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Pore pressure prediction and modeling using well-logging data in one of the gas fields in south of Iran
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Pore pressure prediction and modeling using well-logging data in one of gas fields in south of Iran Morteza Azadpour, Navid Shadmanaman, Ali Kadkhodaie-Ilkhchi, Mohammad-Reza Sedghipour
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PII: DOI: Reference:
S0920-4105(15)00074-1 http://dx.doi.org/10.1016/j.petrol.2015.02.022 PETROL2965
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Journal of Petroleum Science and Engineering
Received date: 13 March 2014 Accepted date: 10 February 2015 Cite this article as: Morteza Azadpour, Navid Shadmanaman, Ali KadkhodaieIlkhchi, Mohammad-Reza Sedghipour, Pore pressure prediction and modeling using well-logging data in one of gas fields in south of Iran, Journal of Petroleum Science and Engineering, http://dx.doi.org/10.1016/j.petrol.2015.02.022 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Pore pressure prediction and modeling using well-logging data in one of gas fields in south of Iran Morteza Azadpour11; Navid Shadmanaman1; Ali Kadkhodaie-Ilkhchi2; Mohammad-Reza Sedghipour3 1. Department of Mining and Petroleum Exploration, Sahand University of Technology, Tabriz, Iran. 2. Geology Department, Faculty of Natural Science, University of Tabriz, Tabriz, Iran. 3. Department of Petroleum Engineering, Petrophysic Directorate of P.O.G.C., Tehran, Iran.
Abstract
Knowledge of pore pressure is essential for cost-effective, safe well planning and efficient reservoir modeling. Pore pressure prediction has an important application in proper selection of the casing points and a reliable mud weight. In addition, using cost-effective methods of pore pressure prediction which give extensive and continuous range of data is much affordable than direct measuring of pore pressure. The main objective of this project is to determine the pore pressure using well log data in one of the Iranian gas fields. To obtain this goal, the formation pore pressure is predicted from well logging data by applying three different methods including Eaton, Bowers and the compressibility methods. Our results show that the best correlation with the measured pressure data is achieved by the modified Eaton method with Eaton’s exponent of about 0.5. Finally, in order to generate the 3D pore pressure model, well-log-based estimated pore pressures from Eaton method is upscaled and distributed throughout the 3D structural grid using a geostatistical approach. The 3D pore pressure model shows good 1
Corresponding author: Tel: +98 917 127 2559; Fax: +98 411 344 4311 E-mail addresses: [email protected] (M. Azadpour), [email protected] (N. Shadmanaman), [email protected](A. Kadkhodaie-Ilkhchi), [email protected] (M. R. Sedghipour)
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agreement with the well-log-based estimated pore pressure and also the measured pressure obtained from Modular formation Dynamics Tester.
Keywords: Pore pressure prediction, Abnormal pressure, Well-logging, Eaton method, Pressure modeling, Geostatistic
1 Introduction Formation pore pressure is traditionally estimated based on well log analysis in combination with Terzaghi’s hypothesis which describes the compaction of the soil due to overburden stress. The pore pressure which is the pressure of the fluid inside the pore space of the formation, is defined with several aspects of the pressure terminologies contains: Hydrostatic pressure (weight of a fluid column), Overburden pressure (the combine weight of formation solid and fluid of overlying sediments) and Effective stress (the grain-to-grain contact stress). The overburden load at any depth is supported by the effective stress and the pore pressure. This relationship is expressed as Terzaghi theory.
Pore pressure, based on the magnitude, can be described as being either normal (hydrostatic) or abnormal (overpressure or underpressure). Overpressure can make many problems such as kicks, blowouts, wellbore instability, hole washouts and loss of drilling mud circulation. Therefore, accurate pore pressure prediction is necessary for a safe and economic drilling. Swarbrick & Osborne (1998) classified the generation mechanism of overpressure in three categories:
1- Stress related mechanisms • Disequilibrium compaction PAGE | 2
• Tectonic stress 2- Fluid volume increase mechanisms • Temperature increase • Water release due to mineral transformation • Hydrocarbon generation • Cracking of oil to gas • Gas expansion with uplift 3- Fluid movement and buoyancy mechanisms • Hydraulic head • Osmosis • Buoyancy due to density contrasts • Lateral transfer All of these mechanisms are effective when they occur faster than the formation ability to expel the excess pressure. The compaction disequilibrium is one of the main mechanisms in creating large magnitude overpressure. During the deposition, the overburden pressure makes compaction on underlying sediments and causes fluid to expel. However, if pore fluid is not expelled fast enough to reach hydrostatic pressure, the pore fluid pressure increases. When the rate of sedimentation in a basin is low, the underlying sediments will be able to compact and dewater in normal way and it reaches to hydrostatic pressure equilibrium. However, high sedimentation rates prevent sediments from dewatering, so the compaction rate decreases and pore space preserve with overpressure.
2 Pore pressure prediction methods So far, several works have been done in pore pressure prediction using well logs and seismic data resulting in some empirical formula for estimation of pore pressure. The first study on the pore pressure prediction was made by Hottman and Johnson (1965) using shale properties derived from well log data. This approach was based on any deviation in the measured
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properties from its normal trend line. Afterwards, many researchers have successfully used resistivity, sonic transit time, porosity and other well log data for pore pressure prediction. Most of these studies are based on the assumption that any change in an area with normal pore pressure leads to change in some petrophysical properties such as compaction, porosity and fluid motion. Therefore, any measurable parameter which can somehow show these changes can be used in interpretation and quantitative evaluation of pore pressure. Conventional methods of the pore pressure prediction are introduced in the following subsections.
2.1 Eaton method In 1975, Eaton proposed an empirical equation to quantify the pore pressure using well log data such as sonic transient time, formation resistivity or dc-exponent. He considered the disequilibrium compaction as the main mechanism of overpressure generation. This method was based on the first prediction approach by Hottman and Johnson. Both methods rely on this assumption that overburden pressure is supported by pore pressure and vertical effective stress, as shown in Terzaghi’s equation. Terzaghi and Peck (1948) designed an experiment to describe the compaction due to overburden stress. They simulated the clay compaction using a vessel containing a spring and fluid. In this experiment, the overburden stress is simulated by a piston. Once the fluid is allowed to drain; any increase in overburden stress makes the system to expel some fluid so that the fluid pressure remains in hydrostatic pressure while the effective stress increases anyway. However, if the fluid is in untrained condition, both fluid pressure and effective stress rise with increase in overburden stress. The fundamental theory for pore pressure prediction is proposed based on Terzaghi's and Biot's effective stress law (Biot, 1941; PAGE | 4
Terzaghi et al., 1996). This theory indicates that pore pressure in the formation is a function of overburden stress and effective stress. The overburden stress, vertical effective stress and pore pressure can be expressed in the following form:
=
S − σ
(1)
where Pp is the pore pressure; S is the overburden stress; σeff is the vertical effective stress; and α is the Biot effective stress coefficient. Biot's coefficient is the ratio of the volume change of the fluid filled porosity to the volume change of the rock when the fluid is free to move out of the rock. It is conventionally assumed α=1 in geopressure studies (Zhang, 2011).
According to equation (1), Eaton (1975) presented the following empirical equation for pore pressure prediction from sonic transit time: ∆t P = S − S − P ∆t
(2)
where Ppg is the formation pressure gradient; Sg is the overburden pressure gradient; Png is the hydrostatic pore pressure gradient; ∆t is the measured sonic transit time in shale by well logging; ∆tn is the sonic transit time in shale at the normal pressure condition obtained from normal trend line; and x is the exponent constant which is originally 3 in Eaton’s study and requires modification to be implemented in tight unconventional reservoirs (Contreras et al, 2011).
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2.2 Bowers’ method Like Eaton’s method, Bowers (1995) used Terzaghi’s equation to calculate the effective stresses from measured pore pressure data of the shale and overburden stresses. Bowers method is a method based on the effective stress which considers disequilibrium compaction and unloading as the main mechanisms of overpressure generations. Disequilibrium compaction cannot cause the effective stress to decrease but unloading is defined as the terms of effective stress reduction which is caused by fluid expansion. Unlike disequilibrium compaction, fluid expansion can cause the pore pressure to increase at a faster rate than the overburden stress. It forces the effective stress to decrease as burial continues (Bowers, 1995).
In disequilibrium compaction conditions, Bowers used an empirically determined method to calculate the effective pressure with the following relationship between the effective stress and sonic velocity: V = V + Aσ
(3)
where V is the velocity at a given depth; V0 is the surface velocity (normally 5000 ft/sec); σ is the vertical effective stress; A and B are the parameters obtained from calibrating regional offset velocity versus effective stress data.
