Mathematical Model to Quantify the Contribution of Thermal Stresses in Pore Pressure, Additional to the Compaction Effect

Transcription

1 Rock Mechanics for Natural Resources and Infrastructure ISRM Specialized Conference 9-13 September, Goiania, Brazil CBMR/ABMS and ISRM, 214 Mathematical Model to Quantify the Contribution of Thermal Stresses in Pore Pressure, Additional to the Compaction Effect Diego A. Vargas Corp. NATFRAC-Bucaramanga-Colombia- Zuly H. Calderón Universidad Industrial de Santander, Escuela de Ingenieria de Petróleos- Bucaramanga-Colombia- Darwin C. Mateus ECOPETROL- Piedecuesta Colombia- Reinel Corzo ECOPETROL- Piedecuesta Colombia- Oscar J Acevedo UT-PEXLAB- Piedecuesta Colombia - osjavi1789@gmail.com SUMMARY: Pore pressure is one of the most critical variables on the geomechanical model design, and upon this variable depends largely the successful drilling of oil wells. This pressure is calculated conventionally considering the mechanical stresses, essentially the disequilibrium for compaction, using empirical correlations developed from information taken mainly from the Gulf of Mexico. The use of these equations, does not reflect real situations most of the time, giving pore pressure values inferior to the formation pressures, which may complicate the drilling operations, especially on exploratory wells, increasing the nonproductive times (NPT). The main objective of this investigation is to implement a mathematical model which includes the most common overpressure causes documented in literature, and which allow to quantify the effects of: the under compaction and the thermal stresses due to the water expansion, the kerogen cracking and the oil in shale formations. In order to include the effect of the water expansion, the geothermal gradient and a sedimentation history of a Colombian basin were taken into account. For the hydrocarbons generation, an organic material maturation model was applied, to determine the oil and gas fraction generated. This model was applied to a Colombian basin and providing as a result, a pressure profile quantifying the effect of each mechanism mentioned above.the results obtained with the model shows coherence with the events reported on the study area wells. Similarly, it could be evidenced that, despite the compaction is the main cause of overpressure in depths no deeper than 3 meters, at greater depths, the thermal stresses contribution may be up to 14% of the total overpressure. For this reason, the proposed model allows to decrease the uncertainty on the pore pressure model. Additionally, the pressure model was simulated with the software PetroMod with the objective of including the boundary conditions, along with the horizontal and vertical flow conditions across the permeable layer, increasing the representativeness of the pore pressure model. KEYWORDS: Pore Pressure, Thermal Stresses, Finite Differences.

2 1 INTRODUCTION Pore pressure studies on sedimentary basins turned out to be the last decades one of the most critical items on the planning of drilling projects in the oil and gas industry. The conventional methodologies used in the pore pressure estimation are based on the disequilibrium for compaction as the main mechanism of overpressure generation, such mentioned by the correlations proposed by Hottmann and Johnson (1965) and Eaton (1975). In order to consider fluids expansion, one of the most popular methodologies was proposed by Bowers (1995). Since the correlations stated above may give values lower than the real ones, the estimation of the pore pressure by the mathematical model implementations which structure depend upon the analyzed variables, merge as an alternative. On this investigation the thermal stresses will be taken into account (fluids expansion and hydrocarbon generation Grauls, (1999)). The aquathermal effect is represented by the term proposed by Lou and Vasseur (1992). For the hydrocarbon generation terms, the maturation model proposed by Tissot, B. and D. H. Welte, (1984), will be considered. This model allows estimating the kerogen fraction which will become oil and then the gas kerogen fraction. With this fraction and the proposed terms for Hantschel and Kauerauf (29), an estimation of the hydrocarbon generation influence may be done. The implementation of these terms, by the construction of a differential model used in onedimension basins modeling will be discussed further in this article For the estimation of the pore pressure from this model, the more representative variables were analyzed, such as the compressibility, porosity, permeability and viscosity on the under compaction term, the temperature on the aquatermal effect term and the organic matter content with their respective mature grading, for the term which represents the hydrocarbon generation effect. The model was solved and it obtained estimating the overpressure corresponding to each one of the studied terms. 2 CAUSES OF OVERPRESSURE The causes of overpressure has been studied and classified according to some authors (Osborne and Swarbrick, (1997) and Grauls, (1999)). On this investigation, the under compaction, water expansion and hydrocarbon generation effects were taken into account. 2.1 Mechanical Stresses The vertical stress is the main cause of overpressure generation Grauls, (1999), although this may be dissipated, if great volumes are conducted along the faulting planes Oscorne and Swarbrick, (1997). The under compaction occurs when the deposition rate of the sediments is highly superior to the fluids expulsion rate, which may be improved for permeability reductions, especially on shales. 2.2 Thermal Stresses According to Barker, (1972), the water expansion consists on the increase on the fluids volume in the pore due to temperature changes. This author shows the importance ofthe hydrothermal effect by making a graphic analysis of water behavior in a closed system. On the other hand, Luo and Vasseur (1992) shows through a mathematical model that the contribution of this term is minimum, even under favorable geological conditions. The hydrocarbon generation effect appears with the oil generation window at 2 F (93 C) and the vitrinite reflectance (Ro) higher than.7% Spcencer, (1987). The conditions for gas generation are a Ro higher than 2% and temperatures above 34 F (175 C) Hedberg, (1974). The contribution of this mechanism, as well the oil mechanism, depends upon the TOC (Total Organic Carbon) and the kerogen type present. 3. PORE PRESSURE ESTIMATION BY A MATHEMATICAL MODEL The Terzaghi s (1923) theory of effective stress,

