SPWLA SYMPOSIUM

SPWLA 46th Annual Logging Symposium, June 26-29, 2005

MONTE CARLO MODELING OF NUCLEAR MEASUREMENTS IN VERTICAL AND HORIZONTAL WELLS IN THE PRESENCE OF MUD-

FILTRATE INVASION AND SALT MIXING

Alberto Mendoza, The University of Texas at Austin, William Preeg, Consultant, Carlos Torres-Verdín, and Faruk O. Alpak, The University of Texas at Austin.

Copyright 2005, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors. This paper was prepared for presentation at the SPWLA 46th Annual Logging Symposium held in New Orleans, Louisiana, United States, June 26-29, 2005.

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ABSTRACT This paper describes a study undertaken to quantify the influence of mud-filtrate invasion on neutron compensated and density measurements acquired in vertical and horizontal wells. Our objective is to assess the influence of non-axial symmetric spatial distributions of fluid saturation on generic nuclear tools. The case of horizontal wells is of primary interest due to the complex spatial distribution of fluids around the borehole due to mud-filtrate invasion combined with fluid density contrasts, permeability anisotropy, fluid mobility, and gravity segregation, among other factors.

Invasion was simulated under the assumption of a water-base mud filtrate invading a gas-bearing formation. In addition, we simulated the mixing of salt between mud-filtrate and connate water. This approach accurately reproduced the effects of porosity, permeability, permeability anisotropy, relative permeability, capillary pressure, and fluid density, on the spatial distribution of fluids and salt concentration around the borehole.

The Monte Carlo N_Particle (MCNP) code was used to simulate the response of nuclear tools with consistent source-sensor configurations. To this end, we introduced generic models of thermal neutron and density tools referred to as Longhorn Nuclear Well Logging Tools.” Calibration of the simulations of nuclear measurements was performed against standard industry models to appraise their reliability and accuracy.

Results from this study indicate that presence of mud-filtrate invasion reduces, and even eliminates the effect of gas on neutron-tool measurements. It was also found that salt concentration of connate water caused an

effect opposite to that of gas on the simulated neutron measurements. More importantly, the effect of salinity contrast, caused by fresh mud filtrate displacing salty connate water, increased the gas effect on neutron measurements for the case of shallow invasion. The effect of salt mixing was less critical for the case of density measurements. It was also found that presence of non-axial symmetric distributions of mud filtrate and salt concentration biased the estimates of density and apparent neutron porosity. Similarly, for the horizontal well case, depending on the location of the tool around the perimeter of the wellbore, both neutron and density measurements were influenced by non-axial symmetric spatial distributions of fluids resulting from invasion. This effect was most noticeable for tool locations at the top and bottom of the borehole. Tool standoff significantly biased both measurements. INTRODUCTION There is a strong industrial need to simulate the response of nuclear well logging tools in special borehole conditions and environments. Such modeling capability has not been widely available because specific details of the design of nuclear well-logging tools are needed to properly simulate their measurements. Service companies’ tool designs are usually proprietary and hence unavailable for accurate modeling by academic and oilfield technical experts. In this paper, we introduce a generic set of nuclear tools referred to as the “Longhorn nuclear well logging tools.” Such generic tools have been “designed” to match the response of service companies’ tools described in the open technical literature. The intent is to synthesize the most important properties and functions of standard measurement acquisition systems of nuclear tools, and to draw general conclusions on the nature of the measurements in complex rock formations. Results from our simulation work show that the Longhorn tools provide an acceptable match to the response of many of the service companies’ assumed borehole environmental properties. These


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results do not represent an exact match to the response of a service company’s tool; there will still be cases where a proprietary design will be needed for the accurate simulation of borehole nuclear measurements. Ellis et al. (2003) described a generic design of thermal neutron tools to illustrate the sensitivity of the measurements to formation porosity and slowing-down length. Their study primarily considered the dependence of slowing-down length on the near-to-far detector count ratio. Thermal neutron measurements were studied for the case of water-saturated rock formations. In a subsequent publication, Ellis et al. (2004) discussed the general sensitivity of thermal-neutron measurements to lithology, gas saturation, and presence of shale. The Longhorn nuclear logging tools (LNLT) introduced in this paper focus primarily on measurements acquired in the presence of mud-filtrate invasion and salt mixing in vertical and horizontal wells. This set of tools includes source-sensor configurations for both thermal neutron and bulk density measurements. We assess the sensitivity of the LNLT to non-symmetric spatial distributions of mud filtrate and salt concentration in the presence of gas-bearing rock formations. The main difference between this paper and previously published studies on the numerical simulation of nuclear tool measurements is that we quantify specific conditions of mud-filtrate invasion using the calibrated tool model as opposed to tool responses for generalized models of water-saturated lithologies. We pay special attention to the effects of salt concentration and mud-filtrate invasion in the detection of gas with nuclear tools. To visualize the response of nuclear tools to perturbations of borehole and rock formation properties, Scott et al. (1982) used a logarithmic cross-plot of the near- and far-detector count rates referred to as “spine and ribs” cross-plot. Similar cross-plots have been prepared for the LNLT and compared to published spine and ribs cross-plots. Previous work on the numerical simulation of neutron logs in horizontal wells includes the assessment of measurements in the presence of beds below and adjacent to the wellbore, and “tear-drop” invasion for logging while drilling (LWD) compensated neutron tool. In that study, Ellis et al. (2000) analyzed the interplay between radial length of investigation and radial length of invasion. They modeled non-axial symmetric “tear-drop” invasion in a 25-p.u. sand. In the present paper, we analyze the response of the LNLT for specific spatial distributions of fluids and salt concentration simulated under the assumption of

