SPE 159197

Improved Detection of Bed Boundaries for Petrophysical Evaluation with Well Logs: Applications to Carbonate and Organic-Shale Formations Zoya Heidari, SPE, Texas A&M University and Carlos Torres-Verdín, SPE, The University of Texas at Austin

Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in San Antonio,Texas,USA, 8-10 October 2012. 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 have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper 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 SPE copyright.

Abstract Petrophysical interpretation of well logs acquired in organic shales and carbonates is challenging because of the presence of thin beds and spatially complex lithology; conventional interpretation techniques often fail in such cases. Recently introduced methods for thin-bed interpretation enable corrections for shoulder-bed effects on well logs but remain sensitive to incorrectly picked bed boundaries. We introduce a new inversion-based method to detect bed boundaries and to estimate petrophysical and compositional properties of multi-layer formations from conventional well logs in the presence of thin beds, complex lithology/fluids, and kerogen. Bed boundaries and bed properties are updated in two serial inversion loops. Numerical simulation of well logs within both inversion loops explicitly takes into account differences in the volume of investigation of all well logs involved in the estimation, thereby enabling corrections for shoulder-bed effects. The successful application of the new interpretation method is documented with synthetic cases and field data acquired in thinly bedded carbonates and in the Haynesville shale-gas formation. Estimates of petrophysical/compositional properties obtained with the new interpretation method are compared to those obtained with (a) nonlinear inversion of well logs with inaccurate bed boundaries, (b) depth-by-depth inversion of well logs, and (c) core/X-Ray Diffraction (XRD) measurements. Results indicate that the new method improves the estimation of porosity of thin beds by more than 200% in the carbonate field example and by more than 40% in the shale-gas example, compared to depth-by-depth interpretation results obtained with commercial software. This improvement in the assessment of petrophysical/compositional properties reduces uncertainty in hydrocarbon reserves and aids in the selection of hydraulic fracture locations in organic shale. Introduction Petrophysical and compositional evaluation of organic-shale and carbonate formations remains an outstanding challenge in the petroleum industry. Common well-log interpretation problems arising in organic-shale and carbonate formations include presence of thin beds, extreme vertical and radial heterogeneity, and uncertainty in physical and pore-structure models. The interpretation method introduced in this paper improves conventional well-log analysis in organic-shale and carbonate formations by simultaneously correcting shoulder-bed effects and quantifying the nonlinear impact of complex lithology on well logs. Shoulder beds can significantly affect estimates of petrophysical and compositional properties in thinly bedded formations. These effects depend on factors such as bed thickness, contrast in physical properties of adjacent beds, vertical resolution of well logs included in the interpretation, and specific petrophysical and compositional properties. Experience shows that shoulder-bed effects can cause significant errors in estimates of porosity, mineral/fluid concentrations, and permeability in beds thinner than 2 ft with conventional depth-by-depth well-log interpretation. This error increases with decreasing bed thickness and increasing rock variability. Conventional techniques do not effectively correct shoulder-bed effects on well-log interpretation because of the lack of fast procedures for the numerical simulation of nuclear logs. New interpretation techniques were recently developed that

