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DE LA FACULTAD DE INGENIERÍA
REVISTA TÉCNICAREVISTA TÉCNICA
“Post nubila phoebus”
“After the clouds, the sun”
“Post nubila phoebus”
“After the clouds, the sun”
LUZ in its 130th
anniversary
Established since
1891
LUZ in its 130th
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Established since
1891
VOLUME 44
SEPTEMBER - DECEMBER 2021
NUMBER 3
Rev. Téc. Ing. Univ. Zulia. Vol. 44, Nº 3, September-December, 2021, 141-153
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Determination of the Initial Water Saturation Model based
on Capillary Pressure Curves by Rock Type
Eddymar Márquez1 , César Aguilar1 , Américo Perozo2
1Estudios Integrados de Yacimientos Occidente. Petróleos de Venezuela (PDVSA). Maracaibo,
Venezuela.
2Facultad de Ingeniería, División de Estudios para Graduados, CP. 4001. Universidad del Zulia.
Maracaibo, Venezuela.
*Corresponding author:marquezeddymar@gmail.com; aguilarcp9@gmail.com
https://doi.org/10.22209/rt.v44n3a01
Received: November 4, 2020 | Accepted: June 4, 2021 | Available: August 1, 2021
Abstract
The log-derived initial water saturation (Swi) is influenced by fluids drainage from the producing wells,
generating underestimation of the Stock-Tank Original Oil in Place (STOOIP). To restore the initial conditions of the
reservoir, it is necessary to use drainage Capillary Pressure (Pc) tests, which determine the distribution of Swi, prior to
any hydrocarbon production. This research aimed to determine the Swi model, based on Pc curves by rock type, for a
better estimation of the STOOIP of LUZ reservoir in the Maracaibo Basin. The methodological procedure included:
data gathering (logs and cores, with 15 plug samples for Pc analysis), description of rock types, determination of the
Swi model and estimation of the STOOIP. Among the results, the following stand out: the J-Leverett model fit best to
the Pc curves of the reservoir for all rock types; the estimated STOOIP using the water saturation (Sw) of the
proposed capillary pressure based model and the one estimated using logs, showed a discrepancy of 19.8 %,
evidencing the importance of a robust model to increase certainty in the estimation of reserves.
Keywords: capillary pressure; initial water saturation; model; rock type; stock-tank original oil in place.
Determinación del Modelo de Saturación de Agua Inicial
basado en Curvas de Presión Capilar por Tipo de Roca
Resumen
La saturación de agua inicial (Swi) a partir de registros está influenciada por el drenaje de fluidos de los
pozos productores, generando subestimación del petróleo original en sitio (POES). Para restaurar las condiciones
iniciales del yacimiento, es necesario utilizar pruebas de presión capilar (Pc) de drenaje, que determinan la
distribución de Swi previa a cualquier producción de hidrocarburos. Esta investigación tuvo como objetivo determinar
el modelo de Swi, basado en curvas de Pc por tipo de roca, para una mejor estimación del POES del yacimiento LUZ
de la cuenca de Maracaibo. El procedimiento metodológico incluyó: recopilación de datos (registros y núcleos, con
15 muestras de Pc), descripción de tipos de roca, determinación del modelo de Swi, y estimación del POES. Entre los
resultados, destacan: el modelo J-Leverett se ajustó mejor a las curvas de Pc del yacimiento para todos los tipos de
roca; el POES estimado utilizando la saturación de agua (Sw) del modelo propuesto basado en presión capilar y la
calculada usando registros, mostró un 19,8 % de discrepancia, evidenciando la importancia de un modelo robusto
para incrementar la certidumbre en el cálculo de reservas.
Palabras clave: modelo; petróleo original en sitio; presión capilar; saturación de agua inicial; tipo de roca.