water-base mud-filtrate invading a gas-bearing formation. DESCRIPTION OF LONGHORN NUCLEAR TOOLS The thermal neutron porosity tool and the density tool assumed in this paper were modeled with the Monte Carlo N_Particle (MCNP) transport code maintained by Los Alamos National Laboratory. This code can be readily adapted to simulate the response of generic neutron and density tools by sequentially simulating individual probabilistic events. Particle histories are simulated to solve the transport equation in a statistical manner. To describe the energy-space location history of each neutron or photon starting from the source and ending with absorption, the probability distribution functions are statistically sampled for each particle interaction with the penetrated material. A detailed description of the MCNP transport code is provided by the X-5 Monte Carlo Team, (2003) in their official manual “A General Monte Carlo N-Particle Transport Code, Version 5.” This section of the paper describes the tool models as well as their calibration and compares them against published models of commercial tools. Thermal Neutron Porosity Tool Figure 1 shows the geometrical configuration of the Longhorn thermal neutron porosity tool. It consists of two helium thermal neutron detectors and a 16-curie AmBe neutron source. The distances between the center of each detector and the source, as well as their volumetric boundaries are important design parameters. A boron carbide block is placed between the long-spaced (far) and short-spaced (near) detectors to prevent the counting of neutrons passing though the tool into the far detector. The detectors, the source, and the boron carbide block are contained in an aluminum housing with an iron tool wall approximately 1 cm thick. The AmBe source is concentric with respect to the tool wall. Its exact location is given by the relative distance with respect to the lower end of the tool. Table 1 provides a complete description of the geometrical dimensions and source-sensor configuration assumed for the Longhorn thermal neutron porosity tool.


Table 1- Geometrical properties of the Longhorn thermal neutron porosity tool. Distances are measured with the respect to the lower end of the tool. Variable Units Value Far detector distance in 28 Near detector distance in 15 Far detector diameter in 2 Far detector length in 10 Near detector diameter in 1 Near detector length in 3 Tool diameter in 3 Tool length in 43 Location of the AmBe source in 7.87

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Figures 2 and 3 graphically compare the near- and far-detector count rates simulated for the Longhorn tool against those of Schlumberger’s CNTT

† thermal tool described by Scott et al. (1982). The count rates for the Longhorn tool are similar to those of the Schlumberger’s CNT at low values of porosity and somewhat better at high porosity values. Figures 4 and 5 indicate that the corresponding environmental corrections for tool standoff and borehole size are very similar for both the Longhorn and Schlumberger’s CNT thermal tools. Each MCNP simulation performed to simulate Longhorn tool measurements took approximately 38 minutes of computer time on a Pentium 4, 2.8 GHz computer. This provided results with high statistical accuracy of ± 2 % for the near-detector, and ± 0.6% for the far-detector after running 2 million particle histories.

Figure 1: Graphical description of the Longhorn thermal neutron porosity tool. The tool consists of an AmBe neutron source as well as long- and short-spaced detectors. In this particular example, the diameter of the borehole is set to 8 in. Simulations of tool measurements consider the presence of both borehole and rock formation properties.

† Mark of Schlumberger

Figure 2: Cross-plots of near- and far-detector count rates as a function of water-filled limestone porosity. Red and blue spines describe the behavior of the Longhorn and CNT-G (Scott et al., 1982) thermal neutron tools, respectively.

Figure 3: Calibration of the Thermal Neutron Porosity Tool and comparison of the near-to-far count ratio against that of published tool models. The curves show the relationship between detector-count ratio and porosity for the case of water-filled limestone. The Longhorn tool model (LNLT) matches the Generic (Ellis et al. 2003) and CNT-G (Scott et. al., 1982) responses at low values of porosity and follows a similar trend at high values of porosity.


Figure 4: Neutron environmental correction for tool standoff. The red and blue curves compare the Longhorn (LNLT) and Dual-Spacing Neutron Log (CNL) water-filled limestone porosity readings, respectively, for the case of a 15 p.u. water-filled limestone.

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Figure 5: Neutron environmental correction for borehole size. The red and blue curves compare the Longhorn (LNLT) and Dual-Spacing Neutron Log (CNL†) water-filled limestone porosity readings, respectively, for the case of a 15 p.u. water-filled limestone. Density Tool Figure 6 graphically describes the components and dimensions of the Longhorn density tool. It consists of two sodium-iodide detectors and a 1.5-curie 662 KeV Cs137 gamma ray source. The detectors and the source are contained in a tungsten-pad housing located inside an iron tool wall. Openings (windows) are inserted into the tool pad over the source and detectors to allow the passage of gamma rays from the source to the † Mark of Schlumberger

formation, and from the formation into the detectors. The source and near-detector windows are oblique cylinders placed at 45 degrees with respect to the tool axis, whereas the far-detector window is square shaped. Low-noise photomultiplier tubes house the long- and short-spaced detectors. Table 2 provides a complete description of the geometrical dimensions and source-sensor configuration assumed for the Longhorn density porosity tool. Table 2- Geometrical properties of the Longhorn density porosity tool. Distances are measured with respect to the lower end of the tool. Variable Units Value Far detector distance in 18 Near detector distance in 9 Far detector diameter in 0.79 Far detector length in 1.5 Near detector diameter in 0.37 Near detector length in 0.51 Far photomultiplier tube diameter in 1.34

Near photomultiplier tube diameter in 1.34

Far photomultiplier tube length in 3.74 Near photomultiplier tube length in 2.76 Tungsten pad housing diameter in 2.56 Tungsten pad housing length in 21.26 Tool diameter in 1.44 Tool length in 24.8 Location of the Cs137 source in 2.85 Source window diameter in 0.06 Near detector window diameter in 0.24 Far detector window area in2 7.05 Figure 7 graphically compares the near- and far-detector count rates associated with both the Longhorn density tool and the BHI (Baker-Atlas) density tool described by Bigelow (1995). The comparison is performed using a traditional “spine and rib” presentation. We found that the count rates of both near and far detectors for the aluminum and magnesium calibration blocks were similar for the Longhorn and BHI density tools. Simulated ribs for the cases of light and heavy mudcake are similar for the two tool designs. We accurately approximated the dynamic ratio (variation of count rates for the calibration blocks) for each detector as well as the slopes of the “spine and ribs.” Low-energy photons (energy lower than 200 KeV) have a higher probability of being absorbed completely on impact with an atom. As a consequence, a photoelectron is ejected from the atom and kinetic energy is transferred to the photoelectron. To eliminate the photoelectric effects on the tool calibration, as well


as in the simulations discussed in a subsequent section, we included only photons with energies above 200 KeV in the count rates of the two detectors.

