model for the OBM filtrate clean-up within the framework of an equation-of-state (EOS) compositional fluid-flow simulator. Our numerical framework simultaneously honors the physics of multi-component fluid flow and the thermodynamics of phase behavior. The numerical model was verified against analytical
solutions for zeroth-order models for which analytical solutions exist. Simulation results exhibited close agreement with the analytical predictions and with field data for the time dependence of contamination during sampling. A rapid approximate response surface based model, which can serve as a pre-job planning or real-time analysis tool, was derived from extensive simulations conducted with the compositional numerical model. Our simulation and rapid modeling results compare well with empirical observations made in the field. In particular, the rate of change of miscible contamination with time has been found empirically to vary as t5/12. For the first time, modeling has been shown to give essentially the same results as empirical observations. The agreement between our model and common field observation motivates use of our model to analyze the more complex WFT probes, which have recently become available. Introduction In the development of deepwater prospects and other capital-intensive exploration and production projects, understanding the nature of hydrocarbon fluids in terms of chemical and physical properties, phase behavior, spatial distribution, and hydraulic and thermodynamic communication are of critical importance. Fit-for-purpose design of completion and production facilities and optimal planning of reservoir production strategies depend strongly on adequate characterization of the physical and chemical properties of the fluids. In many deepwater and other high cost wells, wireline formation tester (WFT) fluid samples may be the only source of fluid properties reliable enough for economic screening. Therefore, it is imperative that representative high-quality WFT samples are collected early in any exploration or appraisal campaign.
Sampling in wells drilled with oil-based mud (OBM) and synthetic-based mud (SBM) presents special challenges. For sampling purposes, OBM and SBM behave similarly; henceforth, we will refer to OBM and SBM simply as OBM. In the case of sampling oil or gas in wells drilled with water-based mud (WBM), or sampling in water wells drilled with OBM, the decision on when to sample is much less critical, since the contaminant can generally be separated from the fluid of interest with greater ease. However, OBM filtrate is typically highly miscible with in-situ hydrocarbon fluid and the two cannot be physically separated subsequent to sampling. Mathematical decontamination is used instead, but
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Compositional Modeling of Oil-Based Mud-Filtrate Clean-Up During Wireline Formation Tester Sampling Faruk O. Alpak, SPE, Hani Elshahawi, SPE, Mohamed Hashem, SPE, Shell International Exploration and Production, Oliver Mullins, SPE, Schlumberger Oilfield Services
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there is some maximum contamination allowable for such methods to work depending on the type of HC and mud involved. For black oils, for example, it is a challenge to determine original crude oil fluid properties from samples contaminated at levels much greater than 10%.1 A robust extrapolation to original crude oil properties requires accurate determination of the level of contamination, which is not trivial to perform, especially in condensates and biodegraded fluids, as evidenced by common discrepancies between various lab analyses.2 The preferable approach is to reduce the contamination to low levels during sampling, yielding clean samples that require little parameter extrapolation. However, it is not acceptable to pump indefinitely to reduce OBM contamination levels since rig-time for some wells can be very costly and since the probability of tool sticking increases with lengthy pumping times. In addition, in certain cases contamination levels may remain high even after extended pumping solely due to the physics of OBM filtrate invasion. Therefore, it is essential that the sample be taken at an optimal time. If the sample is taken too soon, the sample will be overly contaminated and will be worthless for practical purposes. If the sample is taken later than necessary, then valuable rig-time will have been wasted.
The time needed to clean up the filtrate is dependent on a number of fluid and rock properties, the rate of clean up, and the extent of filtrate invasion that occurred during the drilling process. Numerical techniques have been developed in the recent past to predict the time to acceptable levels of WBM filtrate contamination and to understand sampling through a single probe3, a concentric probe, two single probes4, and straddle packers5. Although in-situ monitoring provides an alternative means of assessing contamination2, there is always a need for modeling in order to understand the various drivers that affect the clean-up process as well as to be able to predict the future progress of clean-up after various pumping times. Existing numerical models generally do not take into account the complexities associated with formation anisotropy, OBM filtrate-crude oil viscosity contrast, compositional effects on the clean-up process, and effects of parameters that stem from the geometry of the flow problem, i.e., wellbore radius, probe radius, proximity to a sealing boundary, etc. More importantly, there is little or no published verification of these models using actual miscible sampling field data.
In this paper we develop a high-resolution numerical model by taking into account the compositional effects of the OBM filtrate invasion phenomenon, various reservoir rock, fluid, and geometrical parameters, as well as the sampling process itself. This numerical model is applicable to a wide variety of WFT configurations that integrate optics based Downhole Fluid Analysis capability with single- or multi-probe modules. An example of such a WFT configuration is shown in Fig. 1.
Although the above-described numerical modeling framework could be used for predicting the clean-up time-function for pre-job planning, the full-physics numerical model is computationally too costly to run for concluding an all-inclusive pre-job planning study within a reasonable amount of time. With the exception of a few general mechanistic models, there are no physics-based analytical models available in the open literature that can be used to
predict levels of filtrate contamination for OBM filtrate invasion prior to the fluid sampling job. Therefore, in this paper we also formulate a novel approximate model that accounts for the physics of flow and phase behavior during OBM filtrate invasion process. For this purpose, our robust full-physics compositional numerical model and the simulation results of our extensive sensitivity studies were utilized to construct a response surface. Impacts of reservoir rock and fluid parameters, and OBM filtrate clean-up related geometrical parameters are all included in the construction of the approximate model in a weighted fashion. Example predictions of OBM filtrate contamination levels were performed using the rapid approximate model and validated with full-physics numerical simulations and actual field data.
Fig. 1— WFT tool configuration with Downhole Fluid Analysis (DFT) capability for the in situ characterization of formation fluid samples. The two fluid analyzers are depicted with rainbows. We focus on the modeling of LFA measurements acquired with the fluid analyzer deployed closer to the sandface. Downhole GOR measurements as an indicator for the progress of OBM clean-up. During the drilling process mud filtrate invades into the formation in the form of an annulus around the wellbore. The extent of mud filtrate invasion predominantly depends on the formation and mudcake properties. As the downhole sampling tools remove fluid in the near wellbore formation, the corresponding fraction of OBM filtrate contamination becomes smaller as a function of pumping time. It is essential to monitor quantitatively this level of contamination because if the contamination is too high, sample properties become corrupted, and the value of the sample is greatly reduced. In order to discriminate between OBM filtrate and crude oil, both oil coloration and GOR are measured during formation sampling.2,6,7,8,9,10,11 Differences in the absorption spectra of various hydrocarbon components, shown in Fig. 2, allow the correlation based computation of GOR for hydrocarbon fluid samples. Optical measurements are acquired while sampled formation fluids are flowing through an Optical Fluid Analyzer (OFA) module attached to the WFT string. As far as the hydrocarbon components are concerned, a wide spectrum from 400 nm to 2200 nm is monitored via OFA. The OFA consists of two independent measurement apparatus, namely, a gas detector and a spectrometer. A simple schematic diagram of the OFA module is shown in Fig. 3. Absorption below 1500 nm is primarily due to color. The vibrational overtone of hydrocarbon molecules between 1600 nm and 1800 nm (NIR spectrum) is used to resolve the composition of C1, C2-C5, and C6+. Recent
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developments have made both contamination and GOR measurements significantly more robust allowing expanded application of these techniques.11
Fig. 2— Absorption spectra of hydrocarbons: A wide spectrum from 400 nm to 2200 nm. Absorption below 1500 nm is primarily due to color. The vibrational overtone of hydrocarbon molecules between 1600 nm and 1800 nm (NIR spectrum) is used to resolve the composition of C1, C2-C5, and C6+.
Fig. 3— A schematic diagram of the OFA. The OFA consists of two independent measurement apparati: A gas detector and a spectrometer.
During sampling, pressure reduction is required to move fluid from the formation to the acquisition tool. If this pressure reduction is too large, phase separation can occur when fluid pressure drops below asphaltene onset pressure and/or the saturation pressure. This can have many adverse effects on the sample quality. For instance, if the flowing pressure of retrograde condensate drops below the dew point pressure, liquid may drop in the near-wellbore region and in the tool, while gas, the more mobile phase, would flow preferentially, thus resulting in a non-representative sample. It is now possible to detect the dew point pressure of the fluid sample by measuring its fluorescence properties.12 Fluorescence measurements such as intensities and spectra as well as fluorescence lifetimes are highly sensitive to the hydrocarbon type.13 In turn, fluorescence measurements can be used as a safeguard against multiphase flow by adaptively adjusting the sampling rate to ensure single-phase sampling.