Márquez-Codina et al . 142
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Introduction
To estimate the STOOIP, it is required to know the Sw at the initial reservoir conditions. Well logs
(resistivity) are often affected by fluids drainage of the reservoir; additionally, old resistivity curves had problems of
not being focused and having a poor vertical resolution (Rider and Kennedy, 2011), for which laboratory
experiments are convenient to represent the reservoir saturation history or the hysteresis phenomenon, being the
special core analysis, such as Pc drainage tests, capable of simulating the initial reservoir conditions.
According to Valenti et al. (2002), when the Pc curves are observed together, different shapes of these are
appreciated, as well as dispersion of data, representing the heterogeneity of the reservoir. This behavior suggests that
the data should be classified according to the sample rock quality (Obeida et al., 2005; Xu y Torres, 2012).
The purpose of this research was to determine the Swi model, based on Pc by rock type, of a siliciclastic
reservoir in the Maracaibo basin, to improve the estimation of the STOOIP. Results are based on core and log data
processing and analysis; these consisted on the description of the rock types present in the reservoir, classification of
Pc curves by rock type, selection of the model that best fit and represented the reservoir data, generation of water
saturation equations, comparison of the Sw curves of the proposed model with the log-derived in the first drilled
wells, as well as the contrast of the STOOIP in an area of the reservoir, obtained from the Sw model, with the log-
derived Sw (Obeida et al., 2005; Paradigm and Epos, 2011; Xu and Torres, 2012).
Materials and Methods
Phase I: information gathering and validation
Data were collected and validated from the reservoir (due to confidentiality rules of the PDVSA company, the
original names of the reservoir, study area and wells have been changed), cored wells, among which stand out:
routine or conventional core analysis (RCA) to determine rock types and special core analysis (SCAL) such as Pc
drainage tests to determine the Swi model, as well as conventional logs. A robust database was generated using a
petrophysical software.
Phase II: description of rock types based on statistical parameters
It was used the Flow Zone Indicator (FZI) methodology of Amaefule et al. (1993), based on porosity () and
permeability (k) data, corrected by overburden pressure, in accordance with Jones (1988). The FZI was calculated for
all the samples using Equations 1, 2 and 3, and results were analyzed using statistical tools, which allowed
identifying the rock types present in the reservoir.
Reservoir Quality Index:
(1)
Where, : effective porosity (fraction); k: permeability (md)
Normalized Porosity Index:
- (2)
Flow Zone Indicator:
(3)
Phase III: preparation of Pc data and their relationship with the core-derived petrophysical properties
In this phase, the data obtained from the drainage Pc tests were classified by rock type; previously, corrections were
made to the data obtained from the laboratory Pc tests and converted to reservoir conditions.
The equations to correct data by overburden pressure indicated by Paradigm and Epos (2011) are detailed below:
Pc corrected by overburden pressure:
(4)
Where, : capillary pressure at laboratory conditions (psi); : porosity at initial reservoir conditions (fraction);
: porosity at laboratory conditions (fraction).
143
Determination of the Initial Water Saturation Model based on Capillary Pressure Curves by Rock Type
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Sw corrected by overburden pressure: --
(5)
Where, : water saturation at laboratory conditions (fraction).
Equations for the conversion of data from the system used in the laboratory to the reservoir system (Paradigm and
Epos, 2011):
Capillary pressure converted to reservoir system:
(6)
Where, = interfacial tension * cosine of contact angle at initial reservoir conditions, equal to 26
dyn/cm for the present system (oil/brine), according to Adams and Van den Oord, (1993); = interfacial
tension * cosine of contact angle at laboratory conditions.
Phase IV: determination of Swi model of LUZ reservoir from the Pc tests by rock type
The steps followed are detailed below:
a) Calculate the Pc versus Swi curve, by rock type, for each of the most used models in the literature
(Adams and Van den Oord, 1993; Paradigm and Epos, 2011) in cored wells.
b) Select the model that best fit to the core Pc curves for each rock type, adjusting the coefficients
proposed by the original authors (Paradigm and Epos, 2011).
c) Predict the Swi curve above the Free Water Level (FWL). To do this, the height above the FWL (H)
was calculated for each point. Once the height was obtained, the Pc is calculated at each depth, according
to Obeida et al. (2005):
- (7)
Where, FWL: free water level (feet); : true vertical depth sub sea (feet).