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explicitly correctshoulder-bed effects on low-resolution well logs and, consequently, on estimates of petrophysical and compositional formation properties (Liu et al., 2007; Sánchez-Ramirez, 2010; Heidari et al., 2012) using numerical simulation of nuclear (Mendoza et al., 2010) and electrical resistivity logs. These methods numerically simulate conventional well logs (e.g., density, neutron porosity, apparent electrical resistivity, gamma ray (GR), and photoelectric factor (PEF) logs) in multi-layer formations and iteratively reduce the difference between simulated and measured logs with nonlinear joint inversion algorithms. However,experience shows that inversion results could be deleteriously affected by incorrect detection of bed boundaries in thinly bedded formations. Detection of bed boundaries is often possible using high-resolution well logs (e.g. wellbore image logs) or core images. Inflection points in conventional low-resolution logs are also commonly used to detect bed boundaries. The reliability of conventional well logs for bed-boundary detection, however, is affected by shoulder-bed effectsacross thinly bedded formations, where low-resolution logs measure an average physical property of adjacent beds. Presence of noise in well logs also significantly affects the accuracy of bed-boundary detection methods. Furthermore, the choice of well log for detection of bed boundaries is important because of differences in the corresponding volume of investigation and because of incorrect depth matching of measurements. For instance, PEF and density logs are usually preferred for bed-boundary detection due to high vertical resolution. However, in complex lithology cases with thin beds, these two logs may no be adequate for detecting bed boundaries. The combined interpretation of well logs can improve the accuracy of bed-boundary detection compared to that of conventional techniques. We introduce a double-loop algorithm for joint inversion of well logs to (a) reliably estimate bed boundaries which enables accurate correction of shoulder-bed effects, (b) take into account the nonlinear effect of complex mineral and fluids on well logs, and (c) estimate petrophysical and compositional properties of multi-layer formations in the presence of thin beds, gas, complex lithology, and kerogen (in the case of organic shale). In the following sections, we describe the proposed method and document its application in thinly bedded formations with complex lithology, including one synthetic case and two field examples. The first field example considers a hydrocarbon-bearing carbonate formation while the second example addresses the interpretation of well logs acquired in the Haynesville shale-gas formation. Method Simultaneous Assessment of Bed-Boundary Locations and Petrophysical/Compositional Properties We propose two serial inversion loops for simultaneous assessment of boundaries and bed-by-bed petrophysical and compositional properties of multi-layer formations. Figure 1is a flowchart describing our proposed double-loop algorithm. The first internal loop estimates bed boundaries based on preset bed-by-bed estimates of petrophysical and compositional properties. Subsequently, the second loop takes the output of the first loop as input and updates estimates of petrophysical and compositional properties. In the next iteration, we use the updated estimates as preset values for the first internal loop. It is possible to switch the order of the two inversion loops based on the complexity of the problem. In the case of high uncertainty in estimates of bed boundaries, we first apply inversion loop no. 1 to estimate bed boundaries. Next, inversion loop no. 2 estimates petrophysical and compositional properties. However, whenever reliable a-priori estimates of bed-boundaries are available (for instance in the presence of high-resolution wellbore image logs), we recommend to switch the order of the two internal loops to expedite convergence. Three approaches are suggested to initialize bed-boundary locations: (a) an initial guess based on inflection points of density or PEF logs, (b) an initial guess based on manual detection of bed boundaries using all the available well logs, and (c) an initial guess based on image logs. The number of bed boundaries is an input to the inversion. However, in the case of additional assumed bed boundaries, the thicknesses of extra beds converge to zero. The initial guess for petrophysical and compositional properties is based on interpretation procedures advanced by Heidari et al. (2012). They recommend three choices for initial guess of petrophysical and compositional properties: (a) an initial guess based on XRD/core data, (b) an initial guess based on depth-by-depth nonlinear joint inversion of conventional logs (Heidari et al., 2012), or (c) an initial guess based on conventional well-log interpretation and linear/quasi-linear multi-mineral solvers. Petrophysical and Compositional Rock Model In the petrophysical and compositional models assumed in this paper, the rock includes clay minerals, non-clay minerals, fluids, and kerogen (in the case of organic shale). Figure 2 shows the petrophysical and compositional rock models assumed for carbonate and organic-shale examples. We implement the dual-water model (Clavier et al., 1977) for resistivity-porosity-saturation calculations in all the synthetic and field examples considered in this paper.

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Density

Neutron Porosity

PEF

GR/GR‐Spectroscopy

Apparent Resistivity

Well Logs

Bed‐Boundary Detection:

Nonlinear Joint Inversion of Well Logs

Initial Guess:• Bed‐Boundary Locations• Petrophysical and 

Compositional Properties

Assessment of Petrophysical and Compositional Properties:

Bed‐by‐ Bed Nonlinear Joint Inversion of Well Logs

Updated Bed‐Boundary Locations

Updated Petrophysical and Compositional Properties

Convergence CriteriaNot 

SatisfiedSatisfied

Final Estimates

Loop 1 Loop 2

Main Loop

Figure 1: Workflow of the interpretationmethod introduced in this paper and consisting of two serial inversion algorithms. The nonlinear inversion in each loop progressively improves the agreement between well logs and their numerical simulations. Inputs to the method are well logs while outputs are bed-boundary locations, petrophysical properties, and volumetric/weight concentrations of rock mineral constituents.