The oil industry’s first in-situ measurement of a PVT-type formation fluid property consists of obtaining gas-oil ratio (GOR) via measuring the dissolved methane versus liquid oil fraction in a single-phase crude oil 9, 10 using the Live Fluid
Analyzer (LFA™) tool during openhole fluid sampling. The conventional laboratory method to measure GOR is to flash the fluid to atmospheric surface conditions and measure the volume of gas and liquid. LFA GOR measurements, on the other hand, are performed downhole using the ratio of optical density at the methane peak to the oil peak while retaining the fluid in single phase throughout. Mullins and Schroer2, Mullins et al.7,8, and Mullins et al.9,10 described in detail the physical basis of LFA GOR measurements. Because the LFA GOR is computed from the optical density ratio of the methane channel to the oil channel, it is more sensitive to the change of sample contamination than individual methane and color channels. At very low contamination levels, the methane or the color channel may not be sufficiently sensitive to reflect slight variations in sample contamination. However, the GOR measurement will remain sufficiently sensitive and stable to exhibit build-up behavior and indicate cleaning up of the sample. Compared to color and methane measurements, the GOR measurements are less affected by pumping rate variation. While both methane and color channels may be affected by scattering, calibration, and baseline shifts, GOR measurements build-up more smoothly and continuously, regardless of the pumping rate variations. When compared to the optical density of the methane or color channels, GOR is a more physically meaningful quantity to end users. The apparent measured GOR of the HC in a given layer can be directly compared to the expected GOR (derived from pressure gradient or other sources) to obtain a good estimate of the contamination level of the sample. This allows the planning and execution of more optimized sampling programs.1 Moreover, the practice of comparing measurements acquired in different layers or sections of the same layer can be used to estimate the extent of compositional grading in a reservoir. In addition, measurements of GOR can identify fluid density inversions, higher density fluids higher in the column, thereby indicating compartmentalization.1 Literature survey. Modeling fluid flow has been a useful approach to understand the complexity of fluid dynamics under sampling conditions. In his landmark 1991 paper Hammond formulated fluid mechanics based analytical models for miscible and immiscible flow during clean-up process.14 Analytical models developed by Hammond14 provide significant insight to the physics of clean-up process. However, underlying assumptions of these analytical models impose significant limitations to the practical applicability of these models. For example, the assumption of point source located in an infinite medium neglects the effects of probe, wellbore, and reservoir geometries. More importantly, Hammond’s single-phase model14 does not account for compositional effects during the OBM filtrate clean-up process.
Three-dimensional (3D) models have been developed to simulate the flow of fluids into WFT sampling probes.1 Results of these simulations help analyze the immiscible flow of formation hydrocarbons and mud-filtrate. In turn, they lead to better sampling strategies designed to minimize filtrate contamination in the case of WBM filtrate clean-up. Akram et al.3 applied the results of 3D modeling to build a simulator for studying WBM filtrate contamination levels and clean-up behavior in more than 150 combinations of various rocks with
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different fluid properties. In this study the simulator modeled fluid flow and determined time evolution of the contamination levels. Effects of various parameters such as viscosity, anisotropy, relative fluid permeability, end-point mobilities, fluid density, porosity, and proximity to barriers on clean-up time were analyzed. For model verification field data from sampling were matched with simulated clean-up times. However, the 3D flow model developed by Akram et al.3 applies only to immiscible flow of fluids relevant to WBM filtrate clean-up process. Hence, results derived from these simulations are not applicable for interpreting and predicting miscible OBM filtrate clean-up process.
The oil-based mud-filtrate contamination monitoring (OCM) algorithm was proposed by Mullins and Schroer2 and Mullins et al.8 to quantitatively predict the level of contamination as a function of time. The process can be repeated for multiple sampling stations along a wellbore.2,7,8,9,10,11 This algorithm monitors the level of OBM filtrate contamination in real-time so that a decision can be made on when to sample. OCM algorithm is based on the principle of changing color and/or methane content with time. This principle is exploited to monitor contamination. The OCM time-function, which scales with t5/12, can be traced back to Hammond’s derivations.14 However, OCM constitutes a semi-empirical, parametric, real-time algorithm, and the parameters that govern the OCM predictions are functions of sampling time themselves. Therefore, the performance of OCM changes in real-time as a function of fluid volume withdrawn during clean-up as well as a number of other parameters as we will soon illustrate. As such, OCM cannot be used for sampling job design. Moreover, because the measurements are optical-density based, the relative error in OCM predictions increases with decreasing contamination levels and/or with smaller color/density/GOR contrast between reservoir fluid and contaminant. It’s in those cases, however, that accuracy is needed most to ensure the collection of representative samples. For example, in the case of a black-oil, it is much more important to determine if sample contamination level is closer to 5% or 15% than to determine if the sample contamination is actually 20% or 30%. This is because both samples contaminated at both 20% and 30% are likely not worthwhile for PVT analysis anyway while reducing the contamination from 15% level to 5% is very significant as far as the quality and value of the sample is concerned for PVT and flow assurance-related analyses.
One of the most valuable model for OBM filtrate clean-up process available in the open literature is one proposed by Hashem et al.6. This model makes use of a “normalized time”. The normalized time incorporates physical parameters such as mobility ratio and the pressure differential between the mud (filling the wellbore) and in-situ formation fluids. The semi-empirical nature of this model stems from the fact that the normalized time is related to weight percent contamination by means of a regression function. The regression function is fit to a set of field data mainly from the Gulf of Mexico. The attraction of this model stems from its relative simplicity, the ability to compute most input parameters in advance, and its reliance on real data. Although practically useful within the limits of the data on which the contamination model is constructed, the model remains open to further extension to be
generally applicable. Moreover, like its more theoretical counterparts, this model does not account for the compositional effects, miscible displacement, variability in the flow rate function, and other significant formation parameters such as formation anisotropy and porosity. EOS based compositional numerical model for modeling OBM filtrate clean-up process In order to develop a rigorous high-resolution model for predicting OBM filtrate clean-up as a function of time and to better understand the OBM filtrate clean-up phenomenon for single-probe WFT tools, we devised a compositional modeling strategy using a robust and accurate numerical simulator.15 The numerical model is designed to provide high-accuracy simulations of the clean-up phenomena monitored via transient downhole measurements of GOR. A contamination time-function is derived from numerically simulated GOR measurements to yield contamination fraction as a function of elapsed time of the clean-up process. Having validated the numerical model with field data, an extensive simulation based sensitivity study was conducted to better understand the physics of contamination time-function. In this study our high-resolution numerical model served as a tool for the quantitative identification of rock, fluid, and geometrical parameters that encompass first-order sensitivity about the physics of OBM filtrate clean-up phenomenon. Simulated transient downhole GOR measurements were used in this study to monitor the progress of clean-up phenomenon.
Special purpose numerical simulators have recently been developed to model mud-filtrate invasion and subsequent WFT measurements. The WFT simulator presented by Wei et al.16 emulates OBM as either an independent oil component or an oil-based solvent component. In the former approach, a black-oil formulation with API variations is used. In turn, OBM is treated as a heavy oil (dead oil) component and the formation oil as a light oil component. Immiscibility is assumed between the dead oil component (OBM) and gas and water components. The latter approach treats the OBM as a hydrocarbon solvent and uses Todd-Longstaff’s miscible algorithm17 to generate effective fluid properties as functions of the empirical parameters, where the fluid system can vary between being entirely miscible and immiscible. Chin and Proett18, on the other hand, developed a similar WFT simulator that also makes use of Todd-Longstaff’s miscible algorithm.17
Recent developments of numerical models for the simulation of WFT measurements have been predominantly geared toward the simulation of WFT pressure measurements. In turn, the philosophy of these recent numerical models relies on the development of a flow simulator based on a black-oil formulation to primarily model WBM filtrate invasion process and subsequent WFT pressure measurements. On the other hand, simulation of OBM filtrate invasion phenomena and associated WFT measurements are handled using an extension of the black-oil formulation. Clearly, such a strategy is devised for the flexibility of developing and maintaining a single simulation platform that can model WFT measurements acquired in both WBM and OBM filtrate invasion environments. However, inherent physical assumptions underlying the extended black-oil formulations impose
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limitations on the accuracy and compositional resolution of the simulation outcome. Extended black-oil formulation requires lumping of a wide spectrum of hydrocarbon components encompassed by the OBM filtrate and formation hydrocarbons into a heavy and a light pseudo-component. As such, simulations performed using extended black-oil formulations yield a low compositional resolution in the near-wellbore spatial domain. This low compositional resolution is perhaps sufficiently accurate for the purpose of simulating WFT pressure measurements as reported by Wei et al.16 and Chin and Proett17. However, our preliminary simulation study indicated that two pseudo-component lumping of hydrocarbons, dictated by the extended black-oil formulation, may yield inaccurate simulations of downhole GOR measurements especially when the in-situ hydrocarbons are compositionally complex and the OBM and in-situ hydrocarbon compositions exhibit significant contrasts. Robust and accurate modeling of downhole GOR measurements requires enhanced compositional resolution, and, hence, a more physically consistent, robust, and accurate numerical formulation. Therefore, we make use of a simulator that is based on an equation-of-state (EOS) compositional formulation.