- (8)
Where, : density of water (g/cm3); density of oil (g/cm3).
d) Compare the Swi curve obtained from Pc tests and the one calculated with the information from logs
of the first drilled wells in the study area (PDVSA, 2019).
e) Propagate the model to all the wells of the study area.
Phase V: estimation of STOOIP in the basal sand of LUZ reservoir, P-1 area
The STOOIP was calculated by the volumetric method (PDVSA, 2005), using both the Sw based on the
proposed Pc model, and the log-derived Sw, establishing their level of discrepancy.
Results and Discussion
Phase I: information gathering and validation
The data obtained from conventional and special core analysis of three wells is displayed in Table 1, in
which it is showed the total number of conventional analysis samples used to determine rock types, as well as the
SCAL Pc tests used to build the saturation height model, specifying the test method and the fluid systems handled in
the laboratory, is described.
Márquez-Codina et al . 144
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Table 1. Inventory of Pc tests for the studied reservoir.
Well
Conventional core
analysis (ɸ y k)
Special core analysis
Capillary pressure (drainage)
Number of samples
Number of samples
Method
Fluid system used in
the laboratory
LUZ1246
111
41
Porous plate cell
Air/brine
LUZ1348
152
63
Centrifuge
Oil/brine
LUZ1542
154
55
Centrifuge
Oil/brine
Total samples
41
15
1Omni Laboratories de Venezuela (1997); 2Core Laboratories Venezuela (2000); 3 PDVSA (2019); 4Omni
Laboratories de Venezuela (2007); 5Core Laboratories Venezuela (2008).
Phase II: description of rock types based on statistical parameters
To show the rock types existing in the reservoir, a log-log crossplot RQI vs z (Figure 1) was performed,
where 6 lines of unit slope are shown, corresponding to the 6 rock types in the reservoir; the intercept of these lines
with z = 1 provides an approximate value of the FZI of each rock type, ordered from higher (higher FZI) to lower
quality (lower FZI).
Figure 1. Visualization of the rock types of LUZ reservoir, through the Reservoir Quality Index versus Normalized
Porosity Index.
Some statistical indicators of the FZI for each rock type are presented in Table 2. It is observed that the
standard deviation for each rock type varies between "moderately low" and "low", thus concluding that the identified
classes are consistent from a statistical point of view. For the propagation of rock types, the FZI was calculated using
the permeability generated by the Timur model (Uguru, 2004), with modifications in its coefficients.
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Determination of the Initial Water Saturation Model based on Capillary Pressure Curves by Rock Type
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Table 2. Statistical parameters of the Flow Zone Indicator used to classify the rock types of LUZ reservoir.
Rock Types
Avg FZI
FZI-Min
FZI-Max
Standard Deviation
1
3.593
3.553
3.633
0.056
2
2.347
2.101
2.844
0.217
3
1.460
1.241
1.745
0.180
4
0.960
0.808
1.108
0.102
5
0.630
0.447
0.781
0.141
6
0.237
0.078
0.409
0.166
Avg. FZI: mean value of the Flow Zone Indicator; FZI-Min: minimum value of the Flow Zone
Indicator; FZI-Max: maximum value of the Flow Zone Indicator.
Phase III: preparation of Pc data and their relationship with the core-derived petrophysical properties
Once the Pc data had been corrected and converted to reservoir conditions, the irreducible water saturation (Swirr)
versus RQI was plotted (Figure 2), where it can be seen that rocks with low RQI show high values of Swirr.