Non‐Clay Minerals

Wet Shale

Water

Hydrocarbon

Vr

Vsh

Silt Clay MineralsClay‐Bound Water

Rock Volume

Non‐Shale Porosity

Non‐Clay Minerals

Water (free and bound water)

Hydrocarbon

Clay Minerals

Kerogen

(a) (b) Figure 2: Petrophysical/compositional rock models assumed in this paper for evaluation of (a) carbonate formations and (b) organic-shale formations.

Joint Inversion of Well Logs to Detect Bed Boundaries This step estimates bed boundaries assuming that petrophysical and compositional properties are known beforehand. We optimize bed-boundary locations by minimizing the quadratic cost function

2 22

22 dC x W d x d xm

, (1)

where Wdis a data weighting matrix, d(x) is the vector of numerically simulated logs, dm is the vector of available well logs, α is a regularization (stabilization) parameter, and x is the vector of bed-boundary locations, given by

1 2 1b

T

nx ,x ,...,x x , (2)

where nbis the number of beds and the superscript “T” indicates transposition. The vector of numerically simulated logs is given by

Td N b σ,ρ ,PEF,GR, ,U,Th,K , (3)

where vectorsN, b, PEF, GR, σ, U, Th, and K include nsp(number of sampling points in each well log) measurement points for neutron porosity, density, PEF, GR, apparent electrical conductivity, U (Uranium), Th (Thorium), and K (Potassium) logs;σ is a vector that includes all the available apparent electrical conductivity logs (i.e., inverse of apparent electrical resistivity logs)with variable radial lengths of investigation. In the absence of mud-filtrate invasion (when all the electrical

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conductivity logs overlap), only one electrical conductivity log is input to the inversion. The size of vectordis equal to nl×nsp, where nlis the number of well logs included in the inversion. In the implementation described above, the data-weighting matrix controls the impact of different well logs on the inversion results for bed-boundary locations and is given by

1 . . . 0

. . .

. . .

. . .

0 . . .

sp sp

l sp sp

n n

n n n

w

w

d

I

W

I

, (4)

whereI is the unity matrix and wiis the weight corresponding to well-log i. Accordingly, the effect of well log jon inversion results can be decreased by assigning a small value to wj. We minimize the quadratic cost function, C(x), using Levenberg-Marquardt’s method (Marquardt, 1963). To apply this gradient-based technique, we first numerically calculate the Jacobian matrix at every linear iteration. The corresponding entries of the Jacobian matrix are given by

, 1 , 1iij l sp b

j

dJ i n n j n

x

. (5)