Figure 6: Graphical description of the Longhorn density porosity tool. The diagram shows the relative locations of the Cs137 source of medium-energy gamma rays, and of the long and short-spaced NaI crystals with photomultiplier tubes used as detectors. The tool includes an iron casing (blue), and a tungsten pad housing (orange). In this particular case, the diameter of the borehole is equal to 8 in. Rock formations are indicated in yellow and the small dots display calculated photons. Each point represents a collision of a photon that eventually reaches one of the detectors.

Figure 7: “Spine and rib” cross-plot plot describing the relationship between gamma-ray counts at the short- and long-spaced detectors for density porosity tools. The spine from the longhorn Nuclear Logging Tool (LNLT) is displayed in blue with ribs for “light” and “heavy” mudcake, and the commercially available tool (BA, Bigelow, 1995) is plotted in black along with its rib calibration. The magnesium calibration block is identified with green squares, whereas the aluminum calibration block is identified with red diamonds.

The interaction of the emitted gamma rays with the rock formation is through electrons. Attenuation is caused by Compton scattering for energies above 125 KeV (Schultz et al., 1985). As a consequence, the density tool’s response (ρa) is related to electron density (ρe). The relationship between electron density and bulk density (ρb) is given by

be AZ ρρ 2

= , (1)

where Z and A are the average atomic number and average atomic weight of the rock formation, respectively. A relationship between electron density and bulk density that applies to water-filled limestone is commonly used to calculate values of bulk density. This established relationship is written as (Bigelow, 1995)

1883.004704.1 −= eb ρρ . (2)

The above equation also remains a good approximation for the cases of fluid-saturated sandstone and dolomite if ρb =ρa (Schultz et al., 1985). Based on the use of equation (2), Figure 8 graphically describes the relationship between detector count rate and bulk density.

Figure 8: Relationship between bulk density and gamma-ray detector count rate for the Longhorn density porosity tool. Count rates for each detector are related to bulk density via tool calibration charts. Count rates from each detector for several electron density values were obtained from the spine chart. The corresponding bulk density for each value of electron density was calculated using equation (2) and plotted in red for the long-spaced detector, and in blue for the short-spaced detector.

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Each MCNP simulation with the Longhorn density tool took approximately 106 minutes of computer time on a Pentium 4, 2.8 GHz computer that included the simulation of 30 million particle histories. This provided results with a statistical accuracy of ± 3% for the near-detector, and ± 1% for the far-detector. SIMULATION OF MUD-FILTRATE INVASION We simulated the process of mud-filtrate invasion under the assumption of a water-base mud invading a gas-bearing rock formation. Spatial distributions of water saturation, salt concentration, and gas saturation resulted from the process of mud-filtrate invasion in vertical and horizontal wells. As described by Alpak et al. (2003), the numerical simulation of the invasion process explicitly considers the effects of permeability, fluid viscosity, relative permeability, capillary pressure, fluid density, and gravity segregation. Initially, the rock formation is 70 % saturated with gas and 30 % saturated with water of NaCl concentration equal to 150,000 ppm. The process of mud-filtrate invasion was numerically simulated with the ECLIPSE* commercial black-oil multiphase fluid-flow simulator. A value on the order of 5 x10-5 cm/s is imposed as the speed of radial mud-filtrate invasion along the borehole wall. This value remains consistent with the invasion speeds reported by Dussan V. et al. (1994). With the purpose of simulating the response of the density and thermal neutron porosity tools in the presence of invasion, we considered formation models penetrated by vertical and horizontal wells. The vertical well penetrates a sand-shale sequence consisting of a top sand of 25% porosity, followed in depth by a shale bed, and a bottom sand of 15% porosity. Both sand reservoirs were initially 70% saturated with gas, and 30% saturated with water of salt concentration equal to 150,000 ppm. These initial fluid saturations were displaced by mud-filtrate invasion consisting of water of salt concentration equal to 5,000 ppm. Figure 9 graphically describes the petrophysical and geometrical properties of the vertical well model, including specific properties for each of the two sands. Petrophysical properties critical to the simulation of mud-filtrate invasion include porosity, initial water saturation, permeability, and relative permeability curves along with core-calibrated Brooks-Corey capillary pressure. Table 3 describes the fluid, formation, and rock-fluid properties assumed in the