According to this, the variables introduced by Amaefule et al. (1993) are related to the physical properties of the
reservoir, which confirms how physically they control the flow and storage capacity of the rock.
On the other hand, the Pc curves were classified by rock type, using the FZI parameter (Amaefule et al., 1993). Rock
types 4, 5 and 6 were classified altogether as rock type 4, since only a sample of types 5 and 6 was available, thus
making it impossible to model them.
Figure 2. Irreducible water saturation of each drainage capillary pressure sample versus the Reservoir Quality Index
calculated for each sample.
Márquez-Codina et al . 146
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Phase IV: determination of Swi model of LUZ reservoir from the Pc tests by rock type
As a reference, Figure 3 shows the selection of the model in rock type 1. To the left of the graph are listed the
defined equations and the error found between the water saturation of each point and the one modeled by the fitted
function. In general, the evaluated models generated very low errors; however, the Leverett model was chosen
because it fits the shape of the curves and better reproduces the value of Swirr.
Figure 3. Pc curves corresponding to rock type 1 from the LUZ reservoir. J Leverett correlation.
The Pc curves modeled using the J-Leverett function with constant coefficients for the different rock types, are
shown in Figure 4. The fit parameters of the Sw equation by rock type were obtained with the RQI of each Pc sample,
using the module for coefficients´ fitting of the used software. The proposed equations are shown in table 3. In
Figure 5, a one to one plot between the Sw obtained by Leverett model versus the Sw of the Pc curve measured in
laboratory for each rock type is showed, where each graph shows a unit slope line that passes through the origin; as
the points get closer to that trend, the model has a better fit.
147
Determination of the Initial Water Saturation Model based on Capillary Pressure Curves by Rock Type
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Figure 4. Pc Curves of LUZ reservoir by J-Leverett model and constant coefficients.
Table 3. Proposed equations to determine the water saturation by rock type in LUZ reservoir, using the J Leverett
model.
The models by rock type are represented in 3D (Figure 6), so that each model predicts the Sw as a function
of Pc and Z values of RQI. The model has a good fit to the data points, since the Pc curves are located on or near the
surface. Figure 6 shows the integration of all the parameters involved in Leverett's Sw equation, where it is worth
mentioning that as the RQI is higher, the water saturation decreases, but this in turn is smaller as the Pc increases. So,
Sw at a specific point in the reservoir will depend on the height from such point to the FWL; this will be noticed
when the transformation from Pc to height is made. On the other hand, each rock type has a transition zone; this will
depend on its quality, that is, as the RQI is higher (larger pores), the water-oil zone is narrower.
0.246833+(1-0.246833)*0.931334*
Rock type 1
Rock type 2
Rock type 3
Rock type 4
0.170311+(1-0.170311)*1.165030*
0.398200+(1-0.398200)*0.813689*
0.6+(1-0.6)*0.832188*
Márquez-Codina et al . 148
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Figure 5. Modeled Sw from the J Leverett function versus laboratory - measured Sw, corresponding to LUZ
reservoir
Figure 6. 3D Sw model for all rock types in LUZ reservoir.