The stabilization parameter is selected with Hansen’s (1994) L-curve strategy. At every linear iteration, bed-boundary locations are updated based on the calculated Jacobian matrix together with the difference between well logs and their numerical simulations. The convergence criteria is satisfied if (a) the relative difference between the norm of data residuals yielded by two subsequent iterations is less than 0.01%, (b) the maximum difference between bed boundaries estimated in two subsequent iterations is less than 0.01ft, or (c) after reaching a prescribed maximum number of iterations. Assessment of Bed-by-Bed Petrophysical and Compositional Properties via Nonlinear Joint Inversion of Well Logs In a recent publication, Heidari et al. (2012) introduced a new method for bed-by-bed joint inversion of well logs to estimate petrophysical and compositional properties of multi-layer formations. The main advantages of this method compared to conventional depth-by-depth interpretation techniques are: (a) explicit assessment of the nonlinear correlation between well-log measurements and physical properties of pure formation components, and (b) implicit correction of shoulder-bed effects on well logs. The method takes bed-boundary locations and conventional well logs as input. In the first step, bed-by-bed physical properties (i.e., electrical resistivity, neutron migration length, density, photoelectric factor, and U, Th, and K concentrations) are estimated using separate inversion of conventional well logs (i.e., apparent electrical resistivity, neutron porosity, density, PEF, and GR/GR-spectroscopy logs). Bed-by-bed physical properties are then used in a bed-by-bed joint inversion process to estimate petrophysical and compositional properties. The inversion begins with an initial guess for petrophysical and compositional properties. Schlumberger’s commercial software, SNUPAR1, estimates neutron migration length and photoelectric factor based on volumetric concentrations and chemical compositions of bed-by-bed formation components. We iteratively update bed-by-bed petrophysical and compositional properties to minimize the differences between estimated physical properties and their numerical simulations using a gradient-based optimization algorithm (Heidari et al., 2012). Synthetic Case The synthetic case is constructed to replicate formation properties in a carbonate reservoir. The objective is to investigate the efficiency of our bed-boundary detection methodin the presence of (a) shoulder-bed effects, (b) thin beds, (c) closely-spaced thin beds, (d) gas, and (e) complex lithology. Mineral and fluid constituents in the formation include quartz, calcite, dolomite, chlorite, bound water, and gas. Well logs input to the inversion are array-induction apparent resistivity, neutron porosity, density, PEF, and GR-spectroscopy (Th, Ur, and K logs). Table 1 summarizes the assumed formation properties; mud-filtrate invasion is assumed negligible while the depth-sampling rate is 0.25 ft for all the well logs. Bed-boundary locations and petrophysical/compositional properties were simultaneously estimated using the above-described double-loop inversion method. Figure 3 shows the model, initial guess, and final estimates of bed-boundary locations. The same figure compares model (actual) to numerically simulated logs. Simulated logs are plotted in connection with initial and final estimates of bed-boundary locations and petrophysical/compositional properties. The choice of a parsimonious initial guess for bed-boundary

1 Mark of Schlumberger

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locations verifies the stability of the inversion method, whereas the initial guess for petrophysical and compositional properties is constructed with results obtained from depth by-depth nonlinear joint inversion of well logs (Heidari et al., 2012). We then use center-bed values (based on the initial guess for bed-boundary locations) as initial guess for petrophysical and compositional properties.

Table 1: Synthetic Case: summary of assumed Archie’s parameters and fluid and formation properties. Variable Value Units Archie’s factor, a 1.00 ( ) Archie’s porosity exponent, m 2.00 ( ) Archie’s saturation exponent, n 2.00 ( ) Connate-water salt concentration 80 kppmNaCl Bound-water salt concentration 100 kppmNaCl In situ water density 1.00 g/cm3 In situ gas density 0.19 g/cm3 Formation temperature 230 °F Shale porosity 0.10 ( ) Volumetric concentration of clay in shale 0.50 ( ) Wet shale density 2.64 g/cm3 Wellbore radius 10.16 cm

Figure 4 compares the actual petrophysical/compositional model together with the corresponding estimates of porosity, water saturation, volumetric concentration of shale, and volumetric concentrations of quartz, calcite, and dolomite obtained from (a) depth-by-depth nonlinear joint inversion of well logs, (b) the introduced double-loop serial joint inversion of well logs, and (c) bed-by-bed nonlinear joint inversion of well logs with inaccurate bed boundaries.

0

5

10

15

20

Rel

ativ

e d

epth

(ft

)

Bed-Boundary Locations

ModelInitial guessEstimated

100

101

0

5

10

15

20

Resistivity (ohm-m)

Rel

ativ

e d

epth

(ft

)

R10model

R90model

Restimated

R90initial

3.5 4 4.5 5PEF (b/e)

PEFmodel

PEFestimated

PEFinitial

20 40 60 80 100

GR (GAPI)

GRmodel

GRestimated

GRinitial

1.94 2.2 2.45 2.71b (g/cm3)

b,model

b,estimated

b,initial

00.150.30.45

N (V/V)

N,model

N,estimated

N,initial

Figure 3: Synthetic Case: Comparison of final numerically simulated well logs (dash-dotted black line), input well logs (solid line), and numerically simulated well logs for the initial guess (dashed line). Results are shown for array-induction resistivity (second left-hand panel), PEF (third left-hand panel), GR (fourth left-hand panel), and density and neutron porosity (water-filled limestone porosity units, fifth left-hand panel) logs. The left-hand panel shows assumed values (black solid line), initial guess (dashed green line), and final estimates (dash-dotted red line) of bed-boundary locations.