In basins with the mechanism of unloading, Bowers (1995) proposed the following empirical relation to account for unloading effect:
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V = V + A σ ( σ = (
!
# & ( ) $ ) %
v − 5000 # )& *
(4)
(5)
where U is the unloading parameter which is a measure of how plastic the sediment is. U = 1 implies no permanent deformation and U = ∞ corresponds to completely irreversible deformation. σmax and Vmax are the values of effective stress and velocity at the onset unloading which is the maximum. (Bowers, 1995).
2.3 Compressibility method This method uses the rock compressibility to calculate the pore pressure. Pore pressure depends on the pore volume changes. Any change in pore space is a function of rock and fluid compressibility. In general, when the formation is under compression, pore space reduces and it causes an overpressure on fluid pressure. Hence, compressibility is used as a parameter to determine the pore pressure.
Atashbari (2012) used Zimmerman (1991) and Vangolf (1982) definitions for compressibility and proposed the following relation to calculate pore pressure in Iran carbonate formations (refer to Appendix A for derivations). (1 − ∅)./ P = + 1 (1 − ∅)./ − ∅ .
γ
(6)
where Pp is the pore pressure; fractional ø is the porosity; Cb is bulk compressibility in psi-1; Cp is pore compressibility in psi-1; σeff is the vertical effective pressure (overburden pressure hydrostatic pressure) in psi; and ɣ is empirical constant ranging from 0.9 to 1.0.
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3 Case study The study gas field is located in Persian Gulf basin, South Iran. The first exploration well was drilled in 1990, encountered gas reservoir in the Kangan-Dalan formations. The Kangan Formation and the Upper Dalan member collectively host the gas reservoir in this field. These formations are composed of a sequence including shale, anhydrite, dolomite, and limestone. In Arabian nomenclature, the Kangan and Dalan formations together are known as the Khuff Formation. Khuff Formation is divided into five layers, K1 to K5. K1 plus K2 is equivalent to the Kangan and K3 plus K4 is equivalent to the Upper Dalan formation. In the studied Field, K5 is assumed as non-reservoir and put out of the field. The data from 10 wells (Figure 1), including different types of petrophysical logs such as, sonic transient time, porosity; gamma-ray and density logs are used in this study to predict the pore pressure. Furthermore, the underground contour (UGC) maps in three formations top are available. The UGC maps are used for 3D modeling of pore pressure. Also, the measured pore pressure from Modular formation Dynamics Tester (MDT) is available at 5 wells.
The aim of this study is to evaluate and model pore pressure within the productive reservoir. Here, Eaton, Bower and compressibility methods, with modifications as in an unconventional field with complex geology are applied to predict pore pressure. Finally, the best obtained result of these methods is used to build the 3D pore pressure model in the field.
3.1 Pore pressure from Eaton method In pore pressure prediction, Eaton method is the most common one. Eaton (1975) considered disequilibrium compaction of shale layer as the main factor in abnormal pressure generation. In
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this method, the first step is to analyze the gamma ray in the carbonate formations. We will consider the peak response to the right in gamma-ray log as the result of some shaliness within the rock matrix. With respect to these selected gamma ray peaks, the corresponding velocity points are detected and sonic log velocity trend line is drawn through these points as is shown in Figure 2. Note that the normal trend line is drawn through the normally pressured and normally compacted section of the well log data. Any deviation from the normal trend line indicates as the abnormal pressure. In order to determine the best normal velocity trend line, well A-6 which includes a continuous long set of well log data is selected. Drilling mud weight pressure represents the normally pressured section of this well from 1100 to 2500 m. Therefore, based on the selected points of the measured sonic transient time in this interval, the modified normal compaction trend relation by Zhang (2011) is used: ∆2 = ∆2 + (∆23 − ∆2 )4 567
(7)
where Δtm is the compressional transit time in the shale matrix (with zero porosity); Δtml is the transit time at surface; z is the depth; and c is the constant.
As the velocity at the surface is about 1500-1800 m/sec, the surface transit time, Δtml is considered 185 µs/ft in average. Δtm is determined as 50 µs/ft. Based on the sonic transit time with normal pore pressures (Figure 2), the normal compaction trend of the transit time is proposed as follow:
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∆2 = 50 + (185 − 50)4 5.#:;7
(8)
Substituting Equation (8) into (2), the modified Eaton's sonic equation can be expressed in the following form.
P
50 + (185 − 50)4 5.#:;7 = S − S − P + 1 ∆t
(9)
According to the overall studies in Middle East, especially in Iran, the gradient of normal hydrostatic pressure gradient (P ) is 0.464 psi/ft. Overburden pressure gradient (Sg) is given by: < = 0.433 × @/
(10)
Here ρb is the bulk density. To determine the exponent constant, x, Eaton equation is written in terms of x as in follows: < − BCD < − E A= ∆2 BCD F∆2E H G
(11)
Using a number of points with measured pressure and well-log data, the mean exponent constant, x, is determined as 0.5. Using Equation (9), pore pressure is calculated as shown in Figure 3-a. As stated before, many factors can affect the abnormal pressure. Eaton method considers disequilibrium compaction of shale layer as the main factor in abnormal pressure generation. There is also an amount of overpressure due to buoyancy force within the gas accumulation and some exceed pressure by lateral transfer due to extension of inclined aquifer in the studied area. PAGE | 10
Hydrocarbon buoyancy may cause to increase pressure due to the difference in pressure gradient between gas, oil and formation water. As shown in Figure 4, calculation of the pore pressure gradient in gas and water zone shows that the difference in pressure gradient between the overlying hydrocarbon and underlying water is 0.378 psi/ft for the gas column upward the water contact surface. So, with calculation of water gas contact surface in all wells, this correction is applied to estimate pore pressure. The result of buoyancy effect is demonstrated in Figure 3-a.
An inclined aquifer with enough permeability can redistribute the excess pore pressure laterally in the subsurface. Transference along such inclined aquifers can make an increase in pore pressure at the crest of structure (Mann & Mackenzie, 1990).The Centroid Concept is an empirical method to quantify the pressure contribution from lateral transfer at the crest of inclined aquifers (Traugott, 1996, 1997). According to this concept, pore pressure at the mid height or centre of the aquifer is equal to the adjacent formation. Thus, as in the calculation of the modified lateral transfer effectiveness proposed by Yardley and Swarbrick (1998), by calculation of overpressure at a crestal well, the exceed pressure distribution along the aquifer is calculable at all wells. Yardley and Swarbrick (1998) proposed the following relation to quantify the pressure contribution from lateral transfer as lateral transfer effectiveness: 2D model aquifer XSP − 1D model crestal XSP × 100 1D model crestal XSP
(12)
where XSP is the excess pressure which is the difference between the actual pore pressure and the hydrostatic pressure. 1D and 2D models represent an indication of isolated and connected
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aquifers respectively. It is assumed that the calculated exceed pressure by the pervious mechanisms (disequilibrium compaction and buoyancy effect) indicates isolated aquifers and the measured formation pressure test (MDT pressure test) contains the exceed pressure due to lateral transfer of extensive aquifer in addition. Calculation of lateral transfer effectiveness in well A-8, as a crestal well, gives a lateral transfer effectiveness of 89 %.This value shows the addition contribution to crestal exceed pressure from the lateral transfer compared to the contribution from pervious overpressure mechanism. Based on the Centroid Concept, the lateral transfer effectiveness at the center of the aquifer is zero. Therefore, the exceed pressure along the aquifer decrease at the down dip and increase at the crest of the model. Using the Centroid Concept, the aquifer dip and the lateral transfer effectiveness of well A-8, distribution of the exceed pressure is calculated for all wells. The lateral transfer effect is corrected as shown in Figure 3-a. Lateral transfer makes the maximum increase at the crestal wells and a little effect on the other wells near to the centre of the aquifer.
3.2 Pore pressure from Bowers method Bowers proposed an idea in obtaining effective vertical stress to calculate the pore pressure which is the difference between overburden pressure and effective stress. By calculating the parameters of Bowers’ equation (A and B) and knowledge of rock velocity, the effective pressure can be determined as:
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#
Y − 5000 & σ= *
(13)
Bowers’ equation can be calibrated at well points with measured pressure, density and velocity values. The overburden pressure is calculated from Equation (10). Furthermore, the effective pressure is calculated from subtracting pore pressure from overburden pressure. By fitting the Equation (13) on the cross plot of the calculated effective pressure versus velocity at measured points, the values of A and B is determined as 0.224 and 1.29 respectively as shown in Figure 5.