* Mark of Schlumberger

simulation of invasion for the case of a vertical well. The same rock-fluid properties were assumed for the case of a horizontal well. Table 4 summarizes the corresponding rock formation properties for the case of a horizontal well. Invasion in the vertical well model was numerically simulated with 14,580 grid blocks, whereas the simulation of invasion in the horizontal well model required 29,584 grid blocks. Figures 10 and 11 are section views of gas saturation and salt concentration, respectively, resulting from the simulation of the process of mud-filtrate invasion for the case of a vertical well. In both section views, the assumed time of invasion is 3 days. Table 3- Summary of fluid and rock-formation properties assumed in the simulation of the process of mud-filtrate invasion for the case of a vertical well. Variable Units Value Top sand thickness ft 20 Top sand permeability md 300 Top sand porosity fraction 0.25 Bottom sand thickness ft 15 Bottom sand permeability md 30 Bottom sand porosity fraction 0.15 Initial fluid pressure psi 2,000 Initial water saturation fraction 0.30 Initial gas saturation fraction 0.70 Gas viscosity cp 0.02 Gas density g/cm3 0.04 Mud-filtrate viscosity cp 1.00 Mud-filtrate density g/cm3 1.0027 Mud-filtrate salt concentration ppm 5,000 Connate water salt concentration ppm 150,000 Connate water density g/cm3 1.18 Residual water saturation fraction 0.10 Residual gas saturation fraction 0.05 Gas end-point relative permeability - 0.80

Water end-point relative permeability - 0.25

Wellbore radius cm 10.16 Maximum invasion time days 3.00 Temperature oF 210 Formation outer boundary ft 866.6 Sand chemical composition SiO2Shale chemical composition Al2O32SiO22H2O


Table 4- Summary of fluid and rock-formation properties assumed in the simulation of the process of mud-filtrate invasion for the case of a horizontal well. Variable Units Value Well length ft 50 Formation thickness ft 20 Formation outer boundary ft 98 Horizontal permeability md 300 Vertical permeability md 300 Porosity fraction 0.25 Wellbore radius cm 10.16 Maximum invasion time days 3.00 Temperature oF 210

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Figure 9: Graphical description of the rock formation properties included in the vertical borehole model used for the simulation of mud-filtrate invasion.

Figure 10: Section view of gas saturation for the case of a vertical well and axial-symmetric mud-filtrate invasion after 3 days of invasion. Refer to Figure 9 and Table 3 for a description of fluid and rock formation properties. The figure displays deeper invasion and higher water concentration near the wellbore for the lower sand (15% porosity) than for the upper sand (25% porosity). In addition, mud-filtrate invasion causes a vertical gradient of water saturation.

Figure 11: Section view of salt concentration for the case of a vertical well and axial-symmetric mud-filtrate invasion after 3 days of invasion. Refer to Figure 9 and Table 3 for a description of fluid and rock formation properties. As opposed to the spatial distribution of water saturation shown in Figure 10, the spatial distribution of salt concentration is almost identical in both sands. Figures 12 and 13 are section views of gas saturation and salt concentration, respectively, resulting from the simulation of the process of mud-filtrate invasion for


the case of a horizontal well. The section views are taken on a plane perpendicular to the borehole axis and the assumed time of invasion is 3 days. As in the case of the vertical well, Figure 13 indicates that the spatial distribution of water saturation is non-uniform after invasion; it remains notably affected by gravity segregation. On the other hand, the spatial distribution of salt concentration is not as diffused as the spatial distribution of water saturation. Salt concentration is displaced away from the near-wellbore region more uniformly than water saturation.

Figure 12: Section view of gas saturation for the case of a horizontal well subjected to mud-filtrate invasion. The section view is taken along a plane perpendicular to the borehole axis and the time of invasion is 3 days. Refer to Tables 3 and 4 for a description of the fluid and rock formation properties.

Figure 13: Section view of salt concentration for the case of a horizontal well subjected to mud-filtrate invasion. The section view is taken along a plane perpendicular to the borehole axis and the time of invasion is 3 days. Refer to Tables 3 and 4 for a description of the fluid and rock formation properties.

NUMERICAL SIMULATION OF NUCLEAR TOOL MEASUREMENTS Simulation of Thermal Neutron Porosity Measurements Simulation of thermal neutron measurements was performed with MCNP. We assumed the Longhorn thermal neutron porosity tool configuration described earlier to simulate the measurements. Simulations considered the cases of vertical and horizontal wells described in the previous section both with and without the presence of mud-filtrate invasion. The assumed time of invasion was 3 days. The vertical well model consists of 367 MCNP cells including the formation as well as the tool geometry in a three-dimensional cylindrical coordinate frame. Nine concentric cylinders of increasing radii were used to model the wellbore (radius equal to 10.16 cm) and the rock formation. The geometry of the formation consists of eight cylindrical cells of radial length equal to 0.25 ft, and one of 3 ft for a total of 5 ft of radial distance coverage from the borehole wall into the formation. The thickness of each cylindrical cell is equal to 1 ft in the vertical direction. A total of 360 cylindrical cells were used to model the formation. Every cell contains its corresponding petrophysical properties as well as the corresponding values of salt concentration and fluid saturation resulting from the process of mud-filtrate invasion. Simulation of neutron porosity logs was performed with calculations at every 0.5 ft starting from the bottom of the formation model. Every calculated point is displayed at the depth of the midpoint between the source and the long-spaced detector. Approximately 238 minutes of computer time were required to simulate thermal neutron measurements at each point for the case of an invaded formation on a Pentium 4, 2.8 GHz PC. The accuracy of the measurements is approximately ± 0.3 p.u. for the top sand, and ± 0.4 p.u. for the bottom sand. MCNP simulations generally entail more computer time at the same precision for the case of higher density materials. For the simulation of thermal neutron measurements before the onset of invasion, 166 minutes of computer time were required to perform simulations at the same precision after running 15 million particle histories. Since neutrons interact primarily with hydrogen nuclei in the formation, the spatial distribution of hydrogen index in the formation is critical to accurately simulate thermal neutron measurements. Figure 14 is a section view of hydrogen concentration in atomic weight fraction for the case of a vertical well. This section view was plotted directly from the simulated spatial distributions of water saturation and the calculation

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included the assumed chemical composition of the various rock types present in the model.