For modeling OBM filtrate clean-up phenomenon monitored via transient downhole GOR data, we considered the miscible flow of hydrocarbon and non-hydrocarbon components that make up the OBM filtrate as well as the in-situ crude oil. In order to perform accurate numerical simulations of downhole GOR measurements, our numerical model was constructed within the framework of a finite-difference based fluid-flow simulator. The particular module that we worked with was an equation-of-state (EOS) compositional flow simulator with robust and efficient solvers that can handle multi-component flow on complex discrete meshes with significantly varying grid sizes.15 Within the limits of block-centered finite-difference approximation, we focused our efforts to replicate the accurate geometry of a single-probe WFT. Flow toward a single-probe WFT was simulated using a 3D cylindrical mesh. In our simulation model mesh size variability was adjusted for the precise representation of formation geometry in the vicinity of the WFT probe. In constructing the numerical mesh, care was taken to ensure that computational accuracy was not compromised through use of high grid aspect ratios. In turn, a method was developed for the rapid construction optimal meshes for WFT problems. In our simulations we modeled compositional flow towards a WFT probe pressed through the mudcake against the sandface. The tool remained in direct hydraulic communication with the fluid-saturated formation as shown in Fig. 4. Fluid was produced from the formation by imposing a constant flow rate internal boundary condition at the source locations that represent the open-to-flow section of the probe. The magnitude of the constant flow rate was varied consistently with a discrete rate schedule that can be derived from the WFT volumetric and pump rate measurements. As a result of extensive tests of accuracy and convergence, our EOS based compositional simulation framework emerged as a robust platform for performing accurate numerical simulations of compositional effects on the OBM filtrate clean-up process.
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Wellbore Mudcake OBM filtrate
Fig. 4— Sketch of near-wellbore geometry during the early stages of the OBM filtrate clean-up process. Wireline formation tester probe is pressed against sandface through the mudcake and is in direct hydraulic communication with the fluid-saturated formation. History matching of field downhole GOR measurements The validity of the numerical model was verified using field measurements of GOR. Well-constrained and thoroughly quality-controlled field data sets were selected to for the history matching exercise. Downhole GOR measurements acquired in two wells drilled into the same reservoir were selected for minimum intervention history matching component of the work described in this paper. Each of the selected field data sets contain complete set of rock, fluid, and geometrical information accompanying the downhole GOR measurements recorded in response to a time-varying clean-up flow rate schedule. The near-borehole fluid-flow model is constructed within the framework of our numerical model considering a single-probe tool geometry. Whereas, the actual WFT tool configuration, which is utilized for the fluid sampling jobs, and in turn, for the acquisition of field measurements of downhole GOR, is made up of four probes as displayed in Fig. 5. This is a valid approach since within a given clean-up period only one of the probes was active. Moreover, sampling locations where different probes were active were sufficiently apart from each other such that the flow field imposed by one of the active probes did not interfere with the initial condition of the clean-up process for another probe. While one of the probes was actively cleaning-up, other probes remained in the observation mode. Therefore, in order to simulate the clean-up process, the numerical mesh was adjusted to the near-wellbore flow geometry in the vicinity of the active probe. For each flow duration at a given WFT test depth, the simulator was run with relevant rock, fluid, and geometrical parameters as well as with the rate schedule derived from the volumetric information recorded during clean-up. Within the simulation framework we assumed that the WFT downhole GOR measurements were acquired at the sandface. In other words, it was assumed that the mixing process within the flowline of the WFT was negligible at late times. This assumption is a good approximation of the ground truth. As shown in Fig. 1 for the WFT configuration of interest, the LFA module is located within the very close proximity of the probe.
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Fig. 5— Sketch of the four-probe WFT configuration utilized for the fluid sampling jobs subject to analysis. Field measurements of downhole GOR time-functions subject to history matching are acquired using the above-shown WFT configuration. Probe names are marked on the tool sketch.
The numerical simulation framework described in this paper can be readily used for simulating OBM filtrate invasion process provided that accurate information about the rate of OBM filtrate invasion as a function of time is available. However, in practical applications, it is extremely challenging to accurately estimate the OBM filtrate invasion rate. Moreover, it is numerically taxing to simulate a process (filtrate invasion) that is several orders of magnitude longer and far less understood when compared to the process of interest (formation fluid withdrawal) which is much more critical to the sampling process. Therefore, in our work, instead of simulating the OBM filtrate invasion process, we initialized the clean-up simulations with a known volume and composition of OBM filtrate axisymmetrically located up to a specified discrete depth. A numerical sensitivity study quantitatively demonstrated that for OBM filtrate invasion problems in vertical and nearly vertical wells, above-described sharp invasion boundary approach is proved to be a valid first order approximation. In turn, the only uncertain parameter of the field GOR data history-matching problem remains to be the depth of invasion parameter. In general, the depth of OBM filtrate invasion is shallow, i.e., in the range of one inch to a couple of feet. Therefore, we used the depth of invasion as the only adjustable parameter for history matching field data. All WFT data sets subject to history matching were acquired in the same compartment of the reservoir from the fluid composition viewpoint. In addition, the type of OBM used in the drilling of both wells, where the GOR build-up data were recorded at various depths, remains to be the same. Therefore, for the simulation of downhole GOR measurements within the context of history matching, we made use of the same OBM filtrate and in-situ hydrocarbon compositions for all downhole GOR data sets. Extensive tests confirmed that an eight lumped-component characterization of OBM filtrate and in-situ hydrocarbon fluids yields a balanced fluid model in terms of the accuracy of the PVT properties and computational efficiency. The lumped components used to represent the actual hydrocarbon fluids are as follows: [#1] NON-HC (non-hydrocarbon components), [#2] C1, [#3] C2-C5, [#4] C6-C9, [#5] C10-C13, [#6] C14-C18, [#7] C19-C29, and [#8] C30+. OBM
filtrate and in-situ hydrocarbon compositions used within the history matching framework are shown in Figs. 6(a) and 6(b), respectively, in units of weight fractions. Example near-wellbore visualizations of the compositional initialization strategy, which was implemented to model the presence of OBM filtrate invasion, are shown in Figs. 6(c) and 6(d) in terms of the spatial distribution of lumped component no. 6. Note that lumped component no. 6 exhibits the largest contrast in terms of mole fraction between OBM filtrate and in-situ reservoir fluids. Therefore, in order to visualize the initial extent (spatial distribution) of OBM filtrate invasion around the wellbore, we choose to plot the spatial distribution of the molar concentration of lumped component no. 6. (a) (b)
Fig. 6— (a) OBM filtrate composition. (b) Composition of the in-situ reservoir hydrocarbon. (c), (d) Near-wellbore visualizations of the compositional initialization strategy implemented to represent the presence of OBM filtrate invasion. OBM filtrate invasion is visualized in terms of the spatial distribution of the molar concentration of lumped component no. 6 (high = red; low = blue). Panel (d) focuses on the close proximity of the wellbore.
The sketch of the petrophysical model used for the simulation of downhole GOR measurements acquired in Well #1 is shown in Fig. 7. The petrophysical model for the eight-layer formation penetrated by Well #2 is described in Table 1. Both wells, where the field downhole GOR data were acquired, are deviated. However, since the deviation angles are less than 20 degrees, for practical purposes of simulation, we assumed the wells to be vertical. WFT measurement acquisition depths as well as probe activation sequences (flow toward the encircled probe) for each depth station are also displayed in Fig. 7. An example of the finite-difference mesh of size 31 × 15 × 58 (r × θ × z) used within the context of history matching simulations is shown in Fig. 8(a) from top and in Fig. 8(b) from oblique view angles. Figure 8(c) displays the implementation of the probe opening in the finite-difference mesh. Modeling of the probe opening was implemented using small source conditions (wells) discretely imposed over a vertical and azimuthal interval with a diameter of approximately 1 inch.
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Fig. 8— (a) Top and (b) oblique views of an example finite-difference mesh of size 31 × 15 × 58 (r × θ × z) used in the simulations performed for minimum intervention history matching. (c) Implementation of the probe opening in the first finite-difference grid block.