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Figure 4: Synthetic Case: Comparison of the final estimates of porosity, fluid saturations, and volumetric concentrations of minerals assumed in the actual model (second left-hand panel) and those obtained from depth-by-depth nonlinear joint inversion of well logs (third left-hand panel), the introduced nonlinear bed-by-bed nonlinear joint inversion of well logs after accurate assessment of bed-boundary locations (fourth left-hand panel), and bed-by-bed nonlinear joint inversion of well logs with inaccurate bed-boundary locations (fifth left-hand panel). The left-hand panel shows bed-boundary locations assumed in the model (solid black lines), final estimates of bed-boundary locations using the proposed method (dash-dotted red lines), and perturbed bed-boundary locations (green dashed lines).

Without a reliable bed-boundary detection technique, it is possible to overlook the bed boundary located at 17 ft (relative depth), which gives rise to approximately 12% and 24% relative error in estimates of non-shale porosity and non-shale water saturation, respectively. We also observe a significant underestimate of porosity in the 0.5-ft bed located at 12 ft(relative depth) using both depth-by-depth and bed-by-bed interpretation methods when bed-boundary locations are inaccurate. Table 2 and Table 3 list (a) actual values, (b) initial guess, and (c) final estimates of bed-boundary locations, non-shale porosity, non-shale water saturation, volumetric concentration of shale, and volumetric concentrations of quartz, calcite, and dolomite. Convergence is achieved after five iterations of the main loop (including the two internal inversion loops). The maximum error in final estimates of bed-boundary locations, non-shale porosity, and non-shale water saturation is lower than 0.01 ft (absolute error), 0.1 porosity units (absolute error), and 0.1 saturation units (absolute error), respectively. We also investigated the sensitivity of the bed-boundary detection loop (inversion loop no. 1) to estimates of bed-by-bed petrophysical and compositional properties by perturbing actual properties by 15% of the original value. Results from this exercise indicate high stability of the introduced algorithm for bed-boundary detection. However, experience shows that a decrease in bed thickness increases the uncertainty of bed-boundary detection.Specifically, 15% relative uncertainty in the assessment of bed-by-bed petrophysical and compositional propertiesgives rise to a maximum error of 0.35 ft in the corresponding estimates of bed-boundary locations for a 1-ft bed surrounded by subsequent beds.

Table 2: Synthetic Case: Comparison of actual values, initial guess, and final estimates of bed-boundary locations after simultaneous assessment of bed-boundary locations and petrophysical and compositional properties of the synthetic multi-layer formation.

Relative Bed-Boundary Locations (ft) Actual location 3.000 5.000 8.000 9.000 12.000 12.500 16.000 17.000 19.000 20.000 Initial guess 2.000 6.000 7.000 10.000 11.000 14.000 15.500 17.500 18.500 21.000 Final estimates 3.000 4.994 7.990 8.999 11.996 12.495 15.996 16.999 18.994 19.997

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Table 3: Synthetic Case: Comparison of actual values, initial guess, and final estimates of non-shale porosity, non-shale water saturation, volumetric concentration of shale, and volumetric concentrations of quartz, calcite, and dolomite after simultaneous assessment of bed-boundary locations and petrophysical and compositional properties of the multi-layer formation.

