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Effect of overburden pressure on determination of reservoir rock types using RQI/FZI, FZI* and Winland methods in carbonate rocks

Effect of overburden pressure on determination of reservoir rock types using RQI/FZI, FZI* and... Rock typing is an important tool in evaluation and performance prediction of reservoirs. Different techniques such as flow zone indicator (FZI), FZI and Winland methods are used to categorize reservoir rocks into distinct rock types. Generally, these methods are applied to petrophysical data that are measured at a pressure other than reservoir pressure. Since the pressure changes the pore structure of rock, the effect of overburden pressure on rock typing should be considered. In this study, porosity and permeability of 113 core samples were measured at five different pressures. To investigate the effect of pressure on determination of rock types, FZI, FZI* and Winland methods were applied. Results indicated that although most of the samples remain in the same rock type when pressure changes, some of them show different trends. These are related to the mineralogy and changes in pore system of the samples due to pressure change. Additionally, the number of rock types increases with increasing pressure. Furthermore, the effect of overburden pressure on determination of rock types is more clearly observed in the Winland and FZI* methods. Also, results revealed that a more precise reservoir dynamic simulation can be obtained by considering the reservoir rock typing process at reservoir conditions. Keywords Overburden pressure · Carbonate rocks · Rock type · Reservoir quality index · Flow zone indicator · Winland method 1 Introduction defined as a group of rocks with a similar capillary pressure curve in the drainage process, whereas PDRT is described Classification of reservoir rocks into different rock types, as a set of rocks that shows similar fluid flow behavior (Mir - called reservoir rock typing, is an essential tool in drilling, zaei-Paiaman et al. 2018). Proper application of rock typing production and especially reservoir studies. A petrophysi- provides more real dynamic reservoir behavior in simulation cal rock type is presented as a group of rock samples that models (Attar et al. 2015; Saboorian-Jooybari et al. 2015, have similar petrophysical and geological properties that 2016). Several techniques have been reported in the litera- influence fluid flow (Stolz and Graves 2003). Generally, ture to determine reservoir rock types. These techniques can petrophysical rock typing is categorized into two separate be classified into two general groups: the theoretical and the classes which are petrophysical static rock typing (PSRT) empirical methods. The theoretical methods (such as rock and petrophysical dynamic rock typing (PDRT). PSRT is quality index (RQI)/flow zone indicator (FZI) (Amaefule and Altunbay 1993), shale zone indicator (SZI) (Jongkit- tinarukorn and Tiab 1997; Nooruddin and Hossain 2011), Edited by Yan-Hua Sun modified FZI (Nooruddin and Hossain 2011), FZI* (FZI- star) (Mirzaei-Paiaman et al. 2015) and FZI** (FZI-double * Shahin Kord star) (Mirzaei-Paiaman and Saboorian-Jooybari 2016) and sh.kord@put.ac.ir PSRTI (Mirzaei-Paiaman et al. 2018)) are basically derived Aboozar Soleymanzadeh from the well-known Kozeny–Carman equation. Empirical a.soleymanzadeh@put.ac.ir methods, such as Winland (Kolodzie Jr 1980; Pittman 1992; Saeed Parvin Aguilera 2002), generate relationships between porosity, saeed.parvin.20@gmail.com permeability and a specific size of pore throat which is taken Ahwaz Faculty of Petroleum, Petroleum University from mercury injection capillary pressure tests. of Technology (PUT), Ahwaz, Iran Vol.:(0123456789) 1 3 1404 Petroleum Science (2019) 16:1403–1416 Rock type 1 Rock type 2 Rock type 3 RT 11 RT 12 RT RT 22 RT RT 21 31 32 RT 13 RT RT RT RT RT 14 23 24 34 Rock type 1 Rock type 2 Rock type 3 Extra rock type 1 Extra rock type 2 RT RT 21 22 RT RT RT RT RT RT RT RT RT RT 13 14 31 Fig. 1 Schematic of effect of pressure on rock typing process (RT1: Rock type 1, RT2: rock type 2 and RT3: rock type 3). Each circle represents a rock sample Generally, rock typing approaches are performed at a In this study, first reservoir rock typing is defined. Then, pressure other than reservoir pressure, especially at atmos- three selected methods of rock typing are applied to clas- pheric pressure. However, changes in pressure can alter the sify studied rock samples at different overburden pressures, pore structure of the rock. When pressure is applied to dif- and finally, the results of the three methods are discussed ferent rocks, they respond differently, consequently a rock thoroughly. sample in a rock type that was determined at the atmos- pheric pressure may shift to another rock type when pres- sure changes (see Fig. 1). It should be noted that the effect 2 Reservoir rock typing of overburden pressure on rock is considered in commercial simulators by the rock compressibility (C ) parameter. This Various techniques have been suggested for classification parameter describes the change of porosity with pressure. of reservoir rocks into rock types such as the J-function However, the effect of pressure on permeability is not given method, RQI/FZI technique, capillary pressure approach and as input data into the simulator. In other words, the effect of the Winland method (Soleymanzadeh et al. 2018). Among pressure on the pore structure of rock is considered by using these methods, RQI/FZI and Winland approaches are the C , whereas permeability and porosity change in different most widely used techniques of rock typing (Winland 1972; ways. Therefore, the effects of pressure on the process of Abbaszadeh et al. 1996; Svirsky et al. 2004; Biniwale 2005; rock type determination must be taken into consideration. Obeida et al. 2007; Shenawi et al. 2007; Chekani and Khar- In this work, 113 core samples from one of the carbon- rat 2009; Ye et al. 2011; Riazi 2018). However, as it is con- ate oil reservoirs in the Middle East have been categorized cluded from Mirzaei-Paiaman et al. (2018), the RQI/FZI into different rock types using RQI/FZI, Winland and FZI* method completely fails in complicated cases such as het- methods at five different pressures to investigate the effects erogeneous rocks. Therefore, they suggested that using FZI* of pressure on the process of rock type determination. It is gives more reliable results. These methods are described worth mentioning that the effect of pressure in the rock typ- here briefly, and pressure ee ff cts on these techniques of rock ing process has not yet been investigated. In other words, typing are examined in following sections. most of the research examines rock type determination at a specific pressure. 