Compositional flow toward a single-probe is subject to closed (no-flow) outer and constant rate internal boundary conditions. The outer boundary condition is imposed very far away from the probe (source). On the other hand, boundary conditions are symmetrically imposed in the computational domain with respect to the vertical axis passing through the probe center (slicing the probe into two azimuthally). Therefore, the solution of the compositional flow equations is symmetric with respect to this axis. In other words, the solution in one half of the spatial domain is the mirror image of the one in the other half. Therefore, performing the flow simulation on one half of the spatial domain is sufficient to obtain the entire solution. From the computational viewpoint, this attribute of the initial/boundary value problem at hand is
very desirable. The symmetrical nature of the numerical problem allows us to further refine the computational mesh in the vicinity of the WFT probe and to perform flow simulations using a sufficiently fine numerical mesh that would be otherwise unaffordable. Table 1— Petrophysical model for the 8-layer formation penetrated by Well #2
measurements acquired at two tool-setting depths (Depth #1 and #2) in Well #1. Note that the data set in Fig. 9(b) is the temporal continuation of the data set shown in Fig. 9(a). A loss in seal caused a discontinuity in the data acquisition. Tool mechanical effects dominate the early time very rapid build-up like behavior. This behavior is due to a seal loss and corresponding resealing process; therefore, this period was not considered as a legitimate build-up. Also, note that in Fig. 9(b) the reference time (time zero) was reset. As such, the early time GOR jump is not entirely governed by the physics of OBM filtrate clean-up. Hence, this part of the measurement data was not utilized in the minimum intervention history matching study. On the other hand, downhole GOR measurements recorded in Well #2 are shown in Figs. 9(d) and 9(e) for Depth #1 and Depth #2, respectively. Clean-up and sampling flow rate histories are documented in Figs. 10(a) and 10(b) for Well #1 Depth #1 and Depth #2, respectively. Figures 10(c) and 10(d) illustrate clean-up and sampling flow rate histories for Well #2 Depth #1 and Depth #2, respectively. Continuous flow rate measurements for each data set were averaged into a stepwise rate schedule. In turn, the simplified rate schedule was conveniently imposed as the source condition to the reservoir simulator. Results of the minimum intervention history matching component of our work are shown in Figs. 11(a) through 11(e) for five build-up periods observed in the downhole GOR measurements acquired in Well #1. Figures 12(a) through 12(c) display three build-up periods observed in the downhole GOR measurements acquired in Well #2. In these sets of figures, field downhole GOR measurements and simulated downhole GOR measurements are plotted together as a function of acquisition time. The only adjustable parameter of the history matching procedure was the depth of invasion. The depth of invasion value that yields the best history match is also reported in each of the figures. In fact, in Well #1 the estimated depth of invasion was found to be in the range of 0.2 to 0.3 ft, while in Well #2 this parameter was found to be within the range of 0.2 to 0.475 ft.
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Fig. 9— LFA downhole GOR build-up measurements. (a) in Well #1 at Depth #1 (first GOR build-up period), (b) in Well #1 at Depth #1 (second and third GOR build-up periods), (c) in Well #1 at Depth #2 (first and second GOR build-up periods), (d) in Well #2 at Depth #1 (first and second GOR build-up periods, downhole GOR data acquired only during the second build-up period is used in the minimum intervention history matching study), and (e) in Well #2 at Depth #2 (first and second GOR build-up periods are utilized in the minimum intervention history matching study). (a) (b)
Fig. 10— Clean-up source schedule: Measured and averaged flow rate histories for downhole GOR data acquisition. (a) in Well #1 at Depth #1, (b) in Well #1 at Depth #2, (c) in Well #2 at Depth #1, and (d) in Well #2 at Depth #2.
In field data, there is a rather well-known temporal dependence of contamination. It is often, but of course not always, found that the contamination cleans up as t5/12 as monitored by color and/or dissolved methane.8,9 The model presented herein is in general agreement with this finding.
Fig. 11— Minimum intervention history matching results of downhole GOR measurements for (a) first build-up period acquired in Well #1 at Depth #1, (b) second build-up period acquired in Well #1 at Depth #1, (c) third build-up period acquired in Well #1 at Depth #1, (d) first build-up period acquired in Well #1 at Depth #2, (e) second build-up period acquired in Well #1 at Depth #2. (a) (b)
Fig. 12— Minimum intervention history matching results of downhole GOR measurements for (a) second build-up period acquired in Well #2 at Depth #1, (b) first build-up period acquired in Well #2 at Depth #2, (c) second build-up period acquired in Well #2 at Depth #2.
The long build-up times require a lengthy clean-up process. In addition, the short period of time of putatively pure filtrate barely exists. Moreover, the fastest rate of change of contamination occurs initially with pumping, another difficult modeling objective. Our model reproduces field data accurately (cf Fig. 11). This agreement, which has been elusive in the past, bodes well for the future use of this
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modeling capability to address many complex probes that are being introduced for sampling and pressure measurement.
In the panels of Fig. 13 vertical cross-sections of the near-wellbore region are shown for the downhole GOR data history matching case: Well #1 Depth #2, first GOR build-up period. Each panel of Fig. 13 shows a vertical cross-section of the composition map taken at the probe location, azimuthally. The depth of invasion value was set equal to 0.2 ft. and was derived from multi-depth resistivity and NMR logs. In the panels of this figure, spatial distribution of the lumped component no. 6 is displayed as a function of time in response to the clean-up flow rate schedule. Lumped component no. 6 is the fluid component that exhibits the largest mole fraction contrast as far as the OBM filtrate and the in-situ reservoir fluid are concerned. Therefore, its spatial distribution is a very convenient indicator of clean-up. The WFT probe was located at the vertical center of the panel where the finite-difference mesh is finest. The progress of OBM filtrate clean-up is expressed in terms of a row-echelon panel sequence. Similar horizontal cross-sections taken at the probe level, vertically, are shown in the panels of Fig. 14. Transient analysis of the panels shown in Fig. 14 qualitatively indicates an early time pseudo-spherical flow regime followed by a transition period. Transition flow regime with time converges into a flow regime that is approximately cylindrical in nature (late-time flow regime). t = 0.00 s t = 21.65 s
t = 429.54 s t = 589.14 s
Fig. 13— Progress of the OBM filtrate clean-up. Vertical cross-sections of the near-wellbore region are shown for the downhole GOR data history matching case: Well #1 Depth #2 first GOR, build-up period. Representative numerical simulations Development of high-resolution/high-accuracy knowledge about the OBM filtrate clean-up phenomenon in the vicinity of the borehole is important for the design and operation of new sampling probes. Identification of rock, fluid, and geometrical parameters that encompass significant sensitivity with respect to the GOR build-up function is also imperative for the formulation of rapid approximate asymptotic models for real time analysis of sampling jobs. For this purpose, we conducted a comprehensive set of sensitivity studies. Extensive sets of
simulations of downhole GOR measurements were performed for the purpose of sensitization covering ranges of rock, fluid, and geometrical parameters encountered in realistic oilfield applications of wireline formation testers. t = 0.00 s t = 5.10 s
t = 197.06 s t = 589.14 s
Fig. 14— Progress of the OBM filtrate clean-up. Horizontal cross-sections of the near-wellbore region are shown for the downhole GOR data history matching case: Well #1 Depth #2 first GOR, build-up period.
Finding the most accurate combination of simulator input parameters that will give the most accurate match of the downhole GOR measurements was not the objective of this work. Instead, our goal was to apply a minimum intervention history matching approach in order to build confidence in the numerical model. In turn, quantitative comparisons of simulated and measured downhole GOR data validate the numerical model. They confirm that given a set of representative input data (rock, fluid, and geometrical information) which characterizes the physics of OBM filtrate clean-up reasonably well, a carefully built high-resolution numerical model constructed within a compositional simulation framework successfully captures the significant details of the downhole GOR time-function.
For each simulation conducted within the context of sensitivity studies, an OBM filtrate contamination time-function (inverse of the OBM filtrate clean-up time-function) was computed from simulated downhole GOR measurements using the following transform19
1( )( )( ) ( ) ( ) ( ) 1 .
(1 ( ))STO p
c pm
F tGOR t GOR t
F tρ
ρ
−⎡ ⎤
= +⎢ ⎥−⎣ ⎦ (1)
In this transform F(t) denotes the OBM filtrate contamination time-function expressed in terms of weight fraction, (GOR)c(t) stands for the contaminated downhole GOR time-function, (GOR)p(t) denotes the GOR of the uncontaminated (pure) in-situ hydrocarbon, ρm stands for the density of the base oil of OBM, and (ρSTO)p denotes the density of the uncontaminated (pure) stock-tank oil. For cases where the density of the base oil of OBM, ρm, is not significantly different from the density
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of the uncontaminated (pure) stock-tank oil, (ρSTO)p, one can rearrange and simplify Eq. (1) to obtain
( ) 1 [( ) ( ) ( ) ].c pF t GOR t GOR= − (2)
The underlying assumption of Eq. (2) is valid for a large number of practical OBM filtrate contamination cases observed in hydrocarbon reservoirs.
