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1 SPE Pore-Type Determination From Core Data Using a New Polar-Transformation Function from Hydraulic Flow Units Rodolfo Soto B. /SPE, Digitoil, Duarry Arteaga, Cintia Martin, Freddy Rodriguez / SPE,PDVSA Western Division Copyright 00, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Latin American and Caribbean Petroleum Engineering Conference in Lima, Peru, 3 December 00. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract A new sigmoidal function from polar transformation enables more accurate identification of pore types in fractured/vuggy reservoirs. The function is based on a polar transformation that separates the pore systems into two regions matrix systems and fracture/vug systems on the basis of hydraulic properties, reservoir quality index (RQI), flow-zone index (FZI), and normalized porosity. The polar transformation exhibits a hyperbolic distribution for intergranular/intercrystalline pore sample types at the point where they deviate from the trend so that we can identify pore types more accurately. Our new function has been validated from image log data from wells of Lagomar and/or Lagomedio fields and core data from different fields around the world, and we are certain that it will be of great help to the geoscientist when doing a reservoir characterization. Introduction A great number of reservoir systems are made up of different lithologies and pore types. The pore types could be matrix, fractures and vugs or a combination of these. For example, Nelson (00) defined four types of reservoirs to characterize matrix and fracture systems: Type reservoirs, where fractures provide all of the storage capacity and permeability. This type of reservoir includes the unconventional fractured granite basement reservoirs of the Cuu Long basin in offshore Southern Vietnam and the Amal reservoir in Libya. Type naturally fractured reservoirs, where the matrix has negligible permeability but contains most if not all the hydrocarbons. This type of reservoir includes the shale gas reservoirs in the United States, which contain up to 780 Tcf of gas (Franz. and Jochen, 005); the volcaniclastic reservoir in Cupen Mahuida field, Neuquén, Argentina (Zubiri and Silvestro, 007), and Agha Jari in Iran. In these reservoirs, natural fractures provide permeability and the matrix provides storage of most of the hydrocarbons. Type 3 reservoirs, where the matrix already has good primary permeability. The fractures add to the reservoir permeability and can result in considerably high flow rates. Oil is trapped in both the matrix and fractures. Examples of Type 3 reservois are the giant Kirkut field in Iraq, Ghawar field of Saudi Arabia, Gachsaran in Iran, Dukhan in Qatar, and the big Cusiana field of Colombia. These reservoirs are some of the most prolific producers. Type 4 reservoirs, where the fractures are filled with minerals. Fractures provide no additional porosity or permeability but create a significant reservoir. The definition of these four types of reservoirs, based on matrix and fracture systems, does not cover all the pore systems present in the real world, and in general, one of the potential problems when more than one pore type is present in a reservoir is related to nonreconigtion of one of the them on plug samples and reservoirs. Determining the kind of pore types in core and log data is not easy. Consequently, petrophysicists and geologists developing petrophysical models often erroneously apply the methodologies and equations designed for intergranular/intercrystalline reservoir systems to complex systems (intergranular/ intercrystalline, fracture, and/or vug pore type). However, if we have a complex pore type system, the cementation exponent, m, is not constant but variable; and changes in the cementation exponent value can greatly affect water saturation calculated by the Archie equation, affecting the original oil in place (OOIP), the reserves, and the evaluation of potential pay zones. Often, the difference between economic and noneconomic production

2 SPE depends on the time the presence of fractures is detected in the life of the field. In general, for reservoir types where storage and permeability are presented in the matrix and fractures, virtually all potential problems are related to nonreconigtion of the fracture system. Several investigators have attempted to solve this problem by developing methods from core analysis (Kamath et al., 990 Hopkins, et al., 99; Ning and Holditch, 993), well logging using a series of crossplots (Asquith 995; Soto-B. et al. 00), pressure transient analysis, and 3D seismic data. Each of those methods has certain advantages, limitations, applicability and reliability. This paper discusses a new methodology to recognize the presence of more than one pore type from permeability and porosity core data. Hydraulic Flow Unit Classification Using Reservoir Quality Index (RQI) and Flow Zone Index (FZI) The first step in this methodology is to apply the concepts of reservoir quality index (RQI) and flow unit indicator (FZI) to classify core data in hydraulic flow units (HFU) according to Amaefule et al. (993). This concept lets us average the rock properties with minimal error. In this case, the RQI and FZI parameters are calculated using the following relationships: RQI matrix = * k core core....() z = ( core /( core) () FZI = RQI...(3) z log( RQI) ( ) = log(fzi) + log...(3a) Z Therefore, a plot of RQI versus z on log-log scale will delineate the flow units with FZI constant for each unit. However, these equations were developed assuming a matrix system where the porosity and permeability are intergranular/ intercrystalline, which means they may not be sufficient for more complex formations. Polar Arm and Angle The second step is to validate whether the hydraulic flow units belong to more than one pore system. We found that a good way to identify the pore type of the core data is to make a transformation of FZI and z called the polar arm, r: [ ( FZI ) ] + r *....(4) = z and calculate the polar angle as: θ polar = ATAN(FZI)....(5) If we plot the polar arm vs. polar angle (Fig. ), we can see that polar transformation exhibits a hyperbolic distribution for intergranular/intercrystalline pore samples. On that plot we have used core data from reservoirs in different parts of the world: Venezuela, the USA, Iraq and Saudi Arabia. Those core data sets also include some fractured/vuggy data sets known from lab data. It is easy to see that fractured/vuggy pore samples deviate from the hyperbolic trend and let us identify pore types more accurately. We have developed a sigmoidal function that separates the plot into two regions: { + exp[ -( r-c) /D]} θ A+B/.... (6) polar region = where A = ; B = ; C = ; D =