1 3 Pressure change Petroleum Science (2019) 16:1403–1416 1405 an incorrect rock typing process and inaccurate reservoir 2.1 RQI/FZI approach performance prediction. A proper solution for consider- ing pressure effect on rock type is to perform the RQI/FZI RQI/FZI has been derived from Kozeny–Carman equation which is based on assuming a porous medium as a bundle method at reservoir pressure. of capillary tubes. It is obtained by combining Poiseuille’s equation and Darcy’s law (Zhao et al. 2016; Chen and Yao 2.2 Winland method 2017). The generalized form of the Kozeny–Carman rela- tionship is given by the following equation: Winland performed mercury injection experiments on a large set of sandstone and carbonate rock samples to cor- k = (1) 2 2 2 relate porosity, permeability and the size of the pore throats. F  S (1 − ) gv His multiple regression analysis for various mercury satu- rations revealed that the best correlation coefficient (R ) is where k is permeability (mD), ϕ is porosity, F is the shape related to 35% mercury saturation. The corresponding pore factor, τ is tortuosity, and S is the surface area per unit gv throat radius of 35% mercury saturation was denoted by r35. grain volume. The Winland correlation is as follow: Rearrangement of Eq. (1) results in: � � log r35 = 0.732 + 0.588log k − 0.864log (8) k 1 = where r35 is in µm, k is uncorrected air permeability in mD, (2) (1 − ) F S s gv ϕ is porosity in percentage. r35 can be used as a basis to classify a reservoir into Amaefule and Altunbay (1993) presented FZI as Eq. (3): different rock types. All rock samples with similar r 35 con- stitute a single rock type and lie on an iso-pore throat curve. FZI = (3) F S s gv 2.3 FZI* method Also, RQI is defined as follows: The base form of Kozeny–Carman equation is obtained by RQI = 0.0314 (4) combining Poiseuille’s equation and Darcy’s law, as noted in Sect. 2.1. This form of Kozeny-Carman equation is as where k is permeability in mD. Normalized porosity (ϕ ) is follows: calculated from Eq. (5): mh k =  (9) (5) F 1 − where r is the effective or mean hydraulic unit radius. Substituting Eqs. (3) to (5) into Eq. (2) gives: mh Mirzaei-Paiaman et al. (2015) introduced FZI* from Eq. (9): RQI =  FZI (6) Taking logarithms of both sides of Eq. (6) leads to: FZI = 0.0314 (10) log RQI = log  + log FZI (7) Herein, FZI* is in µm which can be calculated for each where RQI and FZI are in µm, and ϕ is dimensionless. sample from measurement of its porosity and permeability. Equation  (7) shows that a log–log plot of RQI versus ϕ Hence, rocks with the same FZI* lie within an individual results in a straight line with unit slope. This means that group. The fluid flow behavior of this group is assumed to all rock samples with similar FZI value lie on an individual be the same. Taking logarithm from both sides of Eq. (10) straight line. Therefore, the presence of different straight leads to Eq. (11). lines implies different rock types. Each of this rock type is � � denoted by its intercept at ϕ = 1. log 0.0314 k = log  + log FZI (11) The rock typing methods were frequently used to clas- sify reservoir rocks at atmospheric pressure. It is obvious It is inferred from Eq. (11) that in a log–log scale, the plot √ √ that values of porosity and permeability in reservoir condi- of 0.0314 k versus  for an individual rock type shows tions are different from their values at atmospheric pressure. a straight line with the slope of unity and intercept of FZI* Therefore, using data at atmospheric pressure may result in at the ϕ = 1. 1 3 1406 Petroleum Science (2019) 16:1403–1416 (a) (b) 1000 40 100 30 10 20 1 10 0.1 0 Core samples Core samples Fig. 2 Porosity and permeability of 113 core samples at atmospheric conditions The value of r35 at atmospheric conditions is calculated for all samples from Eq. (8) (see Fig. 3). Table 1 summarizes the average (Ave) and median (Med) of permeability, porosity and r35, FZI and FZI at five dif- ferent overburden pressures. 4 Results and discussion The classical approach to reservoir rock typing, a semi- 0.1 log plot of permeability versus porosity (Abbaszadeh et al. Core samples 1996), leads to undesirable results in heterogeneous reser- voirs such as most carbonated reservoirs. It is noted that Fig. 3 r35 of all samples at atmospheric pressure there is not any mathematical support for this traditional method of rock typing (Mirzaei-Paiaman et  al. 2015). Fig. 4 depicts log K versus ϕ for 113 core samples at ambi- 3 Description of rock samples ent pressure. This figure confirms the inappropriateness (R = 0.4882) of the mentioned traditional technique of res- In this work, permeability–porosity data related to 113 ervoir rock typing. Therefore, it is concluded that these data carbonate core samples from a carbonate reservoir were should be classified into distinct rock types. used. These data have been obtained at different confining The first step of the rock typing process is data cluster - pressures (atmospheric pressure, 2000, 4000, 5000 and ing. There are different clustering techniques can be used 6000 psia). Porosity and permeability of these rock sam- in rock typing processes, such as discrete rock type (DRT), ples at atmospheric conditions are illustrated in Fig. 2. histogram, parabolic plots and global hydraulic element Table 1 Average and median of Pressure Permeability, ϕ r35, µm FZI, µm FZI*, µm porosity, permeability and r35 mD of the rock samples at different pressures Ave Med Ave Med Ave Med Ave Med Ave Med 14.7 10.16 0.98 0.169 0.153 0.984 0.534 0.612 0.465 0.138 0.083 2000 9.54 0.7 0.153 0.139 0.947 0.538 0.626 0.460 0.131 0.080 4000 9.26 3.51 0.15 0.135 0.920 0.505 0.611 0.461 0.127 0.073 5000 9.05 0.41 0.149 0.135 0.902 0.455 0.60 0.456 0.125 0.071 6000 8.98 0.45 0.148 0.131 0.845 0.444 0.595 0.450 0.0123 0.070 1 3 r35, µm Permeability, mD Porosity, % Petroleum Science (2019) 16:1403–1416 1407 Since, permeability mostly depends on pore throat size 25.374φ k = 0.0192e rather than pore size, the authors believe that using the Win- R = 0.4882 land method which contains pore throat size (r35) leads to a clearer description of the effect of pressure changes on the rock type determination. Whereas the RQI/FZI method is based on the Kozeny–Carman model in which the pore radius and pore throat are considered equal. In order to investigate the effect of pressure on the rock type determi- nation by the Winland method, this method was applied to rock samples at five different pressures: 14.7, 2000, 4000, 0.1 0 0.05 