3 can be used for the developing of an overpressure model in one-dimension.these variables are calculated as a function of the depth and the temperature. Applying the Terzaghi s law (Equation 1) and Darcy s law (Equation 2), this can derive an equation used to model the basin (Equation 3). For the viscosity, Mercer s model (1975) was used,a correlation as a function of temperature for ranges between -3 C, as shown below, was used. (7) (8) The compressibility of the rock was determined by Athy s law (193). Luo and Vasseur, 1992, based on Terzaghi s previous work, performed a mass balance for the fluid and for the rock material, obtaining a mathematical model which allows calculating the pore pressure by the basins modeling 1D (Equation 4). ( ) ( ) ( ) (9) This one depends on the compaction coefficient (α) and for its calculation, a porosity profile must be determined from sonic logs and afterwards the Athy s law must be applied (Figure 1). With this law (Equation 5), an exponential tendency is generated and this parameter is calculated. Based on this model, other terms were introduced, to take into account the causes undar analysis in this study The previous model depends upon variables such as: porosity ( ), permeability ( ), viscosity ( ) and compressibility ( ), which can be calculated as a function both of depth and temperature. Besides, the compressibility depends on the compaction coefficient (α) POROSITY ( ) The porosity was determined by Athy s law (193) as a function of depth. The permeability is a function of the porosity, as proposed by Terzaghi (1925). When the λ parameter varies between The equation representing this formulation is detailed below. Porosity Athy 193 Figure 1. Calculation of the compaction coefficient. The equation 4 was solved using finite differences and the models were implemented for each one of the variables mentioned above. Finally, a pore pressure profile for compaction effect is obtained, as shown in figure 2. In this figure, by comparing the results obtained with the compaction method with the mud weight used during drilling, a significantly low value is observed. For that reason, the other overpressure causes must be added y the model

4 TEMPERATURE DEP DEP 1 2 PRESSURE (MPa) After that, the equation 11 was solved and the pore pressure profile including water expansion was obtained, as shown on figure 4. After quantifying the water expansion effect, a very irrelevant contribution can be observed (approximately 3%), and therefore, the pore pressure profile is still highly below to the mud weight required to prevent influx 3 4 PRESSURE (MPa) Lithostatic Hidrostatic 1 Compaction Figure 2. Pore Pressure profile for Compaction The next step was to add the thermal expansion effect term, studied by Luo and Vasseur (1992), who add a term ( ) to the equation 4, as seen in equation 11. This additional term stands for the temperature variation as a function of time and a constant (water expansion coefficient). ( ) ( ) ( ) Mud Weight In order to quantify this contribution, a variation model of depth as a function of time (sedimentation history) and a local geothermal gradient of 3 C/Km were used. Having the behaviors previously stated, the variation of temperature as a function of time could be shown (Figure 3) TIME (Ma) Figure 3. Variation of Temperature in function of time Lithostatic Compaction Figure 4. Pore Pressure Profile for Compaction and Water Expansion (blue color). The next term to be evaluatedwas the hydrocarbon generation effect. For this term, an organic matter maturation model proposed by Tissot, B. and D. H. Welte, (1984), was used, which determines the fraction of kerogen becoming oil and subsequently gas (figure 5) Water Expansión HYDROCARBONS Figure 5. Fraction of hydrocarbons generated Hidrostatic Mud Weight Oil Fraction Gas Fraction

5 DEP As seen in the previous figure, the generation of oil starts at shallow depths (1 m) because there is no need of high temperatures for primary cracking to occur (93 C) Spencer (1987). The gas generation coming from secondary cracking needs high temperatures, for that reason, their generation start at deeper depths. Hantschel and Kauerauf, (29) in order to quantify the effect of the oil and gas generation, proposed the terms shown in equations 12 and 13, respectively. Analyzing the previous profiles for each one of the mechanisms, it is observed that at shallow depths (3 m), the thermal stresses represents only the 8% of the total pore pressure (Figure 7A), but below that, the contribution for these stresses rises significantly, reaching values such as 14% for higher depths (45 m). (figure 7B). A 3% 5% B 4% 1% ( ) (12) ( ) (13) 92% 86% Adding the previous terms into the equation 11, the equation 14 is obtained. Water Expansion Compaction Effect hydrocarbon ( ) ( ) ( ) ( ) ( ) The previous model was solved, and a pore pressure profile was obtained, which includes the compaction effect and the thermal effects, as shown in figure PRESSURE (MPa) Lithostatic Compaction Water Expansión Hidrostatic Mud Weight Effect hydrocarbon Figure 6. Pore Pressure Profile for compaction and thermal stresses (orange color). A B Figure 7. Contribution of each mechanism A) 2 m y B) 45 m The mathematical model used in this work was implemented by Vargas (213) where Vargas got pore pressure values for each mechanism. 4. MODELING OF PORE PRESSURE BY PETROMOD SOFTWARE The pore pressure calculation was performed using PetroMod software, used in basins modeling, and pressure profiles including the same overpressure mechanisms studied were obtained. Furthermore, the software takes into account the pressure contribution, generated for the lateral transferences. The obtained results were calibrated with well data. Figure 8 shows the calibration of the model with geochemical properties data, such as vitrinite reflectance, which responds the contour conditions of the model (heat flow, sedimentwater interface temperature SWIT). The models could be calibrated with petrophysical data, temperature or pressure data, the same way with the vitrinite reflectance. An example of porosity calibration