Figure 14: Section view of hydrogen concentration (atomic weight fraction) for the case of a vertical well and axial-symmetric mud-filtrate invasion after 3 days of invasion. Refer to Figure 9 and Table 3 for a description of fluid and rock formation properties The horizontal well model consists of 6,328 cells of a three-dimensional Cartesian spatial discretization that included the tool and the formation. A horizontal cylinder was used to model the borehole (radius equal to 10.16 cm). Discretization cells are uniform along the wellbore surface parallel to the tool; their length is equal to 1,524 cm. We included 80 grid blocks in the vertical direction and 80 grid blocks in the horizontal direction to properly capture the finer details of the spatial distributions of water saturation and salt concentration yielded by the simulation of mud-filtrate invasion. Dimensions of each grid block are 2 cm on the plane perpendicular to the borehole axis, and 1,524 cm parallel to the borehole axis. The formation includes a total of 6,320 cells discretization cells. Each simulation for one particular location of the tool required approximately 271 minutes of computer time on a Pentium 4, 2.8 GHz computer. The accuracy of the measurements is approximately ± 0.5 p.u. for the case of thermal neutron simulations performed in the presence of invasion. The latter simulations entailed 20 million particle histories. By contrast, approximately 227 minutes were needed to simulate thermal neutron measurements acquired before the onset of invasion at the same precision. Figure 15 is a section view of hydrogen concentration in atomic weight fraction for the case of a horizontal well assuming 3 days of invasion. This section view

was plotted directly from the simulated spatial distributions of water saturation and the calculation included the assumed chemical composition of the various rock types present in the model.

Figure 15: Section view of hydrogen concentration (atomic weight fraction) for the case of a horizontal well subjected to mud-filtrate invasion. The section view is taken along a plane perpendicular to the borehole axis and the time of invasion is 3 days. Refer to Tables 3 and 4 for a description of the fluid and rock formation properties. Simulation of Density Tool Measurements We assumed the Longhorn density tool model introduced earlier to perform simulations of density measurements with MCNP. Numerically simulations include the same vertical and horizontal formation models with and without presence of mud-filtrate invasion and salt mixing. Variations of fluid saturation and salt concentration due to invasion altered the original bulk density of the formation. As a consequence, the density tool’s response biases the values of estimated porosity under the assumption of one type of fluid. Figures 16 and 17 are section views of formation bulk density for the cases of invaded vertical and horizontal wells, respectively. The assumed time of invasion is 3 days. These section views were plotted directly from the simulated spatial distributions of water saturation, and salt concentration. We also considered the assumed chemical composition of the rock for the calculation of bulk density. Approximately 118 minutes of computer time were required for the simulation of density measurements for each depth point in the vertical well on a 2.8 GHz PC after computing 30 million particle histories. This resulted in a precision of approximately ± 0.5 p.u. for the invaded case. For the case before the onset of

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invasion, 78 minutes were required to achieve the same precision, whereas for the case of a horizontal well, 168 minutes were required for each simulation prior to invasion to achieve an accuracy of ±0.5 p.u. By contrast, 48 minutes of computer time were required to simulate bulk density measurements at each measurement point for the uninvaded case.

Figure 16: Section view of bulk density for the case of a vertical well and axial-symmetric mud-filtrate invasion after 3 days of invasion. Refer to Figure 9 and Tables 3 and 4 for a description of fluid and rock formation properties.

Figure 17: Section view of bulk density for the case of a horizontal well subjected to mud-filtrate invasion. The section view is taken along a plane perpendicular to the borehole axis and the time of invasion is 3 days. Refer to Tables 3 and 4 for a description of the fluid and rock formation properties.

INTERPRETATION OF SIMULATION RESULTS We simulated neutron and density porosity logs for the case of a vertical well. On the other hand, for the case of a horizontal well, neutron and density porosity measurements were simulated at specific tool locations around the perimeter of the borehole wall. Figure 18 shows the simulated log of neutron porosity for the vertical well model before and after invasion.

Figure 18: Numerically simulated neutron porosity logs (water-filled sandstone porosity units) for the vertical well model. Simulated neutron porosity logs are shown for the cases of virgin and invaded rock formations. Notice the presence of the so-called “horns” at sand-shale and shale-sand transitions. Refer to Figure 9 and Table 3 for a description of fluid and rock formation properties. We observe that the simulated neutron porosity log underestimates the true porosity of the lower sand (15 p.u.) by approximately 9 p.u. before the onset of invasion. This underestimation of porosity is due to presence of gas in the formation. However, the overestimation of neutron porosity is relatively low because of the relatively high salt concentration of connate water. Salt concentration has the opposite effect to that due to presence of gas on the neutron log. On the other hand, after invasion, the simulated neutron porosity is 15 p.u. There is no appreciable gas effect on the simulated neutron porosity measurement after invasion because of the relatively deep radial invasion. Moreover, salty formation water is displaced away from the borehole wall by fresh mud-filtrate, thereby reducing the effect of salt concentration on the simulated neutron log. For the top sand (25 p.u.), the radial length of invasion is shallow enough for the tool to remain sensitive to

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presence of gas. In both cases, before and after invasion, the porosity is underestimated due to presence of gas. However, due to the relatively shallow invasion, saturation of connate water is high near the wellbore and this reduces the effect of gas. Before the onset of invasion, the resulting apparent neutron porosity is 9 p.u., compared to 16 p.u after invasion. In this case, comparison of the neutron logs simulated before and after invasion indicates that the effect of gas decreases because of the displacement of salt water in the formation by fresh mud filtrate, thereby reducing the effect of salt concentration. Figure 19 shows the density log numerically simulated with MNCP both before and after invasion for the case of a vertical well.