Calibrated Bowers’ equation and sonic well log is used to generate effective pressure at each well. Then, the pore pressure is estimated using obtained effective pressure and Terzaghi’s equation. Finally, the buoyancy and lateral transfer effects are considered as explained in Eaton’s method. The result of estimated pore pressure and its corrections is shown in Figure 3b.
3.3 Pore pressure from compressibility method Any change in pore space is a function of rock and fluid compressibility. When a formation place under compaction, the pore spaces reduce and pore fluid pressure increase as a result. Therefore, the compressibility is used as a parameter to determine the pressure.
Atashbari and Tingay (2012) used the compressibility definitions introduced by Zimmerman and Vangolf to calculate the pore pressure as a function of porosity, effective overburden pressure, bulk compressibility and pore compressibility (refer to Appendix A for derivations). In a modified approach we used these compressibility definitions and represent a modified relation
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based on porosity, effective overburden pressure and pore space compressibility to calculate the pore pressure. Combining the following compressibility definitions by Zimmerman (Equations (14) and (15)), will give us the equation (16): .Z =
−1 \V V [ \PZ ]
. =
−1 \V + 1 V [ \P ]
\ =
.Z \Z .
(14)
^
(15)
_
(16)
Since the pore compressibility is calculated from special core analysis (SCAL) and due to keeping the test in constant pore pressure, the determined pore compressibility is Cpc and the compressibility term in denominator (Cpp) is unknown. Zimmerman proposed the following relation the pore compressibility due to pore and confining pressure: . = .Z − .`
(17)
In the above equation, the term Cr is defined as matrix compressibility which is demonstrated by Vangolf as follows. .` =
∅ .Z 1−∅
(18)
where Ø is the porosity. Putting all together, we defined the pressure difference as function of pore compressibility and porosity:
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\ =
(1 − ∅).Z \Z (1 − ∅).Z − ∅ .Z
(19)
With adding an exponential constant to this equation to correlate it for different geological field, the modified equation in pore pressure calculation by Atashbari can be expressed in the following form. ab
(1 − ∅). P = + 1 (1 − ∅). − ∅ .
(20)
where Pp is pore pressure, fractional Ø is porosity, Cp is pore compressibility in psi-1, σeff is the vertical effective pressure determined from the difference between overburden pressure and hydrostatic pressure in psi and ɣ’ is empirical constant ranging from 0.9 to 1.0.
In order to calculate pore compressibility, Cp, we used the results of studies by Akhoundzadeh (2011). Akhoundzadeh proposed pore volume compressibility of Kangan and Dalan formation in our studied area by following relation between the porosity and pore compressibility (Figure 6): 1 . = × 105d 1/fgh 0.444 + 0.131 ln(∅)
(21)
Since the fractional φ in above equation is measured from core analysis, we need to correct the porosity log. According to geological studies, core porosity versus effective porosity log gives the best correlation coefficient of about 0.86 (Figure 7).
Effective porosity log is available only in two wells in the study area. Therefore, the petrolphysical logs are used to estimate the effective porosity in other wells. One of the
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challenges in geoscience is to finding the complex relationship between petrophysical logs and cores or other well-log data. Back propagation is an effective method in solving these complex relations. BP is a training technique that input vectors and the corresponding target vectors are used to train a network. Then difference between calculated output and desired target in training set is computed and propagated backward by adjusting the weights. The LevenbergeMarquardt (LM) back propagation algorithm in MATLAB Neural Network Tool is used for training the neural network in this study. For this propose a two-layer feed forward network with sigmoid hidden neurons and linear output neuron is applied. The input layer has 3 neurons corresponding to sonic transient time, density and neutron porosity logs. The hidden layer has 20 neurons and the output layer has 1 neuron for effective porosity data. The two available effective porosity logs of total 5700 samples are used for training (70%), validation (15%) and testing (15%). It can be clearly seen from Figure 8-a that the linear coefficient of correlation is very high between the observed experimental data and values predicted through neural nets. The error histogram (Figure 8-b) shows that most errors fall between -0.01 and 0.01 indicating high performance of the network.
The effective porosity is predicted by the trained neural network and used to calculate the core porosity. The estimated core porosity is used in pore volume compressibility calculation from Equation (21). The pore pressure is evaluated in all wells by Equation (20) and setting ɣ’ to 0.983. Over pressure generated by buoyancy and lateral transfer effect is corrected as the pervious methods. The result of estimated pore pressure and its correction is shown in Figure 3c.
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3.4 Comparison between above methods In order to select the best pore pressure prediction method, a comparison between these three methods applied is shown in Figure 9. As shown, the results of pore pressure predictions from Eaton and compressibility methods provide a more favorable outcome compared to the Bowers method. Eaton method with exponent coefficient of 0.5 gives the best correlation with MDT measured pressure. However, the predicted pressure from compressibility method also shows good results, but as there was not enough core data; and in spite of using different estimations to obtain pore volume compressibility, this method failed to provide the reliable results. So, the Eaton method is used to 3D modeling of the pore pressure.
3.5 3D pore pressure prediction modeling In order to create the 3D pore pressure model, the structural framework, vertical layering and petrophysical analysis is utilized to model the estimated pore pressure. 3.5.1 Structural Framework Building The 3D structural framework is constrained first by defining the boundary to mark the lateral extent of the model. The boundary has a triangular shape with respect to the well locations distribution. It should be noted that the area of study is about 57 × 58.5 km. After boundary definition, a 3D grid is constructed in order to define the skeleton framework into which the horizons will be inserted later. 3.5.2 Vertical layering This process involves making horizons, zonation and layering. Horizons are defined from geological data including underground contour maps and well tops. In zonation process, an interval is inserted between each horizon by introducing isochore thickness data. The final step PAGE | 17
in vertical layering of the structural model is to define the layers between the horizons in order to make a finer resolution of the 3D grid. The layers are defined based on the lithological changes which are detected from Gamma-ray and sonic logs. 3.5.3 Petrophysical analysis and pressure modeling Estimated pore pressure data from Eaton’s method is treated as a property, upscaled to the resolution of the cells in the 3D structural grid in order to distribute the property values for each cell. Before modeling the distribution of the pore pressure, a variographic analysis is performed by the upscaled pore pressure data to determine the layer thickness and direction of anisotropy. Finally, the pore pressure model is generated based on Sequential Gaussian Simulation method considering the variogram model.
The estimated pore pressure model is shown in Figure 10. To verify the validity of the estimated model, well A-4 containing MDT information is omitted from the work flow for the final validation of the predicted pore pressure (Figure 10).
The predicted pressure values from the model (solid line) are in good agreement with the predicted pore pressure from well logs data (Figure 11). The differences in correlation with MDT points at some intervals, specially in 3150-3250 m, is probably due to the high permeability in these depths. The relationship between permeability and porosity is not always direct. It is possible to have very high porosity without any permeability, such as in pumice stone (zero connectivity). On the other hand, high permeability with a low porosity might also be true, as in the case of micro-fractured carbonates (high connectivity). High permeability in these intervals makes a hydrodynamic relationship between pore pressures in these intervals
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with the adjacent formation pressure. It makes a constant pore pressure gradient in these intervals. Therefore, the estimated pore pressure which is based on porosity and velocity shows lower pore pressure due to low porosity.
The cross correlation between the predicted pore pressure from the model and upscale predicted pore pressure from well logs is shown in Figure 12. Regression coefficient of R=0.90 shows the acceptable accuracy of the model for pore pressure prediction.
4 Conclusions In order to prediction of the pore pressure, common well log data are used along with measured pressure test (MDT) and some geological analysis reports. The results of this study are listed below.
a) Pore pressure prediction and modeling based on conventional well logs provide acceptable results in the studied carbonate formation. b) Analyzing results of three different methods for estimating pore pressure indicate that Eaton and compressibility methods provide better correlations with the measured pressure data compared to the Bowers method. c) Eaton method with exponent coefficient of 0.5 gives the best correlation with MDT measured pressure. The predicted pressure from the compressibility method also show good agreement with MDT measured pressure; however these results have been affected negatively by lack of enough core data to obtain pore volume compressibility. Accordingly, the Eaton method is selected for the 3D pore pressure modeling.