0.10 0.15 0.200.250.300.350.40 5000 and 6000 psia (see Figs. 8, 9, 10, 11, 12). Porosity Figures 8, 9, 10, 11 and 12 show that most of the rock samples shift to the left and downward simultaneously. In other words, this leads to change in the number of rock Fig. 4 Classical method of rock typing: log K versus ϕ types and also changing a rock sample from one rock type to another one. In addition, these figures indicate that the (Abbaszadeh et al. 1996; Corbett and Potter 2004). The DRT number of data in the low k–ϕ zone (blue circle) increases method was used in this work. with an increase in pressure. In order to investigate the effect of pressure on rock type Figure 13 depicts the number of rock samples in each of determination, the RQI/FZI method was applied to deter- the rock types at different pressures. Three points are inferred mine rock types at different pressures. These rock types are from this figure: (1) an increase in pressure increases the illustrated in Fig. 5. Comparing rock types at different pres - number of rock types: two rock types were added to the sures reveals that the rock type of core samples changes in rock types at atmospheric pressure which are indicated by various ways: EX1 and EX2 in Fig. 13. In other words, increasing pressure exacerbates the degree of heterogeneity of this dataset; (2) a) Increasing trend (shift from lower rock type to upper Increasing pressure increases the number of rock samples in one): such as core No. 51 which has been denoted by the lower rock types (EX1, RT1, RT2 and RT3), and (3) for symbol in Fig. 5. pressures greater than 4000 psia, the number of rock samples b) Decreasing trend (shift from upper rock type to lower in upper rock types (RT4, RT5, RT6, EX2) remains constant. one): for example, core No. 47 which has been shown The shift of the rock samples between different rock types by symbol in Fig. 5. (based on the Winland method) during pressure changes c) Fluctuating trend: such as core No. 19 which has been was examined, and results are reflected in Table  3. Indeed, indicated by symbol in Fig. 5. Table 3 reveals that 37% of rock samples jump from one d) No change: major part of studied samples remained in rock type to another one due to change in pressure. This the same RQI/FZI rock type. means that ignoring the effect of pressure on the determina- tion of rock types and considering k-ϕ at atmospheric pres- Table 2 presents the number of samples for each men- sure, make large errors in subsequent processes in a reservoir tioned trend. study. In order to clarify the abovementioned trends, for each Further investigations imply that 60% of rock samples trend, some samples were selected and their FZI values which had remained in the same rock type during changes were plotted versus pressure in Fig. 6. In fact, each trend in pressure are dolomitic. This may be due to lower com- in Table 2 was named according to the change in FZI value pressibility of dolomite rock samples with respect to lime- versus pressure as it is shown in Fig. 6. stone samples. Also, 82% of rock samples which shift from Figure 7 shows the number of rock samples in each rock upper curves to lower curves are limestones. It should be type. This figure reveals that the number of samples in the noted that most of these samples contain vugs. It seems rock types with low values of FZI (EX1, RT7, RT8 and RT9) that the high compressibility of these vuggy limestone increased by increasing pressure. It should be emphasized samples is the main reason of this trend of Table  3. A that rock types EX1 and EX2 did not exist at atmospheric few samples (2%) jump from lower curves to upper curves pressure and were added to the other rock types when pres- which may be related to generation of fractures in the pore sure was increased. It means that by increasing pressure the structure of these samples due to an increase in pressure. number of rock types increases. The fluctuating trend in Table  3 can be attributed to the generation of induced fractures and closeness of some 1 3 Permeability, mD 1408 Petroleum Science (2019) 16:1403–1416 1 1 0.1 0.1 0.01 0.01 0.1 1.0 0.06 0.60 Normalized porosity Normalized porosity (a) RQI vs. normalized porosity at 14.7 psia (b) RQI vs. normalized porosity at 2000 psia 0.5 0.1 0.05 0.01 0.005 0.05 0.50 0.05 0.50 Normalized porosity Normalized porosity (c) RQI vs. normalized porosity at 4000 psia (d) RQI vs. normalized porosity at 5000 psia RT1 RT2 RT3 RT4 0.1 RT5 RT6 Core 47 Core 19 0.01 Core 51 0.05 0.50 Normalized porosity (e) RQI vs. normalized porosity at 6000 psia Fig. 5 RQI/FZI methods at different overburden pressures Table 2 Four different trends due to pressure change based on the pores in successive steps of pressure changes. It is worth RQI/FZI method mentioning that 80% of samples with a fluctuating trend contain anhydrite. Further investigation is required to Trend Percentage, % Remarks explain the effect of anhydrite content on the fluctuating No change 60 58% dolomite, 52% vuggy trend of a rock sample. Figures 14, 15, 16 and 17 illustrate and 28% anhydrite four trends of Table 3: no change, decreasing, increasing Increasing 10 and fluctuating, respectively. In these four figures, arrow Decreasing 23 76% limestone, 88% vuggy Fluctuating 7 1 3 RQI, µm RQI, µm RQI, µm RQI, µm RQI, µm Petroleum Science (2019) 16:1403–1416 1409 0.8 1.2 Core 8 Core 19 Core 47 Core 63 Core 37 Core 64 Core 66 Core 109 0.7 Core 65 Core 67 1.0 Core 106 0.6 0.8 0.5 0.6 0.4 0.3 0.4 0.2 0.2 0.1 0 0 02000400060008000 02000 4000 6000 8000 Pressure, psia Pressure, psia (a) Deacreasing trend (b) Fluctuating trend 3.1 1.4 Core 5 Core 10 2.9 Core 14 Core 15 1.2 2.7 1.0 2.5 Core 89 0.8 2.3 Core 96 0.6 2.1 0.4 1.9 0.2 1.7 1.5 0 02000400060008000 02000 4000 6000 8000 Pressure, psia Pressure, psia (c) Increasing trend (d) No change trend Fig. 6 Change in FZI during increasing pressure for different trends 35 1000 14.7 psia 30 2000 psia 100 4000 psia 5000 psia 10 6000 psia 0.1 0.01 r35 = 0.05 μm r35 = 0.10 μm 0.001 r35 = 0.20 μm r35 = 0.50 μm r35 = 1.00 μm r35 = 2.00 μm 0 r35 = 5.00 μm EX2 0.0001 EX1RT1 RT2RT3 RT4RT5 RT6 EX2 RT1 RT2 RT3 RT4 RT5 RT6 Rock types 0.00001 05 10 15 20 25 30 35 40 Porosity, % Fig. 7 Number of samples in each rock types based on the RQI/FZI method Fig. 8 Flow units based on the Winland method at 14.7 psia 1 3 Number of samples FZI, µm FZI, µm FZI, µm FZI, µm Permeability, mD 1410 Petroleum Science (2019) 16:1403–1416 1000 1000 0.1 0.1 0.01 0.01 r35 = 0.05 μm r35 = 0.10 μm r35 = 0.05 μm r35 = 0.10 μm r35 = 0.20 μm r35 = 0.50 μm r35 = 0.20 μm r35 = 0.50 μm 0.001 0.001 r35 = 1.00 μm r35 = 2.00 μm r35 = 1.00 μm r35 = 2.00 μm r35 = 5.00 μm