149
Determination of the Initial Water Saturation Model based on Capillary Pressure Curves by Rock Type
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
The log information from the first drilled wells in the study area (Figure 7) was obtained several decades
prior to the beginning of LUZ reservoir´s production (1992), therefore this information had not been affected by the
drainage of the reservoir. When predicting the Sw above the FWL in these wells and contrasting it with the log
information, the following can be mentioned: in LUZ0512 and LUZ0584 wells there is a good match between the Pc-
derived curve (dark blue) and the log (light blue), present in track 10 of the well´s petrophysical evaluation; however,
small differences are present in LUZ0512 well, since it involves Long Normal and Short Normal resistivity logs,
which, due to non-focused electrodes configuration, they always have a depth shift. On the other hand, in LUZ0267
well there is an important difference between these two curves, due to the low vertical resolution of the resistivity
w model based on Pc
and, consequently, the range of amplitude of the rock types
As is well known and has been referenced by multiple authors (Walsh et al., 1993; Whitman, 1995;
Griffiths et al., 2000), the quality of the well log information will depend on factors such as tool vertical resolution
and bed thickness; for example, when the bed´s thickness is less than the vertical resolution of the tool, neighboring
beds affects the property measured value, not being this value representative. This effect can be seen in old logs
(approximately of 60's decade), especially in the old generation Induction logs and no-focused devices with very
poor vertical resolution, which is around 8 feet. In old wells, the tool type plays an important role, because the
vertical resolution of a Dual Laterolog log is better than that of an Induction log. Additionally, it is necessary to
consider the drilling mud properties; Induction logs work better with fresh water-based muds, while galvanic logs,
such as the Dual Laterolog, work with saline water-based muds. All this indicates that the data obtained from logs
are not always reliable, and the methodology used in this work is a valid option to reduce the uncertainty in the
quantification of the STOOIP.
Phase V: estimation of STOOIP in the basal sand of LUZ reservoir, P-1 area
Table 4 shows the comparison of the STOOIP obtained from the Sw, based on Pc with that calculated in a
conventional manner (Sw derived from logs), in which a difference of 5.21 MMBN (19.8 %) is observed. This is due
to the fact that the STOOIP obtained from log-derived Sw is affected by the drainage of the reservoir (this is observed
in new wells), not being the most representative. To better illustrate this, in Figure 8 both STOOIP are represented
and it can be observed that the STOOIP calculated with log-derived Sw, is diminished to the East of the area, while
the value of the STOOIP obtained with the proposed Sw model remain high in that same area. By using the log-
derived Sw of all associated wells, the STOOIP would be underestimated, and oil recoverable reserves could be even
less than cumulative oil production. To minimize these problems, a better quantification is obtained through Pc
models by rock type, as developed by Obeida et al. (2005), as well as Gonzalez et al. (2016). Therefore, a better
estimation of the STOOIP for area P-1, in the basal sand of the reservoir, results in 26.28 MMBN.
Márquez-Codina et al . 150
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Figure 7. Comparison of the Sw curve, obtained from the Pc, and the log-deriverd Sw curve. First drilled wells in the
study area.
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Determination of the Initial Water Saturation Model based on Capillary Pressure Curves by Rock Type
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Figure 8. STOOIP map of the study area with Sw from the proposed model and log-derived Sw.
Table 4. Average values used in the STOOIP calculations of the study area.
Average thickness
(feet)
Average effective porosity
(fraction)
Average water
saturation
(fraction)
STOOIP
(MMBN)
Model
Log
Model
Log
Model
Log
Model
Log
10.09
8.96
0.20
0.16
0.54
0.59
26.28
21.07
Conclusions
Six rock types were identified in LUZ reservoir.
The J Leverett model fits better to the Pc curves for all rock types, so with this model Swi equations were
established for the modeled rock types.
The comparison between the Sw curves based on Pc with the log-derived Sw curves in the first drilled wells,
showed a good fit. The differences observed in some of them were due to problems associated with the logs, such as
the effect of neighboring beds, depth shift, among others.
The STOOIP estimated in the P-1 area, in the basal sand of the reservoir, using the Sw of the proposed
model and the one log-derived, represented a difference of 19.8 %, which highlights the importance of a robust
model, such as the one presented in this work to increase the certainty in the calculation of reserves.
Márquez-Codina et al . 152
Rev. Téc. Ing. Univ. Zulia. Vol. 44, No. 3, September-December, 2021.
Acknowledgements
The authors would like to express our recognition to PDVSA, Western Management of Exploration and Integrated
Reservoir Studies for providing the information and authorizing the publication of this work. We also would like to
extend our gratitude to Prof. Edgar Pereira (Petroleum Engineering School of the University of Zulia) for his
valuable collaboration in the preparation of this article.
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