Figure 19: Numerically simulated bulk density logs for the vertical well model. Simulated bulk density logs are shown for the cases of virgin and invaded rock formations. Notice the presence of the so-called “horns” at sand-shale and shale-sand transitions. The red curve shows the difference between the far- and near detector density values. Refer to Figure 9 and Table 3 for a description of fluid and rock formation properties. The bulk density of the formation was calculated from the response of the tool to electron density. Only gamma-ray counts simulated at the far detector were used for the calculation of bulk density given that the simulations did not include borehole environmental effects. However, the density from the near detector was compared to that of the far detector (DRHO) to assess invasion effects based on the difference in depth of investigation inherent to each detector. The simulated log densities consistently increase after invasion because of the displacement of gas by mud filtrate near the borehole wall. Moreover, the simulated density logs are similar across the two sands because the radial length of investigation of the density tool is shallower than that of the neutron tool. Therefore,

radial length of invasion is less critical to density than to neutron measurements. Figures 20 and 21 show the simulated neutron porosity and bulk density logs for the case a vertical well after and before invasion, respectively. Figures 22 and 23 show the same logs plotted in terms on density porosity (DPHI). The latter was calculated assuming quartz matrix of density equal to 2.65 g/cc and a single fluid of density equal to 1.1 g/cc for salty formation water, and 1.0 g/cc for mud filtrate.

Figure 20: Numerically simulated bulk density (gm/cc) and neutron porosity (water-filled sandstone porosity units) logs for the case of a vertical well model with mud-filtrate invasion. The time of invasion is 3 days. Refer to Figure 9 and Table 3 for a description of fluid and rock formation properties.

Figure 21: Numerically simulated bulk density (gm/cc) and neutron porosity (water-filled sandstone porosity units) logs for the case of a vertical well model before invasion. Refer to Figure 9 and Table 3 for a description of fluid and rock formation properties.

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Figure 22: Numerically simulated bulk density and neutron porosity logs (both expressed in water-filled sandstone porosity units) for the case of a vertical well model with mud-filtrate invasion. The time of invasion is 3 days. Refer to Figure 9 and Table 3 for a description of fluid and rock formation properties. Density porosity was calculated for a sand matrix assuming a single fluid of density 1.0 g/cc.

Figure 23: Neutron porosity and density porosity simulated before invasion. Density porosity was calculated assuming a sand matrix of density equal to 2.65 g/cc, and a single fluid of density equal to 1.1gr/cc. The simulated neutron and density porosity logs across the top sand (25 p.u.) exhibit the crossover that is characteristic of gas-saturated formations. Conversely, the two simulated logs overlap across the lower sand (15 p.u.) because in this case both measurements are primarily sensitive to mud filtrate given the relatively deep invasion. The cross-over between the two logs, however, remains visible when the log simulations are performed prior to the onset of invasion.

For the case of horizontal wells, the wellbore, the petrophysical properties of the formation, and the spatial distributions of fluid saturation and salt concentration were input to MCNP for the simulation of neutron and density measurements. Figure 24 is a section view perpendicular to the borehole axis of the numerical grid used for the simulations of both neutron and density measurements with MCNP.

Figure 24: Section view describing the input MCNP model for the case of a horizontal well subjected to mud-filtrate invasion. The section view is taken along a plane perpendicular to the borehole axis and the time of invasion is 3 days. The figure shows the relative locations of the wellbore and the tool (here positioned at the bottom of the borehole). Colored cells illustrate the non-axial symmetric spatial distribution of saturating fluids. Bulk density and apparent porosity measurements for this horizontal model were simulated at several tool locations around the perimeter of the borehole wall, including top, center, bottom, left, and right. Figure 25 graphically describes the simulated values of apparent neutron porosity (water-filled sandstone porosity) both before and after the onset of invasion. Table 5 summarizes these simulations in terms of their percent change with respect to the case of no invasion. Similarly, Figure 26 graphically describes the simulated values of density porosity (water-filled sandstone porosity) for various tool locations around the perimeter of the borehole. Table 6 summarizes the simulations in terms of their percent change with respect to the case of no invasion.

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Figure 25: Numerically simulated values of apparent neutron porosity (water-filled sandstone porosity units) for the case of a horizontal well model. The plots describe porosity values simulated at different tool locations around the perimeter of the borehole wall, both with and without the presence of mud-filtrate invasion. Refer to Tables 3 and 4 for a description of the fluid and rock formation properties. The assumed time of invasion is 3 days. Table 5- Summary of apparent neutron porosity values (water-filled sandstone porosity units) numerically simulated for the case of a horizontal well with and without presence of mud-filtrate invasion. The percent porosity change was calculated with respect to the reading simulated at the bottom-hole location after 3 days of invasion. Tool location NPHI

no invasion (p.u.)

NPHI 3 days of invasion (p.u.)

% of change

Top 9.9 12.11 15.6% Center 21.8 22.0 12.2% Bottom 9.7 14.35 - Right 9.7 12.81 10.7% Left 9.7 12.81 10.7%

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It can be observed that the simulated neutron and density measurements are sensitive to presence of gas regardless of tool location. The sensitivity of the measurements to presence of gas only decreases after invasion. For this case of 25% porosity, the maximum difference before and after invasion was only 4 p.u. approximately. Such a small difference can be explained in similar fashion to the case of a vertical well. As mud filtrate displaces gas near the wellbore, it decreases both, the gas saturation and the salt concentration. Consequently, the sensitivity of the measurements to gas saturation is somewhat diminished by the relative increase of salt concentration. The maximum change of simulated

neutron measurements occurs between the top and bottom locations of the tool along the perimeter of the borehole wall. The simulated tool measurement reads 2 p.u. lower at the top location compared to the reading at the bottom location. This can be explained as due to the relative differences in the spatial distributions of fluid saturation and salt concentration. Moreover, it is observed that the effect is similar when compared to the case of a non-invaded formation. Here, the simulated value of apparent porosity after invasion is 2 p.u. higher than the corresponding value for the case of no invasion at the top tool location, and 4 p.u. higher at the bottom tool location. In both cases, the apparent neutron porosity is lower than the true porosity (25%).