EX1 r35 = 5.00 μm EX1 RT1 RT2 RT1 RT2 0.0001 RT3 RT4 0.0001 RT3 RT4 RT5 RT6 RT5 RT6 EX2 EX2 0.00001 0.00001 05 10 15 20 25 30 35 40 05 10 15 20 25 30 35 40 Porosity, % Porosity, % Fig. 9 Rock types based on the Winland method at 2000 psia Fig. 12 Rock types based on the Winland method at 6000 psia 1000 35 14.7 psia 2000 psia 4000 psia 5000 psia 1 6000 psia 0.1 0.01 r 35 = 0.05 μm r 35 = 0.10 μm 0.001 r 35 = 0.20 μm r 35 = 0.50 μm r 35 = 1.00 μm r 35 = 2.00 μm r 35 = 5.00 μm EX1 EX1 RT1RT2 RT3RT4 RT5RT6 EX2 RT1 RT2 0.0001 RT3 RT4 RT5 RT6 Flow unit EX2 0.00001 05 10 15 20 25 30 35 40 Fig. 13 Frequency of rock types based on the Winland method Porosity, % Fig. 10 Rock types based on the Winland method at 4000 psia Table 3 Four different trends due to pressure change based on the Winland method Trend Percentage, % Remarks No change 63 60% dolomite, 54% vuggy and 30% anhydrite Increasing 2 Decreasing 31 82% limestone, 81% vuggy Fluctuating 4 80% anhydrite 0.1 0.01 r35 = 0.05 μm r35 = 0.10 μm direction indicates the path of change of rock types during r35 = 0.20 μm r35 = 0.50 μm 0.001 r35 = 1.00 μm r35 = 2.00 μm r35 = 5.00 μm EX1 pressure changes. RT1 RT2 0.0001 RT3 RT4 The value of r35 at different pressures was used to explain RT5 RT6 EX2 the observed trends in Fig. 18. This figure shows the value of 0.00001 05 10 15 20 25 30 35 40 r35 at different pressures for four different trends. (Each part Porosity, % of the figure is related to one trend in Table  3.) It is inferred Fig. 11 Rock types based on the Winland method at 5000 psia 1 3 Permeability, mD Permeability, mD Permeability, mD Number of samples Permeability, mD Petroleum Science (2019) 16:1403–1416 1411 0.1 0.01 0.001 r35 = 0.05 μm r35 = 0.10 μm r35 = 0.20 μm r35 = 0.50 μm r35 = 1.00 μm r35 = 2.00 μm Core 5 Core 6 r35 = 5.00 μm 0.0001 Core 9 Core 10 Core 7 Core 13 Core 14 Core 11 Core 15 0.00001 05 10 15 20 25 30 35 40 Porosity, % Fig. 14 Samples remain in the same rock type during pressure changes (no change trend) 0.1 0.01 0.001 r35 = 0.05 μm r35 = 0.10 μm r35 = 0.20 μm r35 = 0.50 μm r35 = 1.00 μm r35 = 2.00 μm r35 = 5.00 μm Core 20 Core 21 0.0001 Core 25 Core 27 Core 45 Core 46 Core 47 Core 54 Core 66 Core 106 0.00001 05 10 15 20 25 30 35 40 Porosity, % Fig. 15 Samples jump from upper curves to lower curves during pressure changes (decreasing trend) from this figure that, all trends in Table  3 can be interpreted pressure (see Fig. 19). Rock samples move to the left and based on the change in r35 during pressure changes. downward simultaneously, which obviously implies that Using the FZI* method, the number of rock types the quality of the majority of the rocks reduces with an increased from six to eight with an increase in overburden increase in pressure. Comparison of rock types at five 1 3 Permeability, mD Permeability, mD 1412 Petroleum Science (2019) 16:1403–1416 0.1 0.01 r35 = 1.00 µm r35 = 2.00 µm Core 78 Core 80 0.001 05 10 15 20 25 30 35 40 Porosity, % Fig. 16 Samples shift from lower curves to upper curves during pressure changes (increasing trend) 0.1 0.01 0.001 r35 = 0.05 µm r35 = 0.10 µm r35 = 0.20 µm r35 = 0.50 µm r35 = 1.00 µm r35 = 2.00 µm 0.0001 r35 = 5.00 µm Core 36 Core 39 Core 65 Core 67 Core 82 0.00001 05 10 15 20 25 30 35 40 Porosity, % Fig. 17 Samples fluctuate between different rock types during pressure changes (fluctuating trend) different pressures shows that rock types change in two The frequencies of FZI* are demonstrated in Fig. 20 trends: decreasing and fluctuating. Core 19 (symbol ) and which confirms the results obtained from the other two Core 65 (symbol ) represent decreasing and fluctuating methods. Increasing pressure causes rock types EX1 and trends, respectively. EX2 to be added to the rock types at atmospheric pressure. 1 3 Permeability, mD Permeability, mD Petroleum Science (2019) 16:1403–1416 1413 0.35 0.8 Core 20 Core 21 0.7 0.30 Core 25 Core 27 0.6 Core 45 Core 46 0.25 Core 36 Core 47 0.5 0.20 Core 65 0.4 0.15 Core 82 0.3 0.10 0.2 0.05 0.1 0 0 0 2000 4000 6000 8000 0 2000 4000 6000 8000 Pressure, psia Pressure, psia (a) Decreasing trend (b) Fluctuating trend 1.52 0.7 1.50 0.6 1.48 0.5 Core 1 Core 4 1.46 0.4 Core 6 1.44 0.3 Core 78 1.42 0.2 Core 80 1.40 0.1 1.38 0 2000 4000 6000 8000 0 2000 4000 6000 8000 Pressure, psia Pressure, psia (c) Increasing trend (d) No change trend Fig. 18 r35 changes due to an increase in pressure for four different trends of Table 3 Table 4 presents the effect of pressure on the rock typ- 5 Conclusions ing process by the FZI* method and details of observed trends due to pressure change. This table shows that, simi- The following conclusions arose from this work: lar to RQI/FZI and Winland methods, more than 50% of studied rock samples have remained in their rock types (1) Studied samples were classified into different rock types at atmospheric pressure. Furthermore, a decreasing trend using RQI/FZI, FZI* and Winland methods at five dif- is the most common trend and vuggy limestone samples ferent pressures. Different behavior was observed for are majority of the rocks which fall within this trend, as rock samples during changes in pressure. The majority observed in RQI/FZI and Winland methods. of the samples remained in the same rock type during Finally, it is noted that having a clearer picture of the pressure increases. Some of the samples shifted from rock pore structure, such as from micro-computed tomog- an upper curve to a lower curve, and a few samples raphy (Micro-CT) scans, improves the analysis of the change from a lower curve to an upper one. In addi- effect of pressure on the determination of rock types. tion, several of the rock samples showed fluctuating trends. These four different trends can be attributed to the mineralogy and change in pore structure of the stud- ied samples. 1 3 r35, μm r35, μm r35, μm r35, μm 1414 Petroleum Science (2019) 16:1403–1416 1 1 0.1 0.1 0.01 0.01 0.001 0.001 0.11.0 0.11.0 φ φ (a) FZI* rock typing at 14.7 psia (b) FZI* rock typing at 2000 psia 1 1 0.1 0.1 0.01 0.01 0.001 0.001 0.11.0 0.11.0 φ φ (c) FZI* rock typing at 4000 psia (d) FZI* rock typing at 5000 psia EX1 RT1 RT2 0.1 RT3 RT4 RT5 0.01 RT6 EX2 Core 19 0.001 Core 65 0.11.0 (e) FZI* rock typing at 6000 psia Fig. 19 Rock typing at different pressures using the FZI* method (2) Most of the rock samples which remained in the same seems that this is related to the lower compressibility rock type during pressure changes are dolomitic. It or higher density of this type of rock. 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Effect of overburden pressure on determination of reservoir rock types using RQI/FZI, FZI* and Winland methods in carbonate rocks