Permeable beds Bed number 1 2 3 4 5 6

Non-shale porosity

Actual value 0.220 0.220 0.220 0.250 0.220 0.150 Initial guess 0.221 0.211 0.149 0.248 0.218 0.151 Final estimates 0.220 0.220 0.220 0.250 0.220 0.151

Non-shale water saturation

Actual value 0.130 0.130 0.130 0.100 0.130 0.160 Initial guess 0.129 0.176 0.183 0.103 0.106 0.201 Final estimates 0.129 0.130 0.130 0.100 0.130 0.160

Volumetric concentration of shale

Actual value 0.260 0.260 0.260 0.250 0.260 0.350 Initial guess 0.262 0.345 0.563 0.285 0.261 0.383 Final estimates 0.259 0.261 0.26 0.25 0.26 0.35

Volumetric concentration of quartz

Actual value 0.150 0.150 0.150 0.050 0.150 0.100 Initial guess 0.153 0.139 0.102 0.056 0.156 0.083 Final estimates 0.150 0.151 0.149 0.050 0.151 0.096

Volumetric concentration of calcite

Actual value 0.220 0.220 0.220 0.350 0.220 0.300 Initial guess 0.220 0.178 0.093 0.326 0.218 0.273 Final estimates 0.220 0.219 0.220 0.350 0.220 0.296

Volumetric concentration of dolomite

Actual value 0.150 0.150 0.150 0.100 0.150 0.100 Initial guess 0.144 0.127 0.093 0.085 0.147 0.110 Final estimates 0.151 0.149 0.151 0.100 0.149 0.107

Field Example No. 1: Hydrocarbon-Bearing Carbonate Formation Field Example No. 1 is intended to verify the reliability of the introduced method in the petrophysical/compositional evaluation of a challenging carbonate formation. We select a thinly bedded depth interval in this oil-bearing carbonate formation, where conventional well-log interpretation methods are not reliable. The well was drilled with oil-base mud (OBM) while thewell-log sampling rate is 0.5 ft. We assume that the effect of mud-filtrate invasion on well logs is negligible due to overlapped array-induction resistivity logs. Assumed components of the formation consist of (a) non-clay minerals, specifically quartz, calcite, and dolomite, (b) clay minerals (smectite and chlorite) in the thinly bedded depth interval, and (c) gas and saline water. Inputs to the joint inversion technique consist of (a) well logs including array-induction resistivity, PEF, density, and neutron porosity, and (b) assumed formation properties such as Archie’s parameters and matrix, fluid, and formation properties, listed in Table 4.

Table 4: Field Example No. 1: Summary of assumed Archie’s parameters and matrix, fluid, and formation properties. Variable Value UnitsArchie’s factor, a 1.00 ( )Archie’s porosity exponent, m 2.50 ( )Archie’s saturation exponent, n 3.00 ( )Connate-water salt concentration 230 kppmNaClIn situ water density 1.00 g/cm3

In situ oil density 0.98 g/cm3

Wet clay density 2.81 g/cm3

Formation temperature 320 °FWellbore radius 15.5 cm

Figure 5 shows final estimates of bed-boundary locations as well as measured and numerically simulated well logs after two iterations of the main loop. We estimated compressional-wave slowness based on the final estimates of petrophysical and compositional properties. The agreement between estimated and measured compressional-wave slowness cross validates the estimations of porosity, fluid saturations, and volumetric concentrations of minerals. In addition, the comparison indicates non-negligible shoulder-bed effects on the compressional wave slowness log. Figure 6 compares the final estimates of total porosity, total water saturation, and volumetric concentrations of quartz, calcite, dolomite, and clay against core/XRD measurements and corresponding depth-by-depth estimates obtained with commercial software. The new method improves

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porosity estimates by more than 200% in the thin bed located at 10ft (relative depth), while the depth-by-depth well-log interpretation is not reliable due to significant shoulder-bed effects. A perturbation of 0.25-foot in the bed-boundary location of this thin bed causes a 447% relative error in porosity.

Figure 5: Field Example No. 1:Comparison of final numerically simulated (dash-dotted black line) and available well logs (solid line). Results are shown for array-induction deep resistivity (fourth left-hand panel), PEF (fifth left-hand panel), and density and neutron porosity (water-filled limestone porosity units, sixth left-hand panel) logs. The left-hand panel and the second left-hand panel show estimates of bed-boundary locations and measured GR, respectively. The third left-hand panel shows the measured and the estimated bed-by-bed compressional-wave slowness (DTCO).