PAGE | 19
d) Validation of the 3D pore pressure reveals that the pressure estimation is reliable (with more than 89% accuracy) and also it is in good agreement with the measured pressure data at the well location. e) Using 3D pore pressure model, we can image the pressure profile throughout the surrounding area with limited data and provide a safe well planning. Also, the results obtained in this study can be considered as a useful tool to replace the formation pressure test for wells in which no measured test data are available
Acknowledgement The authors gratefully acknowledge the Pars Oil and Gas Company (POGC) of Iran for their permission to publish this paper and for their provision of software and dataset.
Appendix A. Derivation of pore pressure prediction from compressibility by Atashbari (2012) Zimerman (1991) has introduced four sets of compressibilities for two independent volume and two pressures in porous rocks. Each of these porous rock compressibilities relates changes in either the pore volume Vp or the bulk volume Vb to changes in the pore pressure Pp or the confining pressure Pc. Using a notation in which the first subscript indicates the relevant volume change, and the second subscript indicates the pressure which is varied, these compressibilities can be defined as follows: ./Z =
−1 \V/ V/ [ \PZ ]
(A 1)
^
PAGE | 20
./ =
−1 \V/ + 1 V/ [ \P ]
.Z =
−1 \V V [ \PZ ]
. =
−1 \V + 1 V [ \P ]
(A 2)
_
(A 3)
^
(A 4)
_
Atashbari and Tingay (2012) selected the first two above equations. In these equations, the superscript “i” is for the initial state of media (before compression), b and p denote bulk and pore. Combining those two equations together will give us the following relation: j =
./Z jZ ./
(A 5)
By assuming the infinitesimally small and equal size of increments of all independent variables (pore pressure and confining pressure), the differentiation could result in: \ =
./Z \Z ./
(A 6)
Bulk frame and pore compressibilities are accountable from special core analysis (SCAL), but since the test is taken by keeping pore pressure as constant, the term in denominator (Cbp) is unknown. Zimmerman demonstrated the relation between the bulk compressibility due to pore and confining pressure. ./ = ./Z − .`
(A 7)
PAGE | 21
where Cr is matrix compressibility. The compressibility of the matrix has been demonstrated by Vangolf as follows: .` =
∅ .Z 1−∅
(A 8)
where ϕ is the porosity. Putting all together, the pressure difference is defined as a function of the compressibility and porosity. \ =
(1 − ∅)./Z \Z (1 − ∅)./Z − ∅ .Z
(A 9)
Adding an exponential constant to this equation to correlate it for different geological field, he proposed the following equation to predict the pore pressure using compressibility: k
(1 − ∅)./ P=+ 1 (1 − ∅)./ − ∅ .
(A 1)
where Pp is the pore pressure; fractional ø is the porosity; Cb is bulk compressibility in psi-1; Cp is pore compressibility in psi-1; σeff is the effective overburden pressure (overburden pressure hydrostatic pressure) in psi; and ɣ is empirical constant ranging from 0.9 to 1.0.
References Akhoundzadeh, Hamid. "Relationship between Pore Volume Compressibility and Porosity in One of Irainan Southern Carbonate Reservoir." Petroleum University Of Technology, Abadan, 2011. Atashbari, Vahid and Mark Tingay. "Pore Pressure Prediction in Carbonate Reservoirs." In SPE Latin America and Caribbean Petroleum Engineering Conference, 2012. Biot, Maurice A. "General Theory of Three Dimensional Consolidation." Journal of applied physics 12, no. 2 (1941): 155-164.
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Bowers, Glenn. "Pore Pressure Estimation from Velocity Data: Accounting for Overpressure Mechanisms Besides Undercompaction." SPE Drilling & Completion 10, no. 2 (1995): 89-95. Contreras, OM, AN Tutuncu, RM Aguilera and GM Hareland. "A Case Study for Pore Pressure Prediction in an Abnormally Sub-Pressured Western Canada Sedimentary Basin." In 45th US Rock Mechanics/Geomechanics Symposium, 2011. Eaton, Ben. "The Equation for Geopressure Prediction from Well Logs." In Fall Meeting of the Society of Petroleum Engineers of AIME, 1975. Hottmann, CE and RK Johnson. "Estimation of Formation Pressures from Log-Derived Shale Properties." Journal of Petroleum Technology 17, no. 06 (1965): 717-722. Mann, David M and Andrew S Mackenzie. "Prediction of Pore Fluid Pressures in Sedimentary Basins." Marine and Petroleum Geology 7, no. 1 (1990): 55-65. Swarbrick, BE and Mark J Osborne. "Mechanisms That Generate Abnormal Pressures: An Overview." MEMOIRS-AMERICAN ASSOCIATION OF PETROLEUM GEOLOGISTS, (1998): 13-34. Swarbrick, Richard E, Mark J Osborne and Gareth S Yardley. "Comparison of Overpressure Magnitude Resulting from the Main Generating Mechanisms." MEMOIRS-AMERICAN ASSOCIATION OF PETROLEUM GEOLOGISTS, (2002): 1-12. Terzaghi, Karl. "Theoretical Soil Mechanics." (1943). Terzaghi, Karl. Soil Mechanics in Engineering Practice: Wiley. com, 1996. Traugott, M. "The Pore Pressure Centroid Concept: Reducing Drilling Risks." Compaction and Overpressure Current Research, Abst., 9-10, December, IFP, Paris, (1996). Traugott, Martin. "Pore/Fracture Pressure Determinations in Deep Water." World Oil 218, no. 8 (1997): 68-70. Van Golf-Racht, Theodor D. Fundamentals of Fractured Reservoir Engineering: Access Online via Elsevier, 1982. Yardley, GS and RE Swarbrick. "Lateral Transfer: A Source of Additional Overpressure?" Marine and Petroleum Geology 17, no. 4 (2000): 523-537. Zhang, Jincai. "Pore Pressure Prediction from Well Logs: Methods, Modifications, and New Approaches." Earth-Science Reviews 108, no. 1 (2011): 50-63. Zimmerman, Robert Wayne. Compressibility of Sandstones: Elsevier, 1991.
PAGE | 23
Figures
Figure 1: Location of available wells in this study. Filled circles show the wells with measured pressure test (MDT).
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Figure 2: Normal velocity trend line corresponding to shale points, calibrated with MDT measured data.
PAGE | 25
Figure 3: Predicted pore pressure from a) Eaton b) Bowers and c) Compressibility methods and their correction.
PAGE | 26
Figure 4: The diagram of the overpressure generated by hydrocarbon buoyancy in the studied field.
PAGE | 27
Figure 5: The cross plot of the effective pressure versus the V-V0. V0 is the velocity at zero effective pressure which is equal 1650 m/sec.
PAGE | 28
Figure 6: Cross plot of pore volume compressibility versus porosity (Akhoundzadeh, 2011).
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Figure 7: Cross plot of effective porosity versus core porosity.
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Figure 8:: a) Cross correlation of the trained neural network and b) Error histogram of the trained neural network.
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Figure 9: A comparison between predicted pore pressure from three methods using Eaton, Bowers and compressibility equations.
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Figure 10: Pore pressure prediction model and the location of validation well (left) and the exported pressure at that point (right) in psi.
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Figure 11: The predicted pressure at well-location from the model (blue line), well logs (black line), upscaled well logs (red line) and measured pore pressure at well location (green dots).
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Figure 12: Cross plot of predicted pore pressure from model versus upscaled predicted pressure from well logs.
PAGE | 35
Highlights We used three different methods to estimate the pore pressure. Comparing the results and finding the Eaton method as the best fitted method. The 3D pore pressure is modeled based on the estimation method. The 3D model can be considered as a useful tool to replace the formation pressure test.