Figure 26: Numerically simulated values of density porosity (water-filled sandstone porosity units) for the case of a horizontal well model. The curves describe porosity values simulated at different tool locations around the perimeter of the borehole wall, both with and without the presence of mud-filtrate invasion. Refer to Tables 3 and 4 for a description of the fluid and rock formation properties. The assumed time of invasion is 3 days and the assumed density of mud filtrate is 1.0 gr/cc. Table 6- Summary of bulk density and density porosity (water-filled sandstone porosity units) values simulated for the case of a horizontal well with and without presence of mud-filtrate invasion. The percent porosity change was calculated with respect to the reading simulated at the bottom-hole location after 3 days of invasion. Tool location

Bulk Density (g/cc)

DPHI (p.u.)

% of change

Top 2.083 36.6 4.8% Center 1.431 73.9 129.1% Bottom 2.109 34.8 - Right 2.100 35.5 1.6% Left 2.100 35.5 1.6%


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When the tool is located at the top of the borehole, the simulated value of bulk density is closer to the one simulated prior to the onset of invasion (2.082 gr/cc). Slightly higher density values resulted from the simulation at the bottom tool location because at this location the measurement is the least influenced by presence of gas. Here, the resulting bulk density was 2.109 g/cc, i.e. 1.3% higher than the density measured at the top location (2.083 g/cc). This difference results in a 4.8% change of the calculated porosity assuming a quartz matrix and mud-filtrate as the single fluid type. Similarly, the density tool underestimates formation bulk density by 45% under tool standoff of 2.56 in. This tool standoff effect results in 129% change of the calculated porosity under the same matrix and fluid assumptions. Percent variations of the simulated values of porosity at different tool locations are more pronounced for the case of density measurements than for the case of neutron measurements. This can be explained by recalling that density measurements involve a spatial average of material density in the neighborhood of the source and sensors. On the other hand, neutron measurements are influenced not only by spatial variations of fluid saturation, but also by the spatial distribution of salt concentration. SUMMARY AND CONCLUSIONS This paper introduced generic compensated thermal neutron and bulk density tools referred to as Longhorn nuclear well logging tools, or LNLT. The intent was to advance open source-sensor configurations that could be used to quantitatively assess, in a general fashion, the sensitivity of borehole nuclear measurements to complex spatial distributions of lithology, fluid saturation, and salt mixing, in the vicinity of vertical, horizontal, and highly deviated wells. These source-sensor configurations provide an open template to quantify the sensitivity of nuclear measurements to a wide array of petrophysical conditions. They also permit a closer, quantitative integration of borehole nuclear measurements with other logging suites, such as resistivity, sonic, and formation testing, to devise new petrophysical interpretation techniques that effectively integrate multi-physics borehole measurements at a much deeper level than currently done. The LNLT were calibrated and compared against results from commercially available tools published in the open technical literature. This exercise indicated that the LNLT included the most important elements and response factors of commercially available borehole nuclear tools. The response of the LNLT was numerically simulated with the MNCP code for the case of both vertical and

horizontal wells. Our objective was to quantify the sensitivity of nuclear borehole measurements to specific conditions of water-base mud-filtrate invasion with salt mixing. Formation models included both low- and high-porosity shale-free sand units. Spatial distributions of fluid saturation and salt concentration resulting from the process of mud-filtrate invasion were simulated by accurately reproducing the effects of porosity, permeability, relative permeability, capillary pressure, fluid density, and viscosity. Results from this study indicate that presence of invasion due a fresh water-base mud on a formation saturated with gas and salty connate water can significantly influence borehole nuclear measurements. For the case of thermal neutron tools, it was found that the radial length of invasion can significantly bias the measurements. Specifically, at low values of formation porosity, radial displacement of gas by mud-filtrate away from the borehole wall causes the measurement to lose sensitivity to in-situ gas. On the other hand, for the case of high values of formation porosity, hence shallow invasion, the effect of gas was visible but somewhat diminished by the high values of salt concentration. Therefore, it can be concluded that radial length of invasion as well as salt concentration constructively combine to reduce the sensitivity of borehole nuclear measurements to presence of gas. For the same vertical well model, it was found that measurements of bulk density were less sensitive to the radial length of invasion than neutron measurements because of the tool’s relatively shallow radial length of investigation (thereby remaining sensitive to mud filtrate only). The characteristic cross-over between neutron and density porosity logs across gas-saturated sands, could only be reproduced for the case of high-porosity sands. For the case of horizontal wells, our simulation results confirmed that non-axial symmetric spatial distributions of mud-filtrate and salt concentration can significantly bias the response of borehole nuclear tools. The maximum change of neutron porosity was observed between the top and bottom locations of the tool around the perimeter of the borehole wall. Salt concentration had a significant influence on the detection of gas. Before the onset of invasion, the neutron measurement was approximately 15 p.u. lower than the 25% true porosity. After invasion, for the case of the tool at the bottom location (where the invasion effect is most evident) the neutron measurement was 10 p.u. lower than the true porosity because of the much lower salt concentration near the borehole resulting from the displacement of formation water by mud-filtrate. Similarly, variations of 4.8% and 1.6% of bulk density were simulated at different tool locations