Figure 6:Field Example No. 1: Comparison of estimated petrophysical and compositional properties obtained with the double-loop nonlinear inversion method introduced in this paper (solid red lines), depth-by-depth inversion obtained with commercial software (dashed blue line), and core/XRD data (blue dots). Results are shown for total porosity (left-hand panel), total water saturation (second left-hand panel), volumetric concentrations of quartz (third left-hand panel), calcite (fourth left-hand panel), dolomite (fifth left-hand panel), and clay (sixth left-hand panel).

Field Example No. 2: Haynesville Shale-Gas Formation An important application of the interpretation method advanced in this paper is in organic-shale formations because of the

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common presence of thin beds and spatially varying lithology. Moreover, this field example is intended to examine the reliability of the introduced method for bed-boundary detection and petrophysical/compositional evaluation in organic-shale formations. The Haynesville formation is a late-Jurassic formation with TOC (Total Organic Carbon) between 2% and 5% and clay content lower than 50% (Quirein et al., 2010; Spain et al., 2010). Table 5 summarizes the assumed Archie’s parameters and matrix, fluid, and formation properties in Field Example No. 2. The well was drilled with water-base mud (WBM) but we assume negligible impact of the process of mud-filtrate invasion on well logs.

Table 5: Field Example No. 2: Summary of assumed Archie’s parameters and matrix, fluid, and formation properties. Variable Value UnitsArchie’s factor, a 1.00 ( )Archie’s porosity exponent, m 1.60 ( )Archie’s saturation exponent, n 2.00 ( )Connate-water salt concentration 200 kppmNaClBound-water salt concentration 200 kppmNaClIn situ water density 1.00 g/cm3

In situ gas density 0.19 g/cm3

Kerogen density 1.2 g/cm3

Dry clay density 2.84 g/cm3

Formation temperature 265 °FWellbore radius 11.11 cm

Input logs include array-induction resistivity, density, neutron porosity, and PEF. We do not include the GR log in the inversion due to uncertainty in U, Th, and K concentrations of kerogen and mineral constituents in the formation. The assumed components consist of (a) non-clay minerals, namely quartz, calcite, plagioclase, pyrite, and negligible amount of dolomite, (b) clay minerals, specificallyillite and chlorite, (c) kerogen type II, and (d) gas and saline water. Outputs from the inversion are weight concentrations of rock constituents. Because of the large number of unknown parameters compared to the number of available well logs, this example constitutes an underdetermined inverse problem. To quantify non-uniqueness of inversion results in this underdetermined estimation problem, we suggest (a) to choose the initial guess for bed-boundary locations based on inflection points in the PEF log, (b) to initialize the inversion with estimates of bed-by-bed petrophysical and compositional properties obtained from the initial guess of bed-boundary locations, and (c) to implement constraints on the volumetric concentrations of mineral constituents. As suggested by Heidari et al. (2011), XRD data in this formation shows a linear relationship between weight concentrations of quartz and plagioclase given by

. 0.32 Plag QuartzW W , (6)

and a linear relationship between weight concentrations of illite and chlorite, given by

2.1 Illite ChloriteW W , (7) where WPlag. is weight concentration of plagioclase, WQuartz is weight concentration of quartz, WIllite is weight concentration of illite, and WChlorite is weight concentration of chlorite. Figure 7 shows final estimates of bed-boundary locations together with available well logs and their corresponding numerical simulations. Figure 8 compares the final estimates of total porosity, total water saturation, and solid weight concentrations of kerogen and minerals estimated using the new interpretation method, commercial software, and core/XRD measurements. The new method improves the estimates of porosity and water saturation as well as the corresponding volumetric concentrations of minerals with respect to those of commercial software.

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Figure 7: Field Example No. 2: Comparison of final numerically simulated (dash-dotted black line) and available well logs (solid line). Results are shown for array-induction deep resistivity (third left-hand panel), PEF (fourth left-hand panel), and density and neutron porosity (water-filled limestone porosity units, fifth left-hand panel) logs. The left-hand panel and the second left-hand panel show estimates of bed-boundary locations and measured GR, respectively.