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Publisher
Springer Journals
Copyright
Copyright © 2019 by The Author(s)
Subject
Earth Sciences; Mineral Resources; Industrial Chemistry/Chemical Engineering; Industrial and Production Engineering; Energy Policy, Economics and Management
ISSN
1672-5107
eISSN
1995-8226
DOI
10.1007/s12182-019-0332-8
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Abstract

Rock typing is an important tool in evaluation and performance prediction of reservoirs. Different techniques such as flow zone indicator (FZI), FZI and Winland methods are used to categorize reservoir rocks into distinct rock types. Generally, these methods are applied to petrophysical data that are measured at a pressure other than reservoir pressure. Since the pressure changes the pore structure of rock, the effect of overburden pressure on rock typing should be considered. In this study, porosity and permeability of 113 core samples were measured at five different pressures. To investigate the effect of pressure on determination of rock types, FZI, FZI* and Winland methods were applied. Results indicated that although most of the samples remain in the same rock type when pressure changes, some of them show different trends. These are related to the mineralogy and changes in pore system of the samples due to pressure change. Additionally, the number of rock types increases with increasing pressure. Furthermore, the effect of overburden pressure on determination of rock types is more clearly observed in the Winland and FZI* methods. Also, results revealed that a more precise reservoir dynamic simulation can be obtained by considering the reservoir rock typing process at reservoir conditions. Keywords Overburden pressure · Carbonate rocks · Rock type · Reservoir quality index · Flow zone indicator · Winland method 1 Introduction defined as a group of rocks with a similar capillary pressure curve in the drainage process, whereas PDRT is described Classification of reservoir rocks into different rock types, as a set of rocks that shows similar fluid flow behavior (Mir - called reservoir rock typing, is an essential tool in drilling, zaei-Paiaman et al. 2018). Proper application of rock typing production and especially reservoir studies. A petrophysi- provides more real dynamic reservoir behavior in simulation cal rock type is presented as a group of rock samples that models (Attar et al. 2015; Saboorian-Jooybari et al. 2015, have similar petrophysical and geological properties that 2016). Several techniques have been reported in the litera- influence fluid flow (Stolz and Graves 2003). Generally, ture to determine reservoir rock types. These techniques can petrophysical rock typing is categorized into two separate be classified into two general groups: the theoretical and the classes which are petrophysical static rock typing (PSRT) empirical methods. The theoretical methods (such as rock and petrophysical dynamic rock typing (PDRT). PSRT is quality index (RQI)/flow zone indicator (FZI) (Amaefule and Altunbay 1993), shale zone indicator (SZI) (Jongkit- tinarukorn and Tiab 1997; Nooruddin and Hossain 2011), Edited by Yan-Hua Sun modified FZI (Nooruddin and Hossain 2011), FZI* (FZI- star) (Mirzaei-Paiaman et al. 2015) and FZI** (FZI-double * Shahin Kord star) (Mirzaei-Paiaman and Saboorian-Jooybari 2016) and sh.kord@put.ac.ir PSRTI (Mirzaei-Paiaman et al. 2018)) are basically derived Aboozar Soleymanzadeh from the well-known Kozeny–Carman equation. Empirical a.soleymanzadeh@put.ac.ir methods, such as Winland (Kolodzie Jr 1980; Pittman 1992; Saeed Parvin Aguilera 2002), generate relationships between porosity, saeed.parvin.20@gmail.com permeability and a specific size of pore throat which is taken Ahwaz Faculty of Petroleum, Petroleum University from mercury injection capillary pressure tests. of Technology (PUT), Ahwaz, Iran Vol.:(0123456789) 1 3 1404 Petroleum Science (2019) 16:1403–1416 Rock type 1 Rock type 2 Rock type 3 RT 11 RT 12 RT RT 22 RT RT 21 31 32 RT 13 RT RT RT RT RT 14 23 24 34 Rock type 1 Rock type 2 Rock type 3 Extra rock type 1 Extra rock type 2 RT RT 21 22 RT RT RT RT RT RT RT RT RT RT 13 14 31 Fig. 1 Schematic of effect of pressure on rock typing process (RT1: Rock type 1, RT2: rock type 2 and RT3: rock type 3). Each circle represents a rock sample Generally, rock typing approaches are performed at a In this study, first reservoir rock typing is defined. Then, pressure other than reservoir pressure, especially at atmos- three selected methods of rock typing are applied to clas- pheric pressure. However, changes in pressure can alter the sify studied rock samples at different overburden pressures, pore structure of the rock. When pressure is applied to dif- and finally, the results of the three methods are discussed ferent rocks, they respond differently, consequently a rock thoroughly. sample in a rock type that was determined at the atmos- pheric pressure may shift to another rock type when pres- sure changes (see Fig. 1). It should be noted that the effect 2 Reservoir rock typing of overburden pressure on rock is considered in commercial simulators by the rock compressibility (C ) parameter. This Various techniques have been suggested for classification parameter describes the change of porosity with pressure. of reservoir rocks into rock types such as the J-function However, the effect of pressure on permeability is not given method, RQI/FZI technique, capillary pressure approach and as input data into the simulator. In other words, the effect of the Winland method (Soleymanzadeh et al. 2018). Among pressure on the pore structure of rock is considered by using these methods, RQI/FZI and Winland approaches are the C , whereas permeability and porosity change in different most widely used techniques of rock typing (Winland 1972; ways. Therefore, the effects of pressure on the process of Abbaszadeh et al. 1996; Svirsky et al. 2004; Biniwale 2005; rock type determination must be taken into consideration. Obeida et al. 2007; Shenawi et al. 2007; Chekani and Khar- In this work, 113 core samples from one of the carbon- rat 2009; Ye et al. 2011; Riazi 2018). However, as it is con- ate oil reservoirs in the Middle East have been categorized cluded from Mirzaei-Paiaman et al. (2018), the RQI/FZI into different rock types using RQI/FZI, Winland and FZI* method completely fails in complicated cases such as het- methods at five different pressures to investigate the effects erogeneous rocks. Therefore, they suggested that using FZI* of pressure on the process of rock type determination. It is gives more reliable results. These methods are described worth mentioning that the effect of pressure in the rock typ- here briefly, and pressure ee ff cts on these techniques of rock ing process has not yet been investigated. In other words, typing are examined in following sections. most of the research examines rock type determination at a specific pressure. 