The base case of the sensitivity studies was a homogeneous and isotropic permeable medium of 58 ft thickness. Similar to the field cases used for history matching, a vertical well penetrates through a single-layer hydrocarbon-bearing formation. Since single-probe WFT configuration is the subject of the work, the fluid flow model was constructed in the 3D cylindrical coordinate system. The probe was located 45 ft from the top and 13 ft from the bottom of the permeable formation. These distances had been chosen so that the probe was sufficiently far from both top and bottom sealing (no-flow) boundaries to ensure that the simulations remained uninfluenced by the boundary effects. This probe setting was modified later during the distance-to-boundary and formation thickness sensitivity runs. Base case permeability and porosity were 250 mD and 0.30 volume fraction, respectively. Base OBM filtrate and in-situ reservoir fluid compositions remained the same as in the case of minimum intervention history matching work and are shown in Figs. 6(a) and 6(b). The finite-difference mesh displayed in Figs. 8(a) and 8(b) was utilized for the simulation-based sensitivity studies. At the datum depth, the reservoir pressure was assumed to be 6845 psia. The magnitude of the initial reservoir pressure and the pressure drops during the simulation runs were carefully inspected to ensure that the fluid pressure in the vicinity of the WFT probe always remained in single phase throughout the clean-up and sampling stages. In this work we focused on single-phase liquid flow, which constitutes the most important downhole fluid sampling application in the oilfield. Special attention is paid in field applications to fine-tune the clean-up flow rate so as to avoid multi-phase flow regimes. This is because WFT samples acquired under conditions of multi-phase flow in the subsurface are largely unusable for PVT or flow assurance-type applications. By avoiding multi-phase flow regimes during simulation, one circumvents the effects of saturation-dependent functions, namely, relative permeabilities and capillary pressure on the downhole GOR measurements. Here, we would like to emphasize the fact that information about saturation-dependent functions are in general unavailable for WFT data interpretation, as such, they impart significant uncertainty in the interpretation of transient downhole GOR measurements acquired in multi-phase flow regimes. As an exception, in order to ensure the enforcement of the single-phase flow regime in our simulations, in the case of viscosity ratio sensitivity study where for some reservoir fluid compositions and clean-up rates the risk of multi-phase flow emerged, we raised the initial reservoir pressure by 3000 psi. For the base case, a constant clean-up flow rate of 14 rb/d was imposed as the internal boundary source condition. Base case simulation duration was selected to be 3 hrs. The simulation time was extended to 9 hrs only in the case of the depth of invasion sensitivity study. This strategy was devised in order
to capture an enlarged window of clean-up time-function for contamination depths larger than 0.45 ft. Sensitivity studies were conducted for the following rock, fluid, and geometrical parameters: Permeability. Figures 15(a) and 15(b) show simulated downhole GOR time-functions, and their corresponding OBM filtrate contamination time-functions, respectively, for a formation fluid permeability range of 50 mD to 750 mD. Time-functions of downhole GOR build-up and contamination appear to have very weak sensitivity with respect to formation permeability. (a) (b)
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Fig. 15— (a) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of formation permeability on downhole GOR time-function. (b) Contamination function. Permeability anisotropy. Mathematical formulation of the compositional fluid-flow model in 3D cylindrical coordinate system is based on the assumption of a transversely anisotropic permeability medium such that the permeability tensor is given by
[ ],h h vdiag k k k=k (3)
where kh and kv denote horizontal and vertical formation permeabilities, respectively. Figures 16(a) and 16(b) show simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions, respectively, for a formation permeability anisotropy ratio, namely, kv/kh, range of 0.05 to 1. (a) (b)
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ANIS. RAT. = 1.00ANIS. RAT. = 0.70ANIS. RAT. = 0.50ANIS. RAT. = 0.25ANIS. RAT. = 0.10ANIS. RAT. = 0.05CLEAN GOR
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Fig. 16— (a) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of formation permeability anisotropy on downhole GOR time-function. (b) Contamination function.
The results indicate that the downhole GOR build-up and contamination time-functions are sensitive to the permeability anisotropy ratio. As the anisotropy ratio decreases, OBM filtrate clean-up accelerates. This behavior can be explained as follows: As anisotropy ratio for a given horizontal permeability decreases, vertical permeability decreases, which acts as a barrier for the flow in the vertical direction.
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Therefore, OBM filtrate clean-up accelerates as larger volumes of OBM filtrate contamination is cleaned up in the horizontal direction in line with the direction of the active flowing probe. Porosity. Figures 17(a) and 17(b) display simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions, respectively, for a formation porosity range of 0.05 to 0.4. Simulation results indicate that time-functions of downhole GOR build-up and contamination exhibit sensitivity with respect to formation porosity. OBM filtrate clean-up accelerates with decreasing porosity. In this sensitivity study all parameters of the base case remained unchanged other than the formation porosity. Note that in the parameterization of the OBM filtrate clean-up model, we worked with the depth of invasion parameter. Using the depth of invasion parameter, we initialize the simulations with the OBM filtrate composition up to a length corresponding to the depth of invasion and with in-situ hydrocarbon composition further than the depth of invasion. Therefore, a modification in the formation porosity implies a modification in the volume of invasion. Therefore, as porosity increases, the volume of OBM filtrate contaminating the in-situ hydrocarbons increases. In turn, as displayed in Fig. 17(b), for lower porosities OBM filtrate clean-up progresses more rapidly. If, instead, we parameterize the OBM filtrate clean-up time-function in terms of the volume of invasion and consistently impose the same volume of OBM filtrate contamination for each case of formation porosity sensitivity study, then we would observe a faster clean-up behavior in response to increasing values of the formation porosity. (a) (b)
Fig. 17— (a) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of formation porosity on downhole GOR time-function. (b) Contamination function. Simultaneous variation of permeability and porosity. We investigated the effect of the simultaneous variation of permeability and porosity on the OBM filtrate contamination function. A permeability-porosity relationship is enforced in our simulations through the correlation below, which has a form that is typical in sandstones 20,
100.1log ( ) 0.05.kφ = + (4)
Permeability, k, has the unit of millidarcy [mD] in this correlation. Figures 18(a) and 18(b) display the simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions, respectively, for a [permeability, porosity] range covering [50 mD, 0.22] to [500 mD, 0.32]. Because of this inter-relationship, time-functions of downhole GOR build-up and contamination appear to
encompass no sensitivity with respect to the simultaneous variation of permeability and porosity. (a) (b)
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Fig. 18— (a) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of the simultaneous variation of formation permeability and porosity on downhole GOR time-function. (b) Contamination function. Clean-up flow rate. The impact of clean-up flow rate on the OBM filtrate contamination time-function is investigated by imposing a constant clean-up flow rate for the duration of OBM filtrate clean-up as the source condition. A practical clean-up flow rate range of 3.5 rb/d to 19.25 rb/d is considered for the sensitivity study simulations consistent with the performance limits of WFT pump operation. Figures 19(a) and 19(b) display the simulated downhole GOR time-functions and corresponding OBM filtrate contamination time-functions, respectively, for the clean-up flow rate sensitivity study.
Simulation results indicate that time-functions of downhole GOR build-up and contamination exhibit strong sensitivity with respect to clean-up flow rate through the WFT probe. OBM filtrate clean-up accelerates with the increasing clean-up flow rate. The key issue here is the formation permeability. Although the formation permeability exhibits negligibly small direct influence on the OBM filtrate clean-up time-function, indirectly it plays a principal role in constraining the maximum possible clean-up rate that can be imposed on the formation as an internal boundary condition. The interplay of formation permeability, mud overbalance, pump dynamics, and bubble point pressure of the formation fluids determine the optimal flow rate to achieve the most-efficient OBM filtrate clean-up without produced fluids crossing into multi-phase flow regime. (a) (b)
Fig. 19— (a) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of clean-up flow rate on downhole GOR time-function. (b) Contamination function. Depth of invasion. One characteristic positive attribute of OBMs is the relatively shallow depth of invasion in the near-wellbore region. In general, the maximum depth of invasion yielded by the OBMs is less than 1 ft. The depth of invasion sensitivity study is performed using two combinations of
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OBM filtrate and in-situ formation fluid composition. The first combination involves the base case OBM filtrate and in-situ fluid compositions reported in Figs. 6(a) and 6(b), respectively. The viscosity ratio is defined as the ratio of the viscosity of uncontaminated in-situ reservoir fluid with respect to the viscosity of pure OBM filtrate at reservoir conditions. The viscosity ratio of the base case was equal to 0.22. Figures 20(a) and 20(b) show simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions, respectively, for depths of invasion ranging from 0.05 ft to 0.774 ft. This depth of invasion sensitivity study was repeated using a different set of compositions for the OBM filtrate and in-situ formation fluids. Throughout, the viscosity ratio was maintained equal to 1.18. The simulated clean-up duration was extended from 3 to 9 hrs such that all simulations of the new sensitivity study can quantify the late-time asymptote of the OBM clean-up time-function. Figures 20(c) and 20(d) display simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions, respectively, for a depth of invasion ranging from 0.05 ft to 1.025 ft.