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around the perimeter of borehole wall. In this latter case, simulation results indicated that the bulk density tool was less sensitive to the spatial distribution of fluids resulting from invasion than the neutron tool. Overall, the simulated variations of neutron and density measurements around the perimeter of the borehole wall were relatively small for the case of high-porosity rock formations. Additionally, tool standoff can significantly bias nuclear measurements acquired in horizontal wells by as much as 12% for the neutron tool, and 56% when the density tool is located at the center of the borehole. The effect of tool standoff is more critical to density than to neutron measurements. Similar to the effect of invasion, and given the tool’s relatively shallow radial length of investigation, density measurements are extremely sensitive to the borehole fluid in the presence of tool standoff. In that situation, the density tool will sense a weighted spatial average of the densities of the invaded formation and the borehole fluid. This can lead to underestimation of formation density by 56% for a tool standoff of 2.56 in (borehole diameter equal to 8 in). We anticipate a wider class of sensitivity analyses to appraise the effects of shale and shale laminations on borehole nuclear measurements acquired across invaded clastic sequences. The LNLT introduced in this paper also seem adequate to quantify the sensitivity of nuclear measurements to complex spatial distributions of fluid saturation in the vicinity of highly deviated wells, both open and cased. Lastly, the generic nuclear tool configurations introduced in this paper could be used to approach the quantitative integration of borehole measurements for the petrophysical interpretation of complex carbonate formations. ACKNOWLEDGEMENTS

Funding for the work reported in this paper was provided by UT Austin’s Research Consortium on Formation Evaluation, jointly sponsored by BP, Baker Atlas, ConocoPhillips, ENI E&P, ExxonMobil, Halliburton Energy Services, Mexican Institute for Petroleum, Occidental Oil and Gas Corporation, Petrobras, Precision Energy Services, Schlumberger, Shell International E&P, Statoil, and TOTAL. We express our deepest gratitude to Harry Smith, Darwin Ellis, Joe Chiaramonte, G. Pingjun, Hugh Scott, and D. K. Steinman for their constructive editorial and technical comments.

REFERENCES Alpak, O.F., Dussan V. E.B., Habashy, T.M., and Torres-Verdín, C., 2003, Numerical simulation of mud filtrate invasion in horizontal wells and sensitivity analysis of array induction tools: Petrophysics, v. 44, no. 6, November-December, p. 396-411.

Bigelow, E., 1995, Introduction to wireline log analysis: Western Atlas International, Inc., Houston, Texas.

Dussan V., E.B. Anderson, B.I., and Auzerais, F., 1994, Estimating vertical permeability from resistivity logs, paper UU, in 35th Annual Logging Symposium Transactions: Society of Professional Well Log Analysts.

Ellis, D.V., and Chiaramonte, J. M., 2000, Interpreting Neutron Logs in Horizontal Wells: A Forward Modeling Tutorial, Petrophysics, vol. 41, no. 1, p. 23-32. Ellis, D.V., Case, Charles, C.R., and Chiaramonte, J.M., 2003, Porosity from Neutron Logs I: Measurement, Petrophysics, vol. 44, no. 6, p. 383-395 Ellis, D.V., Case, Charles, C.R., and Chiaramonte, J.M., 2004, Porosity from Neutron Logs II: Interpretation, Petrophysics, vol. 45, no. 1, p. 73-86. Schwarz, R.A., and Carter, L.L., Visual Editor to create and display MCNP Input Files, Trans. Amer. Nucl. Soc., 77, 311-312 American Nuclear Society, La Grange Park, Illinois, 1997. Scott, H.D., Flaum, C., Sherman, H., 1982, Dual Porosity CNL Count Rate Processing, SPE-11146, in SPE Annual Technical Conference Proceedings: Society of Petroleum Engineers. Shultz, W.E., Nunley, A., Kampler, J. G., Smith, H.D. Jr., 1985, Dual Detector Lithology Measurements with a New Spectral Density Log, SPWLA 26th Annual Logging Symposium. X-5 Monte Carlo Team. MCNP., 2003 – A General Monte Carlo N-Particle Transport Code, Version 5. University of California, Los Alamos National Laboratory. ABOUT THE AUTHORS

Alberto Mendoza is a Research Assistant and a PhD student in the Department of Petroleum and Geosystems Engineering at The University of Texas at Austin. He received both Bachelor of Science and


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Master of Science degrees in Petroleum Engineering from The University of Texas at Austin in 2002 and 2005. From 2002 to 2003 he worked for Schlumberger as a field engineer in well testing. He was granted a 2003-2004 scholarship by the SPWLA. His research interests include petrophysics, log analysis, inverse problems, and well testing. William Preeg received a PhD in Nuclear Science and Engineering from Columbia University in 1970. From 1980 to 2002, he held various positions with Schlumberger including Director of Research at Schlumberger-Doll Research (SDR), Vice President of Engineering in Houston as well as Manager of the Nuclear Department at SDR. Prior to 1980, he had worked for Los Alamos Scientific Laboratory, Aerojet Nuclear Systems Company, and the Atomic Energy Commission, largely in the area of nuclear radiation transport. He has also served on advisory committees at University of Texas, Texas A&M, Colorado School of Mines and Georgia Tech. Carlos Torres-Verdín received a PhD in Engineering Geoscience from the University of California, Berkeley, in 1991. During 1991–1997 he held the position of Research Scientist with Schlumberger-Doll Research. From 1997–1999, he was Reservoir Specialist and Technology Champion with YPF (Buenos Aires, Argentina). Since 1999, he has been with the Department of Petroleum and Geosystems Engineering of The University of Texas at Austin, where he currently holds the position of Associate Professor. He conducts research on borehole geophysics, formation evaluation, and integrated reservoir characterization. Torres-Verdín has served as Guest Editor for Radio Science, and is currently a member of the Editorial Board of the Journal of Electromagnetic Waves and Applications, and an associate editor for Petrophysics (SPWLA) and the SPE Journal. Faruk O. Alpak is a Research Assistant and a PhD candidate in the Department of Petroleum Engineering at The University of Texas at Austin. His research interests include inverse problems, computational methods, reservoir simulation, numerical optimization, and electromagnetic wave propagation. He holds a MSc degree in Petroleum Engineering from The University of Texas at Austin.

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