1 3 Pressure change Petroleum Science (2019) 16:1403–1416 1405 an incorrect rock typing process and inaccurate reservoir 2.1 RQI/FZI approach performance prediction. A proper solution for consider- ing pressure effect on rock type is to perform the RQI/FZI RQI/FZI has been derived from Kozeny–Carman equation which is based on assuming a porous medium as a bundle method at reservoir pressure. of capillary tubes. It is obtained by combining Poiseuille’s equation and Darcy’s law (Zhao et al. 2016; Chen and Yao 2.2 Winland method 2017). The generalized form of the Kozeny–Carman rela- tionship is given by the following equation: Winland performed mercury injection experiments on a large set of sandstone and carbonate rock samples to cor- k = (1) 2 2 2 relate porosity, permeability and the size of the pore throats. F  S (1 − ) gv His multiple regression analysis for various mercury satu- rations revealed that the best correlation coefficient (R ) is where k is permeability (mD), ϕ is porosity, F is the shape related to 35% mercury saturation. The corresponding pore factor, τ is tortuosity, and S is the surface area per unit gv throat radius of 35% mercury saturation was denoted by r35. grain volume. The Winland correlation is as follow: Rearrangement of Eq. (1) results in: � � log r35 = 0.732 + 0.588log k − 0.864log (8) k 1 = where r35 is in µm, k is uncorrected air permeability in mD, (2) (1 − ) F S s gv ϕ is porosity in percentage. r35 can be used as a basis to classify a reservoir into Amaefule and Altunbay (1993) presented FZI as Eq. (3): different rock types. All rock samples with similar r 35 con- stitute a single rock type and lie on an iso-pore throat curve. FZI = (3) F S s gv 2.3 FZI* method Also, RQI is defined as follows: The base form of Kozeny–Carman equation is obtained by RQI = 0.0314 (4) combining Poiseuille’s equation and Darcy’s law, as noted in Sect. 2.1. This form of Kozeny-Carman equation is as where k is permeability in mD. Normalized porosity (ϕ ) is follows: calculated from Eq. (5): mh k =  (9) (5) F 1 − where r is the effective or mean hydraulic unit radius. Substituting Eqs. (3) to (5) into Eq. (2) gives: mh Mirzaei-Paiaman et al. (2015) introduced FZI* from Eq. (9): RQI =  FZI (6) Taking logarithms of both sides of Eq. (6) leads to: FZI = 0.0314 (10) log RQI = log  + log FZI (7) Herein, FZI* is in µm which can be calculated for each where RQI and FZI are in µm, and ϕ is dimensionless. sample from measurement of its porosity and permeability. Equation  (7) shows that a log–log plot of RQI versus ϕ Hence, rocks with the same FZI* lie within an individual results in a straight line with unit slope. This means that group. The fluid flow behavior of this group is assumed to all rock samples with similar FZI value lie on an individual be the same. Taking logarithm from both sides of Eq. (10) straight line. Therefore, the presence of different straight leads to Eq. (11). lines implies different rock types. Each of this rock type is � � denoted by its intercept at ϕ = 1. log 0.0314 k = log  + log FZI (11) The rock typing methods were frequently used to clas- sify reservoir rocks at atmospheric pressure. It is obvious It is inferred from Eq. (11) that in a log–log scale, the plot √ √ that values of porosity and permeability in reservoir condi- of 0.0314 k versus  for an individual rock type shows tions are different from their values at atmospheric pressure. a straight line with the slope of unity and intercept of FZI* Therefore, using data at atmospheric pressure may result in at the ϕ = 1. 1 3 1406 Petroleum Science (2019) 16:1403–1416 (a) (b) 1000 40 100 30 10 20 1 10 0.1 0 Core samples Core samples Fig. 2 Porosity and permeability of 113 core samples at atmospheric conditions The value of r35 at atmospheric conditions is calculated for all samples from Eq. (8) (see Fig. 3). Table 1 summarizes the average (Ave) and median (Med) of permeability, porosity and r35, FZI and FZI at five dif- ferent overburden pressures. 4 Results and discussion The classical approach to reservoir rock typing, a semi- 0.1 log plot of permeability versus porosity (Abbaszadeh et al. Core samples 1996), leads to undesirable results in heterogeneous reser- voirs such as most carbonated reservoirs. It is noted that Fig. 3 r35 of all samples at atmospheric pressure there is not any mathematical support for this traditional method of rock typing (Mirzaei-Paiaman et  al. 2015). Fig. 4 depicts log K versus ϕ for 113 core samples at ambi- 3 Description of rock samples ent pressure. This figure confirms the inappropriateness (R = 0.4882) of the mentioned traditional technique of res- In this work, permeability–porosity data related to 113 ervoir rock typing. Therefore, it is concluded that these data carbonate core samples from a carbonate reservoir were should be classified into distinct rock types. used. These data have been obtained at different confining The first step of the rock typing process is data cluster - pressures (atmospheric pressure, 2000, 4000, 5000 and ing. There are different clustering techniques can be used 6000 psia). Porosity and permeability of these rock sam- in rock typing processes, such as discrete rock type (DRT), ples at atmospheric conditions are illustrated in Fig. 2. histogram, parabolic plots and global hydraulic element Table 1 Average and median of Pressure Permeability, ϕ r35, µm FZI, µm FZI*, µm porosity, permeability and r35 mD of the rock samples at different pressures Ave Med Ave Med Ave Med Ave Med Ave Med 14.7 10.16 0.98 0.169 0.153 0.984 0.534 0.612 0.465 0.138 0.083 2000 9.54 0.7 0.153 0.139 0.947 0.538 0.626 0.460 0.131 0.080 4000 9.26 3.51 0.15 0.135 0.920 0.505 0.611 0.461 0.127 0.073 5000 9.05 0.41 0.149 0.135 0.902 0.455 0.60 0.456 0.125 0.071 6000 8.98 0.45 0.148 0.131 0.845 0.444 0.595 0.450 0.0123 0.070 1 3 r35, µm Permeability, mD Porosity, % Petroleum Science (2019) 16:1403–1416 1407 Since, permeability mostly depends on pore throat size 25.374φ k = 0.0192e rather than pore size, the authors believe that using the Win- R = 0.4882 land method which contains pore throat size (r35) leads to a clearer description of the effect of pressure changes on the rock type determination. Whereas the RQI/FZI method is based on the Kozeny–Carman model in which the pore radius and pore throat are considered equal. In order to investigate the effect of pressure on the rock type