Simulation results for both sets of OBM filtrate and in-situ hydrocarbon compositions indicate that time-functions of downhole GOR build-up and contamination exhibit significant sensitivity with respect to the depth of invasion. As the depth of invasion increases, the OBM filtrate clean-up slows down. Most importantly, both sets of sensitivity studies indicate that for depth of invasion values beyond 0.45 ft the time it takes to reduce the contamination level below 10% weight contamination is well beyond practical sampling limits. (a) (b)
DINV = 0.0500 FT DINV = 0.1000 FT DINV = 0.1500 FTDINV = 0.2000 FT DINV = 0.2500 FT DINV = 0.3000 FTDINV = 0.3625 FT DINV = 0.4375 FT DINV = 0.5250 FTDINV = 0.6250 FT DINV = 0.7250 FT DINV = 0.8250 FTDINV = 0.9250 FT DINV = 1.0250 FT CLEAN GOR
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Fig. 20— (a) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of the depth of invasion on downhole GOR time-function (default base case). (b) Contamination function (default base case). (c) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of the depth of invasion on downhole GOR time-function (modified base case). (d) Contamination function (modified base case). Viscosity contrast between OBM filtrate and formation fluid. As in the case of the previously described sensitivity studies, the impact of viscosity contrast between the OBM filtrate and in-situ formation fluid on the contamination time-
function was investigated by imposing a constant flow rate for the duration of clean-up. Although for the base case of other sensitivity studies we made use of a clean-up flow rate of 14 rb/d, in order to ensure a single-phase flow regime the magnitude of the clean-up flow rate was reduced to 7 rb/d in this study. For the single-phase compositional fluid-flow model, in order to introduce a modification on the viscosity contrast between the OBM filtrate and in-situ formation fluid, one has to either modify the composition of the OBM filtrate or of the in-situ reservoir fluid. The composition of reservoir fluids exhibits a wider spectrum of variability in comparison to the composition of OBMs. In consistence with this physical observation, various cases of viscosity contrast were generated by modifying the composition of reservoir fluids. The composition of the OBM filtrate, shown in Fig. 6(a), remained unchanged.
The reservoir fluid composition of the base case (a relatively lighter hydrocarbon) was gradually shifted towards the composition of a heavier hydrocarbon. In turn, the viscosity ratio was gradually increased from 0.22 up to 8.50. Note that changing the base case reservoir fluid composition also implies altering the bubble point pressure and clean downhole GOR of the reservoir hydrocarbon. As the compositional spectrum of reservoir fluid includes a larger fraction of heavier hydrocarbon components, values of the bubble point pressure and clean downhole GOR tend to shift to lower values. As described earlier, in order to safeguard against the multi-phase flow regime during clean-up, the initial reservoir pressure was boosted by 3000 psi during these simulation runs. In addition, the maximum OBM clean-up flow rate was reduced to 7 rb/d. This is a realistic upper limit adjustment because, in practice, it is nearly impossible to flow such viscous fluids at higher rates through probes without dropping below saturation/solids onset pressure and/or causing rock failure. Figures 21(a) and 21(b) display simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions. (a) (b)
MU OIL / MU OBMF = 0.2217MU OIL / MU OBMF = 0.2587MU OIL / MU OBMF = 0.2986MU OIL / MU OBMF = 0.3412MU OIL / MU OBMF = 0.3864MU OIL / MU OBMF = 1.1793MU OIL / MU OBMF = 2.0435MU OIL / MU OBMF = 3.1033MU OIL / MU OBMF = 3.7314MU OIL / MU OBMF = 4.5291MU OIL / MU OBMF = 5.9889MU OIL / MU OBMF = 6.5046MU OIL / MU OBMF = 7.0288MU OIL / MU OBMF = 7.4272MU OIL / MU OBMF = 7.9641MU OIL / MU OBMF = 8.5048
FLOW RATE = 7.0 RB/D
Fig. 21— (a) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of viscosity contrast between the OBM filtrate and in-situ formation fluid. (b) Contamination function. Probe distance from a sealing boundary. The effect of the distance between the WFT probe and a horizontal no-flow (sealing) layer boundary was also investigated. From the fluid sampling viewpoint, the sealing layer boundary represents a natural barrier for the fluid flow in one of the vertical directions. It is generally a good practice to sample below a sealing boundary. Once the flow is obstructed in one of the vertical directions, relatively less OBM contamination is expected to flow toward the probe in the vertical direction. In
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turn, OBM filtrate clean-up is expected to progress more rapidly in the radial direction in line with the probe orientation. The WFT sampling geometry investigated in this sensitivity study is displayed in terms of a sketch in Fig. 22(a). A sealing horizontal layer boundary was assumed to be present above the permeable formation of interest. The distance between the WFT probe and the sealing boundary was progressively decreased from 45 ft to 0.17 ft. Figures 22(b) and 22(c) display simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions, respectively. Simulation results indicate that the spatial proximity of the probe to a sealing layer boundary has a negligible effect on clean-up behavior for probe-to-boundary distances greater than 2 ft.
Fig. 22— (a) Problem geometry. (b) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of WFT probe distance from a sealing boundary on downhole GOR time-function. (c) Contamination function. Formation thickness. In this sensitivity study the WFT probe was positioned in the middle of a permeable formation. The thickness of the formation was progressively decreased from 52 ft to 1 ft. The WFT sampling geometry investigated in this sensitivity study was displayed in terms of a sketch in Fig. 23(a). Figures 23(b) and 23(c) display simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions, respectively. Simulation results indicate that formation thickness has a significant positive influence in terms of accelerating the progress of OBM filtrate clean-up for thickness values smaller than 2 ft. In accordance with expectations and field experience, it is ideal to conduct the fluid sampling job across a thin disk of reservoir rock for a rapid OBM filtrate clean-up. Similar to the previous sensitivity study, rapid clean-up is predominantly due to negligibly small OBM filtrate flow in the vertical direction. Small thickness of the permeable formation is the controlling factor preventing flow in the vertical direction. The main challenge for efficient fluid sampling entails the identification of these thin reservoir rock streaks and accurate positioning of the WFT probe. Wellbore radius. Shallow invasion depth is a characteristic of formations drilled with OBM. In many cases, the depth of invasion is smaller than or comparable to the radius of the wellbore. Hence, the curvature of the wellbore emerges as a
partially significant factor among other factors that govern the physics of OBM filtrate clean-up.