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Abstract Knowledge of pore pressure is essential for cost-effective, safe well planning and efficient reservoir modeling. Pore pressure prediction has an important application in proper selection of the casing points and a reliable mud weight. In addition, using cost-effective methods of pore pressure prediction which give extensive and continuous range of data is much affordable than direct measuring of pore pressure. The main objective of this project is to determine the pore pressure using well log data in one of the Iranian gas fields. To obtain this goal, the formation pore pressure is predicted from well logging data by applying three different methods including Eaton, Bowers and the compressibility methods. Our results show that the best correlation with the measured pressure data is achieved by the modified Eaton method with Eaton’s exponent of about 0.5. Finally, in order to generate the 3D pore pressure model, well-log-based estimated pore pressures from Eaton method is upscaled and distributed throughout the 3D structural grid using a geostatistical approach. The 3D pore pressure model shows good agreement with the well-log-based estimated pore pressure and also the measured pressure obtained from Modular formation Dynamics Tester. Keywords: Pore pressure prediction, Abnormal pressure, Well-logging, Eaton method, Pressure modeling, Geostatistic
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Pore pressure prediction and modeling using well-logging data in one of gas fields in south of Iran Morteza Azadpour, Navid Shadmanaman, Ali Kadkhodaie-Ilkhchi, Mohammad-Reza Sedghipour
www.elsevier.com/locate/petrol
PII: DOI: Reference:
S0920-4105(15)00074-1 http://dx.doi.org/10.1016/j.petrol.2015.02.022 PETROL2965
To appear in:
Journal of Petroleum Science and Engineering
Received date: 13 March 2014 Accepted date: 10 February 2015 Cite this article as: Morteza Azadpour, Navid Shadmanaman, Ali KadkhodaieIlkhchi, Mohammad-Reza Sedghipour, Pore pressure prediction and modeling using well-logging data in one of gas fields in south of Iran, Journal of Petroleum Science and Engineering, http://dx.doi.org/10.1016/j.petrol.2015.02.022 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Pore pressure prediction and modeling using well-logging data in one of gas fields in south of Iran Morteza Azadpour11; Navid Shadmanaman1; Ali Kadkhodaie-Ilkhchi2; Mohammad-Reza Sedghipour3 1. Department of Mining and Petroleum Exploration, Sahand University of Technology, Tabriz, Iran. 2. Geology Department, Faculty of Natural Science, University of Tabriz, Tabriz, Iran. 3. Department of Petroleum Engineering, Petrophysic Directorate of P.O.G.C., Tehran, Iran.
Abstract
Knowledge of pore pressure is essential for cost-effective, safe well planning and efficient reservoir modeling. Pore pressure prediction has an important application in proper selection of the casing points and a reliable mud weight. In addition, using cost-effective methods of pore pressure prediction which give extensive and continuous range of data is much affordable than direct measuring of pore pressure. The main objective of this project is to determine the pore pressure using well log data in one of the Iranian gas fields. To obtain this goal, the formation pore pressure is predicted from well logging data by applying three different methods including Eaton, Bowers and the compressibility methods. Our results show that the best correlation with the measured pressure data is achieved by the modified Eaton method with Eaton’s exponent of about 0.5. Finally, in order to generate the 3D pore pressure model, well-log-based estimated pore pressures from Eaton method is upscaled and distributed throughout the 3D structural grid using a geostatistical approach. The 3D pore pressure model shows good 1
Corresponding author: Tel: +98 917 127 2559; Fax: +98 411 344 4311 E-mail addresses: [email protected] (M. Azadpour), [email protected] (N. Shadmanaman), [email protected](A. Kadkhodaie-Ilkhchi), [email protected] (M. R. Sedghipour)
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agreement with the well-log-based estimated pore pressure and also the measured pressure obtained from Modular formation Dynamics Tester.
Keywords: Pore pressure prediction, Abnormal pressure, Well-logging, Eaton method, Pressure modeling, Geostatistic
1 Introduction Formation pore pressure is traditionally estimated based on well log analysis in combination with Terzaghi’s hypothesis which describes the compaction of the soil due to overburden stress. The pore pressure which is the pressure of the fluid inside the pore space of the formation, is defined with several aspects of the pressure terminologies contains: Hydrostatic pressure (weight of a fluid column), Overburden pressure (the combine weight of formation solid and fluid of overlying sediments) and Effective stress (the grain-to-grain contact stress). The overburden load at any depth is supported by the effective stress and the pore pressure. This relationship is expressed as Terzaghi theory.
Pore pressure, based on the magnitude, can be described as being either normal (hydrostatic) or abnormal (overpressure or underpressure). Overpressure can make many problems such as kicks, blowouts, wellbore instability, hole washouts and loss of drilling mud circulation. Therefore, accurate pore pressure prediction is necessary for a safe and economic drilling. Swarbrick & Osborne (1998) classified the generation mechanism of overpressure in three categories:
1- Stress related mechanisms • Disequilibrium compaction PAGE | 2
• Tectonic stress 2- Fluid volume increase mechanisms • Temperature increase • Water release due to mineral transformation • Hydrocarbon generation • Cracking of oil to gas • Gas expansion with uplift 3- Fluid movement and buoyancy mechanisms • Hydraulic head • Osmosis • Buoyancy due to density contrasts • Lateral transfer All of these mechanisms are effective when they occur faster than the formation ability to expel the excess pressure. The compaction disequilibrium is one of the main mechanisms in creating large magnitude overpressure. During the deposition, the overburden pressure makes compaction on underlying sediments and causes fluid to expel. However, if pore fluid is not expelled fast enough to reach hydrostatic pressure, the pore fluid pressure increases. When the rate of sedimentation in a basin is low, the underlying sediments will be able to compact and dewater in normal way and it reaches to hydrostatic pressure equilibrium. However, high sedimentation rates prevent sediments from dewatering, so the compaction rate decreases and pore space preserve with overpressure.
2 Pore pressure prediction methods So far, several works have been done in pore pressure prediction using well logs and seismic data resulting in some empirical formula for estimation of pore pressure. The first study on the pore pressure prediction was made by Hottman and Johnson (1965) using shale properties derived from well log data. This approach was based on any deviation in the measured
PAGE | 3
properties from its normal trend line. Afterwards, many researchers have successfully used resistivity, sonic transit time, porosity and other well log data for pore pressure prediction. Most of these studies are based on the assumption that any change in an area with normal pore pressure leads to change in some petrophysical properties such as compaction, porosity and fluid motion. Therefore, any measurable parameter which can somehow show these changes can be used in interpretation and quantitative evaluation of pore pressure. Conventional methods of the pore pressure prediction are introduced in the following subsections.
2.1 Eaton method In 1975, Eaton proposed an empirical equation to quantify the pore pressure using well log data such as sonic transient time, formation resistivity or dc-exponent. He considered the disequilibrium compaction as the main mechanism of overpressure generation. This method was based on the first prediction approach by Hottman and Johnson. Both methods rely on this assumption that overburden pressure is supported by pore pressure and vertical effective stress, as shown in Terzaghi’s equation. Terzaghi and Peck (1948) designed an experiment to describe the compaction due to overburden stress. They simulated the clay compaction using a vessel containing a spring and fluid. In this experiment, the overburden stress is simulated by a piston. Once the fluid is allowed to drain; any increase in overburden stress makes the system to expel some fluid so that the fluid pressure remains in hydrostatic pressure while the effective stress increases anyway. However, if the fluid is in untrained condition, both fluid pressure and effective stress rise with increase in overburden stress. The fundamental theory for pore pressure prediction is proposed based on Terzaghi's and Biot's effective stress law (Biot, 1941; PAGE | 4
Terzaghi et al., 1996). This theory indicates that pore pressure in the formation is a function of overburden stress and effective stress. The overburden stress, vertical effective stress and pore pressure can be expressed in the following form:
=
S − σ
(1)
where Pp is the pore pressure; S is the overburden stress; σeff is the vertical effective stress; and α is the Biot effective stress coefficient. Biot's coefficient is the ratio of the volume change of the fluid filled porosity to the volume change of the rock when the fluid is free to move out of the rock. It is conventionally assumed α=1 in geopressure studies (Zhang, 2011).
According to equation (1), Eaton (1975) presented the following empirical equation for pore pressure prediction from sonic transit time: ∆t P = S − S − P ∆t
(2)
where Ppg is the formation pressure gradient; Sg is the overburden pressure gradient; Png is the hydrostatic pore pressure gradient; ∆t is the measured sonic transit time in shale by well logging; ∆tn is the sonic transit time in shale at the normal pressure condition obtained from normal trend line; and x is the exponent constant which is originally 3 in Eaton’s study and requires modification to be implemented in tight unconventional reservoirs (Contreras et al, 2011).
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2.2 Bowers’ method Like Eaton’s method, Bowers (1995) used Terzaghi’s equation to calculate the effective stresses from measured pore pressure data of the shale and overburden stresses. Bowers method is a method based on the effective stress which considers disequilibrium compaction and unloading as the main mechanisms of overpressure generations. Disequilibrium compaction cannot cause the effective stress to decrease but unloading is defined as the terms of effective stress reduction which is caused by fluid expansion. Unlike disequilibrium compaction, fluid expansion can cause the pore pressure to increase at a faster rate than the overburden stress. It forces the effective stress to decrease as burial continues (Bowers, 1995).
In disequilibrium compaction conditions, Bowers used an empirically determined method to calculate the effective pressure with the following relationship between the effective stress and sonic velocity: V = V + Aσ
(3)
where V is the velocity at a given depth; V0 is the surface velocity (normally 5000 ft/sec); σ is the vertical effective stress; A and B are the parameters obtained from calibrating regional offset velocity versus effective stress data.