3 SPE Above the sigmoidal function, the data fall into the fracture or vuggy system, and below that region, they belong to the intergranular/intercrytalline system. If RQI, z, and FZI are calculated using a spreadsheet, it is easy to also calculate Eqs. 4, 5, and 6 and compare the values from Eqs. 5 and 6: if the value calculated from Eq. 5 is less than or equal to the value calculated from Eq. 6, the core data are intergranular, but if not the core data pore type could be fractured or vuggy. We also validated this sigmoidal function with image log data from the data set of the Lagomar and Lagomedio fields in the Cretaceous formation at Lake of Maracaibo in Venezuela..8.6 Sigmoidal Function to Differenciate Pore Type Systems Fracture/Vuggs polar angle, ATAN(FZI) Intercrystalline USA RESERVOIR ARAB RESERVOIR IRAK RESERVOIR CRETACEOUS LAKE- ALL PORETYPE MODEL_SIGMOIDAL SVS-5_DATE FRACTURE DESCRIPCIÓN SVS-5_DATE INTERGRANULAR DESCRIPCION VLA-56_DATE LOG IMAGEN VUGGY VLA-56_DATE LOG IMAGEN FRACTURE VLA-56_DATE LOG IMAGEN INTERGRANULAR Polar Arm, r,z*(fzi +) / Fig. Sigmoidal function diferentiates pore type systems from core data using polar transformation of FZI and z. Flow Properties Determination for Fracture Pore Systems According to Tiab et al. (993), for a naturally fractured or vuggy reservoir system, permeability is given as a function of total porosity, specific surface area, and m as follows: k = S m+ t gv F S ( t )....(7) Therefore, following the hydraulic flow units concept, Ohen et al. (00) defined RQI for fractured systems as k FRQI = 0.034,....(8) m- t and therefore the relationship between RQI and FZI defined in Eq. 3 for a fractured system is as follows: log( FRQI) ( ) = log(frzi) + log....(9) Z And using the same concept of hydraulic units, HU, for a matrix pore system, a plot of FRQI versus z on a log-log scale will delineate the flow units (Soto B. et al. 993, 00).

4 4 SPE Determination of Hydraulic Flow Units in a Complex Pore System: Cretaceous Formation at Maracaibo Lake The cretaceous formation at Maracaibo Lake contains carbonate reservoirs with a variety of pore types (see Soto-B. et al. 00) such as intergranular/intercrystalline, vugs and fractures. To determine the hydraulic flow units, we used core permeability and porosity from Wells VLA-7, VLA-978, VLA-56, and UD-79 from Lagomar field and Well SVS-5 from Lagomedio field. Some of that data was reported from the core laboratory as fractured and vuggy and was validated with image logs (see Fig. ). To verify the reported data and recognize the presence of various pore types from the other lab, we applied Eqs. through 6 and put the results into Fig.. Then, to determine the hydraulic flow units, we applied the procedure explained by Soto B. et al. )(using the Eqs. through 3 for intercrystalline pore systems and Eqs. 8 and 9 for fracture systems. We found hydraulic flow units that represent all of the pore system types: five hydraulic units for intercrystalline systems, five for fractures, and one for vugs (Fig. 3) Ejemplo Example FM APON FM, Cotejo PHIvuggy PHIfracture and y PHIvuggy PHIfracture con Registro matching de log Imagen image FMI of VLA-56 well VLA56 Fig. Fracture and vuggy pore types from cores compared with the formation microimaging (FMI) log in the VLA-56 well Hydraulic Flow Units: all Pore Type Systems Cretaceus, Maracaibo Lake Fracture Flow Units.000 Vug Flow Units RQI Intercrystalline Flow Units z HU_F HU_F HU3_F HU4_F HU5_F HU6_Interc HU7_Interc HU8_Interc HU9_Interc HU0_interc HU_VUG Fig.3 The hydraulic flow units appear clearly in the pore complex system for Cretaceous Formation at Lake of Maracaibo. Table shows the ranges or limits of FZI and RQI for fractures and intergranular pore and rock types. From this rock typing discrimination, we were able to determine a complex permeability model using fuzzy logic to predict the permeability for all