determi- nation by the Winland method, this method was applied to rock samples at five different pressures: 14.7, 2000, 4000, 0.1 0 0.05 0.10 0.15 0.200.250.300.350.40 5000 and 6000 psia (see Figs. 8, 9, 10, 11, 12). Porosity Figures 8, 9, 10, 11 and 12 show that most of the rock samples shift to the left and downward simultaneously. In other words, this leads to change in the number of rock Fig. 4 Classical method of rock typing: log K versus ϕ types and also changing a rock sample from one rock type to another one. In addition, these figures indicate that the (Abbaszadeh et al. 1996; Corbett and Potter 2004). The DRT number of data in the low k–ϕ zone (blue circle) increases method was used in this work. with an increase in pressure. In order to investigate the effect of pressure on rock type Figure 13 depicts the number of rock samples in each of determination, the RQI/FZI method was applied to deter- the rock types at different pressures. Three points are inferred mine rock types at different pressures. These rock types are from this figure: (1) an increase in pressure increases the illustrated in Fig. 5. Comparing rock types at different pres - number of rock types: two rock types were added to the sures reveals that the rock type of core samples changes in rock types at atmospheric pressure which are indicated by various ways: EX1 and EX2 in Fig. 13. In other words, increasing pressure exacerbates the degree of heterogeneity of this dataset; (2) a) Increasing trend (shift from lower rock type to upper Increasing pressure increases the number of rock samples in one): such as core No. 51 which has been denoted by the lower rock types (EX1, RT1, RT2 and RT3), and (3) for symbol in Fig. 5. pressures greater than 4000 psia, the number of rock samples b) Decreasing trend (shift from upper rock type to lower in upper rock types (RT4, RT5, RT6, EX2) remains constant. one): for example, core No. 47 which has been shown The shift of the rock samples between different rock types by symbol in Fig. 5. (based on the Winland method) during pressure changes c) Fluctuating trend: such as core No. 19 which has been was examined, and results are reflected in Table  3. Indeed, indicated by symbol in Fig. 5. Table 3 reveals that 37% of rock samples jump from one d) No change: major part of studied samples remained in rock type to another one due to change in pressure. This the same RQI/FZI rock type. means that ignoring the effect of pressure on the determina- tion of rock types and considering k-ϕ at atmospheric pres- Table 2 presents the number of samples for each men- sure, make large errors in subsequent processes in a reservoir tioned trend. study. In order to clarify the abovementioned trends, for each Further investigations imply that 60% of rock samples trend, some samples were selected and their FZI values which had remained in the same rock type during changes were plotted versus pressure in Fig. 6. In fact, each trend in pressure are dolomitic. This may be due to lower com- in Table 2 was named according to the change in FZI value pressibility of dolomite rock samples with respect to lime- versus pressure as it is shown in Fig. 6. stone samples. Also, 82% of rock samples which shift from Figure 7 shows the number of rock samples in each rock upper curves to lower curves are limestones. It should be type. This figure reveals that the number of samples in the noted that most of these samples contain vugs. It seems rock types with low values of FZI (EX1, RT7, RT8 and RT9) that the high compressibility of these vuggy limestone increased by increasing pressure. It should be emphasized samples is the main reason of this trend of Table  3. A that rock types EX1 and EX2 did not exist at atmospheric few samples (2%) jump from lower curves to upper curves pressure and were added to the other rock types when pres- which may be related to generation of fractures in the pore sure was increased. It means that by increasing pressure the structure of these samples due to an increase in pressure. number of rock types increases. The fluctuating trend in Table  3 can be attributed to the generation of induced fractures and closeness of some 1 3 Permeability, mD 1408 Petroleum Science (2019) 16:1403–1416 1 1 0.1 0.1 0.01 0.01 0.1 1.0 0.06 0.60 Normalized porosity Normalized porosity (a) RQI vs. normalized porosity at 14.7 psia (b) RQI vs. normalized porosity at 2000 psia 0.5 0.1 0.05 0.01 0.005 0.05 0.50 0.05 0.50 Normalized porosity Normalized porosity (c) RQI vs. normalized porosity at 4000 psia (d) RQI vs. normalized porosity at 5000 psia RT1 RT2 RT3 RT4 0.1 RT5 RT6 Core 47 Core 19 0.01 Core 51 0.05 0.50 Normalized porosity (e) RQI vs. normalized porosity at 6000 psia Fig. 5 RQI/FZI methods at different overburden pressures Table 2 Four different trends due to pressure change based on the pores in successive steps of pressure changes. It is worth RQI/FZI method mentioning that 80% of samples with a fluctuating trend contain anhydrite. Further investigation is required to Trend Percentage, % Remarks explain the effect of anhydrite content on the fluctuating No change 60 58% dolomite, 52% vuggy trend of a rock sample. Figures 14, 15, 16 and 17 illustrate and 28% anhydrite four trends of Table 3: no change, decreasing, increasing Increasing 10 and fluctuating, respectively. In these four figures, arrow Decreasing 23 76% limestone, 88% vuggy Fluctuating 7 1 3 RQI, µm RQI, µm RQI, µm RQI, µm RQI, µm Petroleum Science (2019) 16:1403–1416 1409 0.8 1.2 Core 8 Core 19 Core 47 Core 63 Core 37 Core 64 Core 66 Core 109 0.7 Core 65 Core 67 1.0 Core 106 0.6 0.8 0.5 0.6 0.4 0.3 0.4 0.2 0.2 0.1 0 0 02000400060008000 02000 4000 6000 8000 Pressure, psia Pressure, psia (a) Deacreasing trend (b) Fluctuating trend 3.1 1.4 Core 5 Core 10 2.9 Core 14 Core 15 1.2 2.7 1.0 2.5 Core 89 0.8 2.3 Core 96 0.6 2.1 0.4 1.9 0.2 1.7 1.5 0 02000400060008000 02000 4000 6000 8000 Pressure, psia Pressure, psia (c) Increasing trend (d) No change trend Fig. 6 Change in FZI during increasing pressure for different trends 35 1000 14.7 psia 30 2000 psia 100 4000 psia 5000 psia 10 6000 psia 0.1 0.01 r35 = 0.05 μm r35 = 0.10 μm 0.001 r35 = 0.20 μm r35 = 0.50 μm r35 = 1.00 μm r35 = 2.00 μm 0 r35 = 5.00 μm EX2 0.0001 EX1RT1 RT2RT3 RT4RT5 RT6 EX2 RT1 RT2 RT3 RT4 RT5 RT6 Rock types 0.00001 05 10 15 20 25 30 35 40 Porosity, % Fig. 7 Number of samples in each rock types based on the RQI/FZI method Fig. 8 Flow units based on the Winland method at 14.7 psia 1 3 Number of samples FZI, µm FZI, µm FZI, µm FZI, µm Permeability, mD 1410 Petroleum Science (2019) 16:1403–1416 1000 1000 0.1 0.1 0.01 0.01 r35 = 0.05 μm r35 = 0.10 μm r35 = 0.05 μm r35 = 0.10 μm r35 = 