In basins with the mechanism of unloading, Bowers (1995) proposed the following empirical relation to account for unloading effect:
PAGE | 6
V = V + A σ ( σ = (
!
# & ( ) $ ) %
v − 5000 # )& *
(4)
(5)
where U is the unloading parameter which is a measure of how plastic the sediment is. U = 1 implies no permanent deformation and U = ∞ corresponds to completely irreversible deformation. σmax and Vmax are the values of effective stress and velocity at the onset unloading which is the maximum. (Bowers, 1995).
2.3 Compressibility method This method uses the rock compressibility to calculate the pore pressure. Pore pressure depends on the pore volume changes. Any change in pore space is a function of rock and fluid compressibility. In general, when the formation is under compression, pore space reduces and it causes an overpressure on fluid pressure. Hence, compressibility is used as a parameter to determine the pore pressure.
Atashbari (2012) used Zimmerman (1991) and Vangolf (1982) definitions for compressibility and proposed the following relation to calculate pore pressure in Iran carbonate formations (refer to Appendix A for derivations). (1 − ∅)./ P = + 1 (1 − ∅)./ − ∅ .
γ
(6)
where Pp is the pore pressure; fractional ø is the porosity; Cb is bulk compressibility in psi-1; Cp is pore compressibility in psi-1; σeff is the vertical effective pressure (overburden pressure hydrostatic pressure) in psi; and ɣ is empirical constant ranging from 0.9 to 1.0.
PAGE | 7
3 Case study The study gas field is located in Persian Gulf basin, South Iran. The first exploration well was drilled in 1990, encountered gas reservoir in the Kangan-Dalan formations. The Kangan Formation and the Upper Dalan member collectively host the gas reservoir in this field. These formations are composed of a sequence including shale, anhydrite, dolomite, and limestone. In Arabian nomenclature, the Kangan and Dalan formations together are known as the Khuff Formation. Khuff Formation is divided into five layers, K1 to K5. K1 plus K2 is equivalent to the Kangan and K3 plus K4 is equivalent to the Upper Dalan formation. In the studied Field, K5 is assumed as non-reservoir and put out of the field. The data from 10 wells (Figure 1), including different types of petrophysical logs such as, sonic transient time, porosity; gamma-ray and density logs are used in this study to predict the pore pressure. Furthermore, the underground contour (UGC) maps in three formations top are available. The UGC maps are used for 3D modeling of pore pressure. Also, the measured pore pressure from Modular formation Dynamics Tester (MDT) is available at 5 wells.
The aim of this study is to evaluate and model pore pressure within the productive reservoir. Here, Eaton, Bower and compressibility methods, with modifications as in an unconventional field with complex geology are applied to predict pore pressure. Finally, the best obtained result of these methods is used to build the 3D pore pressure model in the field.
3.1 Pore pressure from Eaton method In pore pressure prediction, Eaton method is the most common one. Eaton (1975) considered disequilibrium compaction of shale layer as the main factor in abnormal pressure generation. In
PAGE | 8
this method, the first step is to analyze the gamma ray in the carbonate formations. We will consider the peak response to the right in gamma-ray log as the result of some shaliness within the rock matrix. With respect to these selected gamma ray peaks, the corresponding velocity points are detected and sonic log velocity trend line is drawn through these points as is shown in Figure 2. Note that the normal trend line is drawn through the normally pressured and normally compacted section of the well log data. Any deviation from the normal trend line indicates as the abnormal pressure. In order to determine the best normal velocity trend line, well A-6 which includes a continuous long set of well log data is selected. Drilling mud weight pressure represents the normally pressured section of this well from 1100 to 2500 m. Therefore, based on the selected points of the measured sonic transient time in this interval, the modified normal compaction trend relation by Zhang (2011) is used: ∆2 = ∆2 + (∆23 − ∆2 )4 567
(7)
where Δtm is the compressional transit time in the shale matrix (with zero porosity); Δtml is the transit time at surface; z is the depth; and c is the constant.
As the velocity at the surface is about 1500-1800 m/sec, the surface transit time, Δtml is considered 185 µs/ft in average. Δtm is determined as 50 µs/ft. Based on the sonic transit time with normal pore pressures (Figure 2), the normal compaction trend of the transit time is proposed as follow:
PAGE | 9
∆2 = 50 + (185 − 50)4 5.#:;7
(8)
Substituting Equation (8) into (2), the modified Eaton's sonic equation can be expressed in the following form.
P
50 + (185 − 50)4 5.#:;7 = S − S − P + 1 ∆t
(9)
According to the overall studies in Middle East, especially in Iran, the gradient of normal hydrostatic pressure gradient (P ) is 0.464 psi/ft. Overburden pressure gradient (Sg) is given by: < = 0.433 × @/
(10)
Here ρb is the bulk density. To determine the exponent constant, x, Eaton equation is written in terms of x as in follows: < − BCD < − E A= ∆2 BCD F∆2E H G
(11)
Using a number of points with measured pressure and well-log data, the mean exponent constant, x, is determined as 0.5. Using Equation (9), pore pressure is calculated as shown in Figure 3-a. As stated before, many factors can affect the abnormal pressure. Eaton method considers disequilibrium compaction of shale layer as the main factor in abnormal pressure generation. There is also an amount of overpressure due to buoyancy force within the gas accumulation and some exceed pressure by lateral transfer due to extension of inclined aquifer in the studied area. PAGE | 10
Hydrocarbon buoyancy may cause to increase pressure due to the difference in pressure gradient between gas, oil and formation water. As shown in Figure 4, calculation of the pore pressure gradient in gas and water zone shows that the difference in pressure gradient between the overlying hydrocarbon and underlying water is 0.378 psi/ft for the gas column upward the water contact surface. So, with calculation of water gas contact surface in all wells, this correction is applied to estimate pore pressure. The result of buoyancy effect is demonstrated in Figure 3-a.
An inclined aquifer with enough permeability can redistribute the excess pore pressure laterally in the subsurface. Transference along such inclined aquifers can make an increase in pore pressure at the crest of structure (Mann & Mackenzie, 1990).The Centroid Concept is an empirical method to quantify the pressure contribution from lateral transfer at the crest of inclined aquifers (Traugott, 1996, 1997). According to this concept, pore pressure at the mid height or centre of the aquifer is equal to the adjacent formation. Thus, as in the calculation of the modified lateral transfer effectiveness proposed by Yardley and Swarbrick (1998), by calculation of overpressure at a crestal well, the exceed pressure distribution along the aquifer is calculable at all wells. Yardley and Swarbrick (1998) proposed the following relation to quantify the pressure contribution from lateral transfer as lateral transfer effectiveness: 2D model aquifer XSP − 1D model crestal XSP × 100 1D model crestal XSP
(12)
where XSP is the excess pressure which is the difference between the actual pore pressure and the hydrostatic pressure. 1D and 2D models represent an indication of isolated and connected
PAGE | 11
aquifers respectively. It is assumed that the calculated exceed pressure by the pervious mechanisms (disequilibrium compaction and buoyancy effect) indicates isolated aquifers and the measured formation pressure test (MDT pressure test) contains the exceed pressure due to lateral transfer of extensive aquifer in addition. Calculation of lateral transfer effectiveness in well A-8, as a crestal well, gives a lateral transfer effectiveness of 89 %.This value shows the addition contribution to crestal exceed pressure from the lateral transfer compared to the contribution from pervious overpressure mechanism. Based on the Centroid Concept, the lateral transfer effectiveness at the center of the aquifer is zero. Therefore, the exceed pressure along the aquifer decrease at the down dip and increase at the crest of the model. Using the Centroid Concept, the aquifer dip and the lateral transfer effectiveness of well A-8, distribution of the exceed pressure is calculated for all wells. The lateral transfer effect is corrected as shown in Figure 3-a. Lateral transfer makes the maximum increase at the crestal wells and a little effect on the other wells near to the centre of the aquifer.
3.2 Pore pressure from Bowers method Bowers proposed an idea in obtaining effective vertical stress to calculate the pore pressure which is the difference between overburden pressure and effective stress. By calculating the parameters of Bowers’ equation (A and B) and knowledge of rock velocity, the effective pressure can be determined as:
PAGE | 12
#
Y − 5000 & σ= *
(13)
Bowers’ equation can be calibrated at well points with measured pressure, density and velocity values. The overburden pressure is calculated from Equation (10). Furthermore, the effective pressure is calculated from subtracting pore pressure from overburden pressure. By fitting the Equation (13) on the cross plot of the calculated effective pressure versus velocity at measured points, the values of A and B is determined as 0.224 and 1.29 respectively as shown in Figure 5.