5 SPE of the pore-type systems in these reservoirs. Table Ranges of FZI and RQI for Fracture and Intergranular Pore and Rock Type Characterization of Rock Typing Cretaceous Formation PORE TYPE ROCK TYPE Range of Values of FZI and RQI FZI>59 RQI>0 4<FZI<=59 3<RQI<= <FZI<=4 <FZI<=4 0<FZI<= FZI> <FZI<= <FZI<= <FZI<=0.49 0<FZI<=0.308 <RQI<=3 0.3<RQI<= 0<RQI<=0.3 RQI> <RQI<= <RQI<= <RQI<= <RQI<= Fracture system Intergranular system Conclusion We have found that a plot of the the polar arm, r, against the polar angle, θ polar, exhibits a hyperbolic distribution for intergranular/intercrystalline pore samples, so that fractured/vuggy pore samples deviate from the trend and let us identify pore types more accurately. The polar angle, θ polar, comes from the polar-transformation of the flow zone index, FZI, and z. A new sigmoidal function from that polar-transformation separates the pore systems into two regions: matrix systems and fracture/vug systems. This new methodology enabled us to discriminate the presence of more than one pore type from permeability and porosity core data. When this occurs, the hydraulic flow units are calculated more accurately and reduce the uncertainty in developing confident permeability and water saturation models or any other implication in the development of petrophysical models. Nomenclature ATAN = arctangent m = cementation exponent e = effective porosity core = core porosity t = total porosity K = permeability K core = core permeability Sgv = grain specific surface area Fs = pore throat shape factor FRQI = reservoir quality index for fractured rock system. FRZI = flow zone index for fractured rock system. FZI = flow zone index for intercrystalline rock system. r = polar arm RQImatrix = reservoir quality index for intercrystalline rock system. θ polar = polar angle

6 6 SPE References Amaefule, J.O., Altunbay, M., Tiab, D., Kersey, D.G., and Keelan, D.K Enhanced Reservoir Description: Using Core and Log Data to Identify Hydraulic (Flow) Units and Predict Permeability in Uncored Intervals/Wells. Paper SPE 6436 presented at the Annual Technical Conference and Exhibition, Houston, 3-6 October. Asquith, G Determining Carbonate Pore Types From Petrophysical Logs, Department of Geosciences and the Center for Applied Petrophysical Studies, Texas Teach University, Lubbock, Texas. Franz, J.H. Jr. and Jochen, V Shale Gas. Schlumberger White Paper. Hopkins et al. 99 Hopkins, C. W., Ning, x., and Lancaster, D. E.: " Reservoir Engineering and Treatment Design Technology - A Numerical Investigation of Laboratory Transient Pulse Testing for Evaluating Low Permeability, Naturally Fractured Core Samples," a Topical Report (Jan. - June 99) submitted to Gas Research Institute, 8600 West Bryn Mawr Avenue, Chicago, IL 6063, GRI contract No , Recipient's Accession No. GRI Kamath, J., Boyer, R. E., and Nakagawa, F. M. 990: " Characterization of Core Scale Heterogeneities Using Laboratory Pressure Transients," paper SPE 0575 presented at the 65th Annual Technical Conference and Exhibition of the Society of petroleum Engineers held in New Orleans, LA,Sep Ohen, H.A., Enwere, P., and Daltaban, S. 00. The Role of Core Analysis Data in the Systematic and Detailed Modeling of Fractured Carbonate Reservoir Petrophysical Properties To Reduce Uncertainty in Reservoir Simulation. SCA00-49 Nelson, R.A. 00. Geologic Analysis of Naturally Fractured Reservoir, nd Edition, Gulf Professional Publishing. Ning, X., Holditch, S. and Lee,W.J Texas A&M Univesity, The Measurement of Matrix and Fracture Properties in Naturally Fractured Cores. SPE 5898 presented at the SPE Rocky Mountain Regional/Low Permeability Reservoirs Symposium held in Denver, CO, U.S.A., April -4. Soto B., R., Arteaga, D., Martin, C., and Rodriguez, F. 00. Carbonate Pore Type Indentification Using Fuzzy Logic and Open HoleLogs; Case of Study: Cretaceous Formation in Lake Maracaibo. Paper IBP30_0 presented at the Rio Oil & Gas Expo and Conference 00, Rio de Janeiro, 3-6 September. Soto B., R., Garcia, J.C., Torres, F., and Perez, G.S Permeability Prediction Using Hydraulic Flow Units and Hybrid Soft Computing Systems. Paper SPE 7455-MS presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October. Soto B.,R., Torres, F., Arango, S., and Cobaleda, G. 00. Improved Reservoir Permeability Models From Flow Units and Soft Computing Techniques: A Case Study, Suria and Reforma-Libertad Fields, Colombia. Paper SPE 6965 presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, 5-8 March. Tiab, D Modern Core Analysis, Vol. -Theory, Core Laboratories, Houston, Texas. Zubiri, M. and Silvestro, J Fracture Modeling in a Dual Porosity Volcaniclastic Reservoir: A Case Study of the Precuyo Group in Cupen Mahuida Field, Neuquén, Argentina. Paper presented at the AAPG Annual Convention, Long Beach, California, -4 April.