6 DEPT using the Athy s law (193) is shown in the figure 9. %Ro Software %Ro Laboratory Figure 8. Calibration of the vitrinite reflectance Figure 1. Pore Pressure obtained by the software Comparing both software and mathematical model profiles of pore pressure (figure 11), it is shown that the result obtained by PetroMod is higher than the obtained by mathematical model, approaching more to the drilling events. This could be explained by the lateral transferences between layer. PRESSURE (MPa) Figure 9. Porosity calibration for a formation. The pressure distribution obtained numericallyof the two-dimensional model, using the same mechanisms implemented on the mathematical model is shown on the figure 1, which shows at shallow depths (less than 2 meters) the increases of pressure are completely normal, while at higher depths, where the effect of thermal stresses is important, significant increases of pressure are observed, as well as their distribution along the layer Presure PetroMod Hidrostatic Effect hydrocarbon Lithostatic Mud Weight Figure 11. Pressure Profile by mathematical model and software.

7 The comparison of the numerical results with the drilling events (influx) is observed on figure PRESSURE (ppg) INFLUX PRESSURE MUD OF DRILLING PRESSURE MUD PETROMOD Figure 12. Comparison between the software results and the drilling events. 7) It was corroborate that aquathermal effect is rather irrelevant, because it wasshown that the excess of pressure is compensated with the viscosity reduction, as stated by Luo and Vasseur (1992) (Figure 4). It was shown in this application, that at depths greater than 45 m the effect of hydrocarbons generation, is important because, the contribution reached a value of 14% further to the pressure generated by compaction (Figure 7B). It was shown that the results obtained with basin modeling are more reliable than those of the mathematical model, because the 2D model can include lateral transferences between the layers. Analyzing results, it can be shown that at depths inferior to 17m, the mud weight is enough to control the pore pressure. Between 17 and 27m, influxes were observed, which indicates that the pore pressure is higher than the mud weight. This pressure excess could be demonstrated by the 2D basins modeling. Besides the overpressure mechanisms studied, this prediction includes lateral transferences between layers. Finally, at depths greater than 27 m it was observed that the mud weight is enough to control the pore pressure. If only undercompaction is taken into account to get the pore pressure profile (figure 2) it does not fit with the events, particularly influxes that occurred during the drilling phase, this is due to thermal stresses generate a pore pressure increasing (Figure 6) reaching an additional 14% (Fig. 7B) 5. CONCLUSIONS It was confirmed that if geological conditions are favorable (TOC higher than 1%, temperatures higher than 93 C), other mechanisms of overpressure may occur (thermal stresses), but still yet, the compaction is the main cause of overpressure (Figure NOMENCLATURE T = Temperature t = Time Effective stress, [M/Lt 2 ], [psi] = Vertical stress, [M/Lt 2 ], [psi] P = Pore pressure, [M/Lt 2 ], [psi] Depth, [L], [ft] Cr= Compressibility of the rock [1/(M/Lt 2 )], [1/psi] = Density [ML -3 ], [lb/ft 3 ] = Kerogen density [ML -3 ], [lb/ft 3 ] = Gas density [ML -3 ], [lb/ft 3 ] µ = Viscosity [M/Lt 1 ] Porosity k =Permeability [L 2 ] = Variation of gfas density [ML -3 ], [lb/ft 3 ] = Variation of oil density [ML -3 ], [lb/ft 3 ] = Coefficient of thermal expansion [T -1 ], = Relationship between porosity and permeability [L 2 ] α = Compaction coefficient [L -1 ] [ft -1 ] b = Compaction coefficient [1/(M/Lt 2 )], [1/psi] g = Gravity[Lt -2 ], [ft.s -2 ] V=Velocity [L.s -1 ] Variation ACKNOWLEDGMENT I acknowledge mainly to GOD for everything, to the workers of Colombian Institute of Oil (ICP), to the Universidad Industrial de Santander (UIS) and to the Wellbore Stability research Group (GIEP) for the oportunity of acquire new kwnoledges.

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