Calibrated Bowers’ equation and sonic well log is used to generate effective pressure at each well. Then, the pore pressure is estimated using obtained effective pressure and Terzaghi’s equation. Finally, the buoyancy and lateral transfer effects are considered as explained in Eaton’s method. The result of estimated pore pressure and its corrections is shown in Figure 3b.
3.3 Pore pressure from compressibility method Any change in pore space is a function of rock and fluid compressibility. When a formation place under compaction, the pore spaces reduce and pore fluid pressure increase as a result. Therefore, the compressibility is used as a parameter to determine the pressure.
Atashbari and Tingay (2012) used the compressibility definitions introduced by Zimmerman and Vangolf to calculate the pore pressure as a function of porosity, effective overburden pressure, bulk compressibility and pore compressibility (refer to Appendix A for derivations). In a modified approach we used these compressibility definitions and represent a modified relation
PAGE | 13
based on porosity, effective overburden pressure and pore space compressibility to calculate the pore pressure. Combining the following compressibility definitions by Zimmerman (Equations (14) and (15)), will give us the equation (16): .Z =
−1 \V V [ \PZ ]
. =
−1 \V + 1 V [ \P ]
\ =
.Z \Z .
(14)
^
(15)
_
(16)
Since the pore compressibility is calculated from special core analysis (SCAL) and due to keeping the test in constant pore pressure, the determined pore compressibility is Cpc and the compressibility term in denominator (Cpp) is unknown. Zimmerman proposed the following relation the pore compressibility due to pore and confining pressure: . = .Z − .`
(17)
In the above equation, the term Cr is defined as matrix compressibility which is demonstrated by Vangolf as follows. .` =
∅ .Z 1−∅
(18)
where Ø is the porosity. Putting all together, we defined the pressure difference as function of pore compressibility and porosity:
PAGE | 14
\ =
(1 − ∅).Z \Z (1 − ∅).Z − ∅ .Z
(19)
With adding an exponential constant to this equation to correlate it for different geological field, the modified equation in pore pressure calculation by Atashbari can be expressed in the following form. ab
(1 − ∅). P = + 1 (1 − ∅). − ∅ .
(20)
where Pp is pore pressure, fractional Ø is porosity, Cp is pore compressibility in psi-1, σeff is the vertical effective pressure determined from the difference between overburden pressure and hydrostatic pressure in psi and ɣ’ is empirical constant ranging from 0.9 to 1.0.
In order to calculate pore compressibility, Cp, we used the results of studies by Akhoundzadeh (2011). Akhoundzadeh proposed pore volume compressibility of Kangan and Dalan formation in our studied area by following relation between the porosity and pore compressibility (Figure 6): 1 . = × 105d 1/fgh 0.444 + 0.131 ln(∅)
(21)
Since the fractional φ in above equation is measured from core analysis, we need to correct the porosity log. According to geological studies, core porosity versus effective porosity log gives the best correlation coefficient of about 0.86 (Figure 7).
Effective porosity log is available only in two wells in the study area. Therefore, the petrolphysical logs are used to estimate the effective porosity in other wells. One of the
PAGE | 15
challenges in geoscience is to finding the complex relationship between petrophysical logs and cores or other well-log data. Back propagation is an effective method in solving these complex relations. BP is a training technique that input vectors and the corresponding target vectors are used to train a network. Then difference between calculated output and desired target in training set is computed and propagated backward by adjusting the weights. The LevenbergeMarquardt (LM) back propagation algorithm in MATLAB Neural Network Tool is used for training the neural network in this study. For this propose a two-layer feed forward network with sigmoid hidden neurons and linear output neuron is applied. The input layer has 3 neurons corresponding to sonic transient time, density and neutron porosity logs. The hidden layer has 20 neurons and the output layer has 1 neuron for effective porosity data. The two available effective porosity logs of total 5700 samples are used for training (70%), validation (15%) and testing (15%). It can be clearly seen from Figure 8-a that the linear coefficient of correlation is very high between the observed experimental data and values predicted through neural nets. The error histogram (Figure 8-b) shows that most errors fall between -0.01 and 0.01 indicating high performance of the network.
The effective porosity is predicted by the trained neural network and used to calculate the core porosity. The estimated core porosity is used in pore volume compressibility calculation from Equation (21). The pore pressure is evaluated in all wells by Equation (20) and setting ɣ’ to 0.983. Over pressure generated by buoyancy and lateral transfer effect is corrected as the pervious methods. The result of estimated pore pressure and its correction is shown in Figure 3c.
PAGE | 16
3.4 Comparison between above methods In order to select the best pore pressure prediction method, a comparison between these three methods applied is shown in Figure 9. As shown, the results of pore pressure predictions from Eaton and compressibility methods provide a more favorable outcome compared to the Bowers method. Eaton method with exponent coefficient of 0.5 gives the best correlation with MDT measured pressure. However, the predicted pressure from compressibility method also shows good results, but as there was not enough core data; and in spite of using different estimations to obtain pore volume compressibility, this method failed to provide the reliable results. So, the Eaton method is used to 3D modeling of the pore pressure.
3.5 3D pore pressure prediction modeling In order to create the 3D pore pressure model, the structural framework, vertical layering and petrophysical analysis is utilized to model the estimated pore pressure. 3.5.1 Structural Framework Building The 3D structural framework is constrained first by defining the boundary to mark the lateral extent of the model. The boundary has a triangular shape with respect to the well locations distribution. It should be noted that the area of study is about 57 × 58.5 km. After boundary definition, a 3D grid is constructed in order to define the skeleton framework into which the horizons will be inserted later. 3.5.2 Vertical layering This process involves making horizons, zonation and layering. Horizons are defined from geological data including underground contour maps and well tops. In zonation process, an interval is inserted between each horizon by introducing isochore thickness data. The final step PAGE | 17
in vertical layering of the structural model is to define the layers between the horizons in order to make a finer resolution of the 3D grid. The layers are defined based on the lithological changes which are detected from Gamma-ray and sonic logs. 3.5.3 Petrophysical analysis and pressure modeling Estimated pore pressure data from Eaton’s method is treated as a property, upscaled to the resolution of the cells in the 3D structural grid in order to distribute the property values for each cell. Before modeling the distribution of the pore pressure, a variographic analysis is performed by the upscaled pore pressure data to determine the layer thickness and direction of anisotropy. Finally, the pore pressure model is generated based on Sequential Gaussian Simulation method considering the variogram model.
The estimated pore pressure model is shown in Figure 10. To verify the validity of the estimated model, well A-4 containing MDT information is omitted from the work flow for the final validation of the predicted pore pressure (Figure 10).
The predicted pressure values from the model (solid line) are in good agreement with the predicted pore pressure from well logs data (Figure 11). The differences in correlation with MDT points at some intervals, specially in 3150-3250 m, is probably due to the high permeability in these depths. The relationship between permeability and porosity is not always direct. It is possible to have very high porosity without any permeability, such as in pumice stone (zero connectivity). On the other hand, high permeability with a low porosity might also be true, as in the case of micro-fractured carbonates (high connectivity). High permeability in these intervals makes a hydrodynamic relationship between pore pressures in these intervals
PAGE | 18
with the adjacent formation pressure. It makes a constant pore pressure gradient in these intervals. Therefore, the estimated pore pressure which is based on porosity and velocity shows lower pore pressure due to low porosity.
The cross correlation between the predicted pore pressure from the model and upscale predicted pore pressure from well logs is shown in Figure 12. Regression coefficient of R=0.90 shows the acceptable accuracy of the model for pore pressure prediction.
4 Conclusions In order to prediction of the pore pressure, common well log data are used along with measured pressure test (MDT) and some geological analysis reports. The results of this study are listed below.
a) Pore pressure prediction and modeling based on conventional well logs provide acceptable results in the studied carbonate formation. b) Analyzing results of three different methods for estimating pore pressure indicate that Eaton and compressibility methods provide better correlations with the measured pressure data compared to the Bowers method. c) Eaton method with exponent coefficient of 0.5 gives the best correlation with MDT measured pressure. The predicted pressure from the compressibility method also show good agreement with MDT measured pressure; however these results have been affected negatively by lack of enough core data to obtain pore volume compressibility. Accordingly, the Eaton method is selected for the 3D pore pressure modeling.