0.20 μm r35 = 0.50 μm r35 = 0.20 μm r35 = 0.50 μm 0.001 0.001 r35 = 1.00 μm r35 = 2.00 μm r35 = 1.00 μm r35 = 2.00 μm r35 = 5.00 μm EX1 r35 = 5.00 μm EX1 RT1 RT2 RT1 RT2 0.0001 RT3 RT4 0.0001 RT3 RT4 RT5 RT6 RT5 RT6 EX2 EX2 0.00001 0.00001 05 10 15 20 25 30 35 40 05 10 15 20 25 30 35 40 Porosity, % Porosity, % Fig. 9 Rock types based on the Winland method at 2000 psia Fig. 12 Rock types based on the Winland method at 6000 psia 1000 35 14.7 psia 2000 psia 4000 psia 5000 psia 1 6000 psia 0.1 0.01 r 35 = 0.05 μm r 35 = 0.10 μm 0.001 r 35 = 0.20 μm r 35 = 0.50 μm r 35 = 1.00 μm r 35 = 2.00 μm r 35 = 5.00 μm EX1 EX1 RT1RT2 RT3RT4 RT5RT6 EX2 RT1 RT2 0.0001 RT3 RT4 RT5 RT6 Flow unit EX2 0.00001 05 10 15 20 25 30 35 40 Fig. 13 Frequency of rock types based on the Winland method Porosity, % Fig. 10 Rock types based on the Winland method at 4000 psia Table 3 Four different trends due to pressure change based on the Winland method Trend Percentage, % Remarks No change 63 60% dolomite, 54% vuggy and 30% anhydrite Increasing 2 Decreasing 31 82% limestone, 81% vuggy Fluctuating 4 80% anhydrite 0.1 0.01 r35 = 0.05 μm r35 = 0.10 μm direction indicates the path of change of rock types during r35 = 0.20 μm r35 = 0.50 μm 0.001 r35 = 1.00 μm r35 = 2.00 μm r35 = 5.00 μm EX1 pressure changes. RT1 RT2 0.0001 RT3 RT4 The value of r35 at different pressures was used to explain RT5 RT6 EX2 the observed trends in Fig. 18. This figure shows the value of 0.00001 05 10 15 20 25 30 35 40 r35 at different pressures for four different trends. (Each part Porosity, % of the figure is related to one trend in Table  3.) It is inferred Fig. 11 Rock types based on the Winland method at 5000 psia 1 3 Permeability, mD Permeability, mD Permeability, mD Number of samples Permeability, mD Petroleum Science (2019) 16:1403–1416 1411 0.1 0.01 0.001 r35 = 0.05 μm r35 = 0.10 μm r35 = 0.20 μm r35 = 0.50 μm r35 = 1.00 μm r35 = 2.00 μm Core 5 Core 6 r35 = 5.00 μm 0.0001 Core 9 Core 10 Core 7 Core 13 Core 14 Core 11 Core 15 0.00001 05 10 15 20 25 30 35 40 Porosity, % Fig. 14 Samples remain in the same rock type during pressure changes (no change trend) 0.1 0.01 0.001 r35 = 0.05 μm r35 = 0.10 μm r35 = 0.20 μm r35 = 0.50 μm r35 = 1.00 μm r35 = 2.00 μm r35 = 5.00 μm Core 20 Core 21 0.0001 Core 25 Core 27 Core 45 Core 46 Core 47 Core 54 Core 66 Core 106 0.00001 05 10 15 20 25 30 35 40 Porosity, % Fig. 15 Samples jump from upper curves to lower curves during pressure changes (decreasing trend) from this figure that, all trends in Table  3 can be interpreted pressure (see Fig. 19). Rock samples move to the left and based on the change in r35 during pressure changes. downward simultaneously, which obviously implies that Using the FZI* method, the number of rock types the quality of the majority of the rocks reduces with an increased from six to eight with an increase in overburden increase in pressure. Comparison of rock types at five 1 3 Permeability, mD Permeability, mD 1412 Petroleum Science (2019) 16:1403–1416 0.1 0.01 r35 = 1.00 µm r35 = 2.00 µm Core 78 Core 80 0.001 05 10 15 20 25 30 35 40 Porosity, % Fig. 16 Samples shift from lower curves to upper curves during pressure changes (increasing trend) 0.1 0.01 0.001 r35 = 0.05 µm r35 = 0.10 µm r35 = 0.20 µm r35 = 0.50 µm r35 = 1.00 µm r35 = 2.00 µm 0.0001 r35 = 5.00 µm Core 36 Core 39 Core 65 Core 67 Core 82 0.00001 05 10 15 20 25 30 35 40 Porosity, % Fig. 17 Samples fluctuate between different rock types during pressure changes (fluctuating trend) different pressures shows that rock types change in two The frequencies of FZI* are demonstrated in Fig. 20 trends: decreasing and fluctuating. Core 19 (symbol ) and which confirms the results obtained from the other two Core 65 (symbol ) represent decreasing and fluctuating methods. Increasing pressure causes rock types EX1 and trends, respectively. EX2 to be added to the rock types at atmospheric pressure. 1 3 Permeability, mD Permeability, mD Petroleum Science (2019) 16:1403–1416 1413 0.35 0.8 Core 20 Core 21 0.7 0.30 Core 25 Core 27 0.6 Core 45 Core 46 0.25 Core 36 Core 47 0.5 0.20 Core 65 0.4 0.15 Core 82 0.3 0.10 0.2 0.05 0.1 0 0 0 2000 4000 6000 8000 0 2000 4000 6000 8000 Pressure, psia Pressure, psia (a) Decreasing trend (b) Fluctuating trend 1.52 0.7 1.50 0.6 1.48 0.5 Core 1 Core 4 1.46 0.4 Core 6 1.44 0.3 Core 78 1.42 0.2 Core 80 1.40 0.1 1.38 0 2000 4000 6000 8000 0 2000 4000 6000 8000 Pressure, psia Pressure, psia (c) Increasing trend (d) No change trend Fig. 18 r35 changes due to an increase in pressure for four different trends of Table 3 Table 4 presents the effect of pressure on the rock typ- 5 Conclusions ing process by the FZI* method and details of observed trends due to pressure change. This table shows that, simi- The following conclusions arose from this work: lar to RQI/FZI and Winland methods, more than 50% of studied rock samples have remained in their rock types (1) Studied samples were classified into different rock types at atmospheric pressure. Furthermore, a decreasing trend using RQI/FZI, FZI* and Winland methods at five dif- is the most common trend and vuggy limestone samples ferent pressures. Different behavior was observed for are majority of the rocks which fall within this trend, as rock samples during changes in pressure. The majority observed in RQI/FZI and Winland methods. of the samples remained in the same rock type during Finally, it is noted that having a clearer picture of the pressure increases. Some of the samples shifted from rock pore structure, such as from micro-computed tomog- an upper curve to a lower curve, and a few samples raphy (Micro-CT) scans, improves the analysis of the change from a lower curve to an upper one. In addi- effect of pressure on the determination of rock types. tion, several of the rock samples showed fluctuating trends. These four different trends can be attributed to the mineralogy and change in pore structure of the stud- ied samples. 1 3 r35, μm r35, μm r35, μm r35, μm 1414 Petroleum Science (2019) 16:1403–1416 1 1 0.1 0.1 0.01 0.01 0.001 0.001 0.11.0 0.11.0 φ φ (a) FZI* rock typing at 14.7 psia (b) FZI* rock typing at 2000 psia 1 1 0.1 0.1 0.01 0.01 0.001 0.001 0.11.0 0.11.0 φ φ (c) FZI* rock typing at 4000 psia (d) FZI* rock typing at 5000 psia EX1 RT1 RT2 0.1 RT3 RT4 RT5 0.01 RT6 EX2 Core 19 0.001 Core 65 0.11.0 (e) FZI* rock typing at 6000 psia Fig. 19 Rock typing at different pressures using the FZI* method (2) Most of the rock samples which remained in the same seems that this is related to the lower compressibility rock type during pressure changes are dolomitic. It or higher density of this type of rock. 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