Fig. 23— (a) Problem geometry. (b) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of formation thickness on downhole GOR time-function. (c) Contamination function. In near-wellbore fluid-flow simulation the wellbore curvature information is embedded within the wellbore radius (or wellbore diameter) as a geometrical parameter. The effect of wellbore radius on the OBM filtrate contamination time-function is investigated via performing simulations of transient downhole GOR measurements for practical wellbore sizes used in the drilling of hydrocarbon wells. The range of the investigated wellbore radii was 0.25 ft to 0.73 ft. Figures 24(a) and 24(b) display simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions, respectively. The results show that the magnitude of the influence of wellbore radius on the OBM filtrate clean-up is relatively small. The outcome of this sensitivity study indicates that, everything else remaining constant, the progress of OBM filtrate clean-up is more rapid for relatively smaller wellbore sizes. (a) (b)
Fig. 24— (a) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of wellbore radius on downhole GOR time-function. (b) Contamination function. WFT probe radius. Having set up a high-resolution finite-difference mesh for the simulation of WFT downhole GOR measurements, we investigated the impact of WFT probe radius on the time-function of OBM filtrate contamination. We represent the WFT probe opening using a number of small source conditions discretely imposed on the finest portion of the finite-difference mesh. These small source conditions
14 SPE 100393
approximate the geometry of the probe opening. Therefore, by the changing the number of discrete small sources open to flow, WFT probe opening size can be adjusted. We considered probe radii of 0.2 in., 0.3 in., and 0.5 in. Figures 25(a) and 25(b) display simulated downhole GOR time-functions and their corresponding OBM filtrate contamination time-functions, respectively, for the probe radius sensitivity study. Simulations results indicate that the OBM filtrate clean-up function remains unaffected by the WFT probe sizes considered in this sensitivity study. This is indeed the case when the rate schedule is left unchanged. In practice, however, increasing the probe size does lead to indirect benefits through the increase of possible flow rate for a given permissible pressure drop or, conversely, decreasing the pressure drop for a given imposed flow rate. (a) (b)
0
500
1000
1500
2000
2500
0 2000 4000 6000 8000 10000TIME [SEC]
GO
R [S
CF/
STB
]
RP = 0.5 INRP = 0.3 INRP = 0.2 INCLEAN GOR
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2000 4000 6000 8000 10000TIME [SEC]
CO
NTA
MIN
ATI
ON
[FR
AC
TIO
N]
RP = 0.5 INRP = 0.3 INRP = 0.2 IN
Fig. 25— (a) Simulated downhole GOR build-up data of the sensitivity study performed to quantify the effect of probe radius on downhole GOR time-function. (b) Contamination function. A response surface based model for simulating OBM filtrate clean-up process Above-described sensitivity studies allow us to identify rock, fluid, and geometrical parameters that dominate the physics OBM filtrate clean-up time-function. The parameters that encompass a first-order of impact on the clean-up time-function are permeability anisotropy [kv/kh], porosity [φ], clean-up flow rate [q], depth of invasion [dinv], viscosity ratio [µo/µOBMF], WFT probe distance from a sealing boundary [h], formation thickness [H], and wellbore radius [rw].
Having constructed a robust and accurate high-resolution numerical model to simulate OBM filtrate contamination time-function and having identified the key rock, fluid, and geometrical parameters that govern the physics of OBM filtrate clean-up via comprehensive sensitivity studies, the results of these studies are condensed into an approximate rapid response surface based clean-up model. Numerous diagnostic plotting procedures have been explored to identify generic features of the numerically generated OBM contamination time-functions. Moreover, various functional relations have been investigated to express OBM contamination time-functions in terms of a simplified parametric model. We have found out that the diagnostic plot log10[F(t)] versus log10[V(t)] characteristically exhibits a third-order polynomial behavior for contamination levels below 0.3 weight fraction. Here, t denotes elapsed clean-up time, F(t) denotes the OBM contamination time-function obtained using the transform shown in Eq. (2). V(t), on the other hand, stands for the pumped volume at a given time of the progress of OBM filtrate clean-up given by
( ) ( ) ,o
t
t
V t q t dt= ∫ (5)
where to stands for the starting time of the OBM filtrate clean-up. At this point, we would like to emphasize the fact that from the fluid sampling viewpoint, modeling accuracy is pivotal at low contamination levels, especially, at contamination levels below 10% by weight. The impact of OBM contamination on the fluid sample is large at contamination levels above 30% by weight rendering the fluid sample practically useless for PVT, phase behavior, and flow assurance applications. Therefore, modeling accuracy is of secondary importance at relatively large contamination weight fractions. However, a parametric OBM contamination time-function model that is accurate at relatively lower levels of contamination is very desirable from the fluid sampling perspective. Another positive attribute of the diagnostic plot is that it makes use of volumetric information as a function of time instead of flow rate schedules to monitor the progress of the OBM clean-up. As such, it can be flexibly applied to field OBM contamination data in which the clean-up schedule typically comprises multiple flow and build-up periods.
The response surface that honors the compositional numerical simulations of contamination time-function is well characterized by a third-order polynomial. The model has the following functional form:
3 2( ) ( ) ( )( ( )) ( ) 10 ,aV t bV t cV t dF V t F V + + += = (6)
where
[ , , , ] ( , , , , , , , ).v h w o OBMFa b c d f k k dinv q r h Hφ µ µ= (7)
Our model is closely related to the contamination model derived by Hammond14 through the contamination time-function. Hammond’s model14 is based on the following assumptions: (a) OBM filtrate and in-situ formation hydrocarbon fluid are perfectly miscible; (b) OBM filtrate and in-situ formation hydrocarbon fluids have the same PVT properties (density, viscosity, etc.); (c) Incompressible flow; (d) Hydrodynamic and molecular dispersion are negligible (sharp fronts); (e) No chemical alteration of the formation by the OBM filtrate; (f) Constant clean-up flow rate implying steady state flow. The rapid model developed in this paper eliminates most of the above-listed assumptions.
Numerical simulations conducted in the context of sensitivity studies were used to construct polynomial functions that map each individual model parameter kv/kh, φ, dinv, q, rw, h, H, and, µo/µOBMF to an individual value of a, b, c, and d. Using the polynomial maps values of a, b, c, and d can be computed in response to a given set of input parameters via
8
1
, , , , .i ii
w a b c dαα α α=
= =∑ (8)
In Eq. (8) wαi denote weight coefficients that are utilized to allocate a quantitative normalized significance of impact for each physical parameter in the computation of a, b, c, and d.
SPE 100393 15
For shallow miscible mud-filtrate invasion, which is the case for the majority of OBM wells, Hammond14 proposed the following contamination time-function form:
( ) ,n
dtF tt
β ⎛ ⎞= ⎜ ⎟⎝ ⎠
where 1,β = (9)
and 32 ( )
3ddinvtq
πφ= (10)
The OBM contamination model developed in this study was put into equal footing with the contamination model reported by Hammond14 as follows
3 23( ) ( ) ( )2 ( )( ) 10 ,
3
naV t bV t cV t ddinvF t
qtπφ + + +⎛ ⎞
= =⎜ ⎟⎜ ⎟⎝ ⎠
(11)
where V(t) = qt. Hammond reports a constant n of 0.3314. In order to compare the results computed using our model to Hammond’s model14 we derive the following expression for the time-function n
3 2
3
10 10
( ) ( ) ( )( ) .2 ( )log ( ) log ( ( ))
3
aV t bV t cV t dn tdinv V tπφ
+ + +=−
(12)
Our rapid model treats the contamination time-function exponent, n, as a function of time in the form of n(t). Then, a comparison of n(t) values computed using the above equation to the value of n reported by Hammond14, namely, 0.33 is equivalent to comparing the OBM contamination time-functions computed using both models. Validation. In order to validate the accuracy and robustness of the rapid OBM clean-up model we devised a numerical test case. We compare the OBM clean-up time-function obtained from the rapid model to the one derived using the full-physics numerical model (Fig. 26). We consider the following case: kv/kh = 1, φ = 0.3 volume fraction, dinv = 0.3 ft, q = 14 rb/d, rw = 0.35 ft, h = 45 ft, H = 58 ft, and, µo/µOBMF = 0.22. For the test example absolute error drops very quickly (after 150 seconds) below 1 weight percent contamination. We also compute n(t) function and display it in Fig. 27. For the time-interval where our rapid approximate model remains accurate (t > 150 seconds) the value of n(t) varies within the range 0.43 to 0.47, steadily growing from 0.43 to 0.47. It is interesting to observe that the overall average n value of 0.45 remains consistent with the range of n values reported by Hammond14: 0.33, Mullins and Schroer2: 0.42, and Hashem et al.6: 0.59. Unlike previously developed OBM contamination models, our model treats the value of n as a function of time. Moreover, instead of fitting physically meaningless empirical constants, our response surface based model was constructed on the foundations of relevant physical parameters, namely, kv/kh, φ, dinv, q, rw, h, H, and, µo/µOBMF.
Fig. 26— Comparison of response surface based model simulation of OBM filtrate contamination time-function to the numerical simulation performed using a compositional model. (a) Contamination weight fraction versus time; (b) Contamination weight fraction versus produced clean-up volume; (c) Logarithmic contamination weight fraction versus logarithmic time; (d) Absolute error of response surface based model simulation with respect to numerical simulation of OBM filtrate clean-up time-function. Absolute error is expressed in terms of percent weight contamination as a function of time.
Fig. 27— Behavior of the OBM contamination time-function exponent, n(t), plotted as a function of time.