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d) Validation of the 3D pore pressure reveals that the pressure estimation is reliable (with more than 89% accuracy) and also it is in good agreement with the measured pressure data at the well location. e) Using 3D pore pressure model, we can image the pressure profile throughout the surrounding area with limited data and provide a safe well planning. Also, the results obtained in this study can be considered as a useful tool to replace the formation pressure test for wells in which no measured test data are available
Acknowledgement The authors gratefully acknowledge the Pars Oil and Gas Company (POGC) of Iran for their permission to publish this paper and for their provision of software and dataset.
Appendix A. Derivation of pore pressure prediction from compressibility by Atashbari (2012) Zimerman (1991) has introduced four sets of compressibilities for two independent volume and two pressures in porous rocks. Each of these porous rock compressibilities relates changes in either the pore volume Vp or the bulk volume Vb to changes in the pore pressure Pp or the confining pressure Pc. Using a notation in which the first subscript indicates the relevant volume change, and the second subscript indicates the pressure which is varied, these compressibilities can be defined as follows: ./Z =
−1 \V/ V/ [ \PZ ]
(A 1)
^
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./ =
−1 \V/ + 1 V/ [ \P ]
.Z =
−1 \V V [ \PZ ]
. =
−1 \V + 1 V [ \P ]
(A 2)
_
(A 3)
^
(A 4)
_
Atashbari and Tingay (2012) selected the first two above equations. In these equations, the superscript “i” is for the initial state of media (before compression), b and p denote bulk and pore. Combining those two equations together will give us the following relation: j =
./Z jZ ./
(A 5)
By assuming the infinitesimally small and equal size of increments of all independent variables (pore pressure and confining pressure), the differentiation could result in: \ =
./Z \Z ./
(A 6)
Bulk frame and pore compressibilities are accountable from special core analysis (SCAL), but since the test is taken by keeping pore pressure as constant, the term in denominator (Cbp) is unknown. Zimmerman demonstrated the relation between the bulk compressibility due to pore and confining pressure. ./ = ./Z − .`
(A 7)
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where Cr is matrix compressibility. The compressibility of the matrix has been demonstrated by Vangolf as follows: .` =
∅ .Z 1−∅
(A 8)
where ϕ is the porosity. Putting all together, the pressure difference is defined as a function of the compressibility and porosity. \ =
(1 − ∅)./Z \Z (1 − ∅)./Z − ∅ .Z
(A 9)
Adding an exponential constant to this equation to correlate it for different geological field, he proposed the following equation to predict the pore pressure using compressibility: k
(1 − ∅)./ P=+ 1 (1 − ∅)./ − ∅ .
(A 1)
where Pp is the pore pressure; fractional ø is the porosity; Cb is bulk compressibility in psi-1; Cp is pore compressibility in psi-1; σeff is the effective overburden pressure (overburden pressure hydrostatic pressure) in psi; and ɣ is empirical constant ranging from 0.9 to 1.0.
References Akhoundzadeh, Hamid. "Relationship between Pore Volume Compressibility and Porosity in One of Irainan Southern Carbonate Reservoir." Petroleum University Of Technology, Abadan, 2011. Atashbari, Vahid and Mark Tingay. "Pore Pressure Prediction in Carbonate Reservoirs." In SPE Latin America and Caribbean Petroleum Engineering Conference, 2012. Biot, Maurice A. "General Theory of Three Dimensional Consolidation." Journal of applied physics 12, no. 2 (1941): 155-164.
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Bowers, Glenn. "Pore Pressure Estimation from Velocity Data: Accounting for Overpressure Mechanisms Besides Undercompaction." SPE Drilling & Completion 10, no. 2 (1995): 89-95. Contreras, OM, AN Tutuncu, RM Aguilera and GM Hareland. "A Case Study for Pore Pressure Prediction in an Abnormally Sub-Pressured Western Canada Sedimentary Basin." In 45th US Rock Mechanics/Geomechanics Symposium, 2011. Eaton, Ben. "The Equation for Geopressure Prediction from Well Logs." In Fall Meeting of the Society of Petroleum Engineers of AIME, 1975. Hottmann, CE and RK Johnson. "Estimation of Formation Pressures from Log-Derived Shale Properties." Journal of Petroleum Technology 17, no. 06 (1965): 717-722. Mann, David M and Andrew S Mackenzie. "Prediction of Pore Fluid Pressures in Sedimentary Basins." Marine and Petroleum Geology 7, no. 1 (1990): 55-65. Swarbrick, BE and Mark J Osborne. "Mechanisms That Generate Abnormal Pressures: An Overview." MEMOIRS-AMERICAN ASSOCIATION OF PETROLEUM GEOLOGISTS, (1998): 13-34. Swarbrick, Richard E, Mark J Osborne and Gareth S Yardley. "Comparison of Overpressure Magnitude Resulting from the Main Generating Mechanisms." MEMOIRS-AMERICAN ASSOCIATION OF PETROLEUM GEOLOGISTS, (2002): 1-12. Terzaghi, Karl. "Theoretical Soil Mechanics." (1943). Terzaghi, Karl. Soil Mechanics in Engineering Practice: Wiley. com, 1996. Traugott, M. "The Pore Pressure Centroid Concept: Reducing Drilling Risks." Compaction and Overpressure Current Research, Abst., 9-10, December, IFP, Paris, (1996). Traugott, Martin. "Pore/Fracture Pressure Determinations in Deep Water." World Oil 218, no. 8 (1997): 68-70. Van Golf-Racht, Theodor D. Fundamentals of Fractured Reservoir Engineering: Access Online via Elsevier, 1982. Yardley, GS and RE Swarbrick. "Lateral Transfer: A Source of Additional Overpressure?" Marine and Petroleum Geology 17, no. 4 (2000): 523-537. Zhang, Jincai. "Pore Pressure Prediction from Well Logs: Methods, Modifications, and New Approaches." Earth-Science Reviews 108, no. 1 (2011): 50-63. Zimmerman, Robert Wayne. Compressibility of Sandstones: Elsevier, 1991.
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Figures
Figure 1: Location of available wells in this study. Filled circles show the wells with measured pressure test (MDT).
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Figure 2: Normal velocity trend line corresponding to shale points, calibrated with MDT measured data.
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Figure 3: Predicted pore pressure from a) Eaton b) Bowers and c) Compressibility methods and their correction.
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Figure 4: The diagram of the overpressure generated by hydrocarbon buoyancy in the studied field.
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Figure 5: The cross plot of the effective pressure versus the V-V0. V0 is the velocity at zero effective pressure which is equal 1650 m/sec.
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Figure 6: Cross plot of pore volume compressibility versus porosity (Akhoundzadeh, 2011).
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Figure 7: Cross plot of effective porosity versus core porosity.
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Figure 8:: a) Cross correlation of the trained neural network and b) Error histogram of the trained neural network.
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Figure 9: A comparison between predicted pore pressure from three methods using Eaton, Bowers and compressibility equations.
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Figure 10: Pore pressure prediction model and the location of validation well (left) and the exported pressure at that point (right) in psi.
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Figure 11: The predicted pressure at well-location from the model (blue line), well logs (black line), upscaled well logs (red line) and measured pore pressure at well location (green dots).
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Figure 12: Cross plot of predicted pore pressure from model versus upscaled predicted pressure from well logs.
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Highlights We used three different methods to estimate the pore pressure. Comparing the results and finding the Eaton method as the best fitted method. The 3D pore pressure is modeled based on the estimation method. The 3D model can be considered as a useful tool to replace the formation pressure test.
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Abstract Knowledge of pore pressure is essential for cost-effective, safe well planning and efficient reservoir modeling. Pore pressure prediction has an important application in proper selection of the casing points and a reliable mud weight. In addition, using cost-effective methods of pore pressure prediction which give extensive and continuous range of data is much affordable than direct measuring of pore pressure. The main objective of this project is to determine the pore pressure using well log data in one of the Iranian gas fields. To obtain this goal, the formation pore pressure is predicted from well logging data by applying three different methods including Eaton, Bowers and the compressibility methods. Our results show that the best correlation with the measured pressure data is achieved by the modified Eaton method with Eaton’s exponent of about 0.5. Finally, in order to generate the 3D pore pressure model, well-log-based estimated pore pressures from Eaton method is upscaled and distributed throughout the 3D structural grid using a geostatistical approach. The 3D pore pressure model shows good agreement with the well-log-based estimated pore pressure and also the measured pressure obtained from Modular formation Dynamics Tester. Keywords: Pore pressure prediction, Abnormal pressure, Well-logging, Eaton method, Pressure modeling, Geostatistic
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