Figure 8: Field Example No. 2: Comparison of estimates of petrophysical and compositional properties obtained with the bed-by-bed nonlinear inversion method introduced in this paper (solid red lines), depth-by-depth inversion using commercial software (dashed blue line), and core/XRD data (blue dots). Results are shown for total porosity (left-hand panel), total water saturation (sixth left-hand panel), and solid weight concentrations of quartz (second left-hand panel), calcite (third left-hand panel), kerogen (fourth left-hand panel), plagioclase (fifth left-hand panel), illite (seventh left-hand panel), chlorite (eight left-hand panel), and pyrite (ninth left-hand panel).

SPE 159197 11

Conclusions We documented the successful applications of a new method for bed-boundary detection and petrophysical evaluation of thinly bedded organic-shale and carbonate formations. Results indicate that even though bed-by-bed well-log interpretation significantly improves the evaluation of thinly bedded formations compared to conventional depth-by-depth interpretation methods, an uncertainty of 0.25-foot in bed-boundary detection in a 0.5-ft bed can cause 35% and 48% relative errors in estimates of non-shale porosity and non-shale water saturation, respectively. A synthetic interpretation example confirmed the stability and accuracy of the new method for assessment of bed-boundary locations and bed-by-bed formation properties across thin beds. The reliability of the method was verified for beds with thickness greater than two times the depth-sampling interval. It was found that the new interpretation method will not provide reliable bed-boundary locations (a) when beds are thinner than two times the depth-sampling interval, or (b) in the absence of measurable property contrast between adjacent beds. We described two successful field applications of the introduced method in carbonate and shale-gas formations exhibiting thin beds and complex lithology. Estimates of porosity improved by more than 200% (relative improvement) and 30% compared to depth-by-depth interpretation techniques in the carbonate and the shale-gas formations, respectively. The synthetic and field examples studied in this paper verified that reliable assessment of bed boundaries combined with bed-by-bed interpretation of low-resolution well logs improves estimates of bed-by-bed petrophysical and compositional properties, thereby reducing the uncertainty of hydrocarbon reserves. Acknowledgements The work reported in this paper was funded by The University of Texas at Austin’s Research Consortium on Formation Evaluation, jointly sponsored by Anadarko, Apache, Aramco, Baker-Hughes, BG, BHP Billiton, BP, Chevron, ConocoPhillips, ENI, ExxonMobil, Halliburton, Hess, Maersk, Marathon Oil Corporation, Mexican Institute for Petroleum, Nexen, ONGC, Petrobras, Repsol, RWE, Schlumberger, Shell, Statoil, Total, and Weatherford. Special thanks go to BP for providing some of the field data reported in this paper. List of Symbols a Archie’s factor, ( ) C(x) Cost function, ( ) d Vector of simulated logs dm Vector of measured or model logs I Unity matrix, ( ) J Jacobian matrix m Archie’s porosity exponent, ( ) n Archie’s saturation exponent, ( ) nb Number of beds, ( ) nl number of well logs, ( ) nsp number of sampling points in each well log, ( ) R Apparent resistivity measurements, (ohm-m) Sw Total water saturation, ( ) Vr Volume of rock, ( ) Vsh Volumetric concentration of shale, ( ) Wchlorite Weight concentration of chlorite, ( ) Wd Data weighting matrix, ( ) Willite Weight concentration of illite, ( ) Wplag. Weight concentration of plagioclase, ( ) Wquartz Weight concentration of quartz, ( ) α Regularization parameter, ( ) N Neutron porosity, (V/V) s Non-shale porosity, ( ) b Bulk density, (g/cm3) σ Electrical conductivity, (S/m)

12 SPE 159197

List of Acronyms DTCO Delta-T Compressional GR Gamma-Ray K Potassium kppm Kilo Parts Per Million OBM Oil-Base Mud PEF Photo Electric Factor SNUPAR Schlumberger Nuclear Parameter code Th Thorium TOC Total Organic Carbon U Uranium WBM Water-Base Mud XRD X-Ray Diffraction References Clavier, C., Coates, G., and Dumanoir, J. 1977, The theoretical and experimental basis for the dual water model for the

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