16 SPE 100393
Table 2 shows an example case where we compare rapid model computation of OBM filtrate contamination with the contamination computation using the model formulated by Hashem et al.6. Our rapid model appears to yield a contamination percentage of 5.81%, which is quite close to the value computed using Hashem et al.’s model6 (i.e., 5.20%). Further tests indicate the degree of closeness of both model computations depend mainly on the following conditions: (1) Establishing an accurate relationship between the overbalance pressure required by Hashem et al.’s model6 and the depth of invasion parameter of our response surface based model; (2) Accurate knowledge about the viscosity ratio, µo/µOBMF. Experimentations using both models indicate that the value of the viscosity ratio, which enters into our model, may potentially cause significant variations in the values of computed percent OBM contamination with respect to the ones computed using Hashem et al.’s model6. As far as the time-function exponent, n(t), is concerned, in most cases we obtained values in the following range: 0.3 < n(t) < 0.6 with 0.45 representing a good average value. Table 2— Comparison of response surface based model computation of OBM filtrate contamination with respect to the one computed using the empirical model of Hashem et al.6 Contamination Model of Hashem et al.6
Further quantitative assessments have helped us to
establish the validity range and limitations of our response surface based model. Comparisons of rapid approximate and numerical model solutions for OBM clean-up indicate that the rapid approximate model provides an overall accuracy of 2.5% weight live oil contamination within the following ranges: • Live oil contamination less than 30% by weight, • kv/kh range: 0.2 to 1.1,
• φ range: 0.05 to 0.5 volume fraction, • dinv range: 0.1 to 0.33 ft (or 1.2 to 4 in.), • q range: 1 to 20 rb/d, • rw range: 0.1 to 0.65 ft, • h range: if less than 2 ft, expect lower contaminations, • H range: if less than 2 ft, expect lower contaminations, • µo/µOBMF range: 0.1 to 3.5. Conclusions We have developed an efficient and robust high-resolution numerical model to simulate downhole GOR measurements using a computational fluid-flow simulator. The component material balance and hydrocarbon phase behavior calculations are performed using an EOS compositional model. Robustness and accuracy of the numerical model was validated by comparing simulation results to field measurements. Sensitivity studies of OBM filtrate clean-up process were conducted with respect to parameters associated with rock and fluid properties and measurement geometry. Simulated downhole GOR measurements were transformed into time-functions of OBM contamination. In these sensitivity studies, behavior of solutions for downhole GOR and OBM filtrate contamination time-functions (computed from downhole GOR data) appeared intuitively meaningful and consistent with field observations and the physics of compositional fluid-flow in porous media. Results of sensitivity studies allow us to identify rock, fluid, and geometrical parameters that dominate the physics OBM filtrate clean-up time-function. The parameters that encompass a first-order of impact on the clean-up time-function are listed as follows:
• permeability anisotropy [kv/kh], • porosity [φ], • clean-up flow rate [q], • depth of invasion [dinv], • viscosity ratio [µo/µOBMF], • WFT probe distance from a sealing boundary [h], • formation thickness [H], and • wellbore radius [rw].
Based on the numerical simulations performed within the framework of sensitivity studies and diagnostic approaches used in the contamination monitoring literature, we developed an approximate rapid but accurate model for real-time modeling and assessment. The rapid model is a nonlinear map that makes use of weighted response functions that link rock, fluid, and geometrical parameters (input), which govern the physics of OBM filtrate contamination, to an OBM filtrate weight percent contamination time-function (output). Numerically generated synthetic downhole GOR measurements were utilized to validate the accuracy and robustness of the approximate model.
The high-resolution numerical model we have introduced is a tool for planning, analysis, and quality control of formation sampling jobs. It can be deployed to reduce uncertainty and maximize probability of collecting representative fluid samples from hydrocarbon-bearing formations subject to OBM filtrate invasion. Our numerical modeling tool can be used for conducting parametric sensitivity studies with the purpose of developing physical
SPE 100393 17
insight for the design of new generation WFT probes that can operate in OBM filtrate environments with improved efficiency. Our rapid approximate model provides an accurate and efficient pre-job planning and real-time analysis tool. The resultant rig-time and sampling cost savings and improved sampling quality can strongly impact fluid evaluation and project economics. Acknowledgment The authors would like to thank Shell International E&P for permission to publish this paper. References [1] Elshahawi, H., Venkataramanan, L., McKinney, D., Flannery,
M., Mullins, O., Hashem, M.: “Combining Continuous Fluid Typing, Wireline Formation Tester, and Geochemical Measurements for an Improved Understanding of Reservoir Architecture,” paper SPE 100740, SPE 2006 Annual Technical Conference and Exhibition, San Antonio, Texas, 24-27 September, 2006.
[2] Mullins, O.C., and Schroer, J.: “Real-Time Determination of Filtrate Contamination during Openhole Wireline Sampling by Optical Spectroscopy,” paper SPE 63071, presented at the SPE 2000 Annual Technical Conference and Exhibition, Dallas, Texas, 1-4 October.
[3] Akram, A.H., Fitzpatrick, A.J., and Halford, F.R.: “A Model to Predict Wireline Formation Tester Sample Contamination,” paper SPE 59559, SPE Reservoir Evaluation and Engineering (1999), v. 2, no. 6, p. 499-505.
[5] El Battawy, A.: Simulating Near Wellbore Flow During Sampling with a Formation Tester Packer Tool String, Heriot Watt University (2001), M. Sc. Thesis.
[6] Hashem, M.N., Thomas, E.C., McNeil, R.I., and Mullins, O.C.: “Determination of Producible Hydrocarbon Type and Oil Quality in Wells Drilled with Synthetic Oil-Based Muds,” paper SPE 55959, SPE Reservoir Evaluation and Engineering (1999), v. 2, no. 2, p. 125-133.
[7] Mullins, O.C., Joshi, N.B., Groenzin, H., Daigle, T., Crowell, C., Joseph, M.T., and Jamaluddin, A.: “Linearity of Alkane Near-Infrared Spectra,” Applied Spectroscopy (2000a), v. 54, p. 624-629.
[8] Mullins, O.C., Schroer, J., and Beck, G.: “Realtime Quantification of OBM Filtrate Contamination in the MDT Using OFA Data,” paper SS, Transactions of 41st Annual Logging Symposium (2000b), Society of Well Log Analysts.
[9] Mullins, O.C., Beck, G., Cribbs, M.Y., Terabayashi, T., and Kegasawa, K.: “Downhole Determination of GOR on Single-Phase Fluids by Optical Spectroscopy,” paper M, Transactions of 42nd Annual Logging Symposium (2001a), Society of Well Log Analysts.
[10] Mullins, O.C., Daigle, T., Crowell, C., Groenzin, H., and Joshi, N.B.: “Gas-Oil Ratio of Live Crude Oils Determined by Near-Infrared Spectroscopy,” Applied Spectroscopy (2001b), v. 55, p. 197-201.
[11] Dong, C., Mullins, O.C., Hegeman, P.S., Teague, R., Kurkjian, A., and Elshahawi, H.: “In-Situ Contamination Monitoring and GOR Measurement of Formation Samples,” paper SPE 77899, presented at the SPE 2002 Asia Pacific Oil and Gas Conference and Exhibition, Melbourne, Australia, October 8-10.
[12] Betancourt, S., Fujisawa, G., Dong, C., Mullins, O.C., and Eriksen, K.O.: “Exploration Applications of Downhole Measurement of Crude Oil Composition and Fluorescence,” paper SPE 87011, presented at the 2004 SPE Asia Pacific
Conference on Integrated Modelling for Asset Management, Kuala Lumpur, Malaysia, 29-30 March.
[13] Mullins, O.C., and Sheu, E.Y.: “Optical Interrogation of Aromatic Moieties in Crude Oils and Asphaltenes,” Structures and Dynamics of Asphaltenes, Chapter 2, Plenum Press (1998), New York.
[14] Hammond, P.S.: “One- and Two-Phase Flow During Fluid Sampling by a Wireline Tool,” Transport in Porous Media (1991), v. 6, p. 299-330.
[16] Wei, L., Hildebrand, M.A., Lee, J., and Sheng J.: High-Resolution Near-Wellbore Modeling and Its Applications in Formation Testing,” paper SPE 90767, presented at the SPE 2004 Annual Technical Conference and Exhibition, Houston, Texas, 25-29 September.
[17] Todd, M.R., and Longstaff, W.J.: “The Development, Testing and Application of a Numerical Simulator for Predicting Miscible Flood Performance,” Journal of Petroleum Technology (1972), v. 24, p. 874-882.
[18] Chin, W.C., and Proett, M.A.: “Formation Tester Immiscible and Miscible Flow Modeling for Job Planning Applications,” paper L, Transactions of 46th Annual Logging Symposium (2005), Society of Well Log Analysts.
[19] Austad, T., and Isom, T.B.: “Compositional and PVT Properties of Reservoir Fluids Contaminated by Drilling Fluid Filtrate,” Journal of Petroleum Science and Engineering (2001), v. 30, p. 213-244.
[20] Dussan V., E.B., Anderson, B.I., and Auzerais, F.: “Estimating Vertical Permeability from Resistivity Logs,” paper UU, Transactions of 35th Annual Logging Symposium (1994), Society of Well Log Analysts.
