ENRECAP roject Enhanced research capacity to meet VIETNAM future oil and gas challenges in Vietnam PETRO Petro ietnam
An Official Publication of the Vietnam National Oil and Gas Group Vol 10 - 2017
ISSN-0866-854X
EXPANDING OIL AND GAS EXPLORATION AND PRODUCTION AREAS PETROVIETNAM JOURNAL IS PUBLISHED MONTHLY BY VIETNAM NATIONAL OIL AND GAS GROUP
ENRECA Project Enhanced research capacity to meet VIETNAM future oil and gas challenges in Vietnam PETRO Petro ietnam
An Official Publication of the Vietnam National Oil and Gas Group Vol 10 - 2017
IISSN-0866-854XSSN-0866-854X
EXPANDING OIL AND GAS EXPLORATION AND PRODUCTION AREAS
EDITOR-IN-CHIEF Dr. Nguyen Quoc Thap
DEPUTY EDITOR-IN-CHIEF Dr. Le Manh Hung Dr. Phan Ngoc Trung
EDITORIAL BOARD MEMBERS Dr. Hoang Ngoc Dang Dr. Nguyen Minh Dao BSc. Vu Khanh Dong Dr. Nguyen Anh Duc MSc. Tran Hung Hien MSc. Vu Van Nghiem MSc. Le Ngoc Son Eng. Le Hong Thai MSc. Nguyen Van Tuan Dr. Phan Tien Vien Dr. Tran Quoc Viet Dr. Nguyen Tien Vinh Dr. Nguyen Hoang Yen
SECRETARY MSc. Le Van Khoa M.A. Nguyen Thi Viet Ha
DESIGNED BY Le Hong Van
MANAGEMENT Vietnam Petroleum Institute
CONTACT ADDRESS Floor M2, VPI Tower, Trung Kinh street, Yen Hoa ward, Cau Giay district, Ha Noi Tel: (+84-24) 37727108 * Fax: (+84-24) 37727107 * Email: [email protected] Mobile: 0982288671 Cover photo: Cam Lam - Nha Trang. Photo: Le Khoa
Publishing Licence No. 100/GP-BTTTT dated 15 April 2013 issued by Ministry of Information and Communications FOCUS FOCUS
Prime Minister Nguyen Xuan Phuc: Deputy Prime Minister Trinh Dinh Dung: PETROVIETNAM TO STAND FIRM IN THE DUNG QUAT REFINERY IS THE LEVER MIDST OF DIFFICULTIES OF QUANG NGAI’S ECONOMY On 19 October 2017, eporting to the Deputy capacity (106 - 108% on average). Prime Minister, General BSR has focused on implementing On 12 October 2017, at the Government’s headquarters, Prime Minister Nguyen Deputy Prime Minister Trinh RDirector of BSR Tran solutions to optimise production Xuan Phuc worked with key leaders of the Vietnam Oil and Gas Group to evaluate Dinh Dung paid a working Ngoc Nguyen said Dung Quat operation; promoting scientific the results of implementation of the production and business plan in 2017 and the visit to Binh Son Refining and Refinery has always been operating research, with primary emphasis deployment of key oil and gas projects. Petrochemical Co. Ltd. (BSR). stably, reaching the optimal on energy savings, and optimising
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SCIENTIFIC RESEARCH
PETROLEUM EXPLORATION & PRODUCTION PETROLEUM PROCESSING PETROLEUM ECONOMICS & MANAGEMENT
14. Application of deep learning in 51. Testing antibacterial effect of 59. Energy efficiency in predicting fracture porosity silver nanoparticles Vietnamese enterprises: The on sulfate-reducing bacteria predominance of gas consumers 23. Different forms of Gassmann equation and implications for the estimation of rock properties 30. Merging of 3D seismic data 40. Quick pre-stack seismic inversion to predict reservoir properties at a gas and condensate field in Nam Con Son basin 45. Application of geochemical technique to reduce allocation cost for commingled production wells from multiple reservoirs CONTENTS
FOCUS PETROLEUM EXPLORATION & PRODUCTION
APPLICATION OF DEEP LEARNING IN PREDICTING FRACTURE Prime Minister Nguyen Xuan Phuc: POROSITY Pham Huy Giao, Kushan Sandunil Geo-exploration & Petroleum Geoengineering Program, Asian Institute of Technology (AIT) Petrovietnam to stand firm in the midst of difficulties ...... 4 Email: [email protected]
Summary
Deep learning (DL) neural network analysis is the latest development from the Artificial Neural Network (ANN) and it is being used more and more in petroleum engineering. In this study, the way to develop a new DL model for well log analysis was attempted and Deputy Prime Minister Trinh Dinh Dung: successfully implemented using well log data from a location in the Cuu Long basin, Vietnam. Three sets of analyses were conducted, i.e., the first analysis set with a single hidden layer ANN model, the second analysis set with multiple hidden layer ANN modeland the third with a DL neural network model. The DL-predicted porosity for a fractured granite basement reservoir of an oil field in the Cuu Long Dung Quat Refinery is the lever of Quang Ngai’s economy ...... 8 basin was found in the range from 0.0 to 0.082, showing a good match with the conventionally-calculated values. The final deep earningl model consists of 5-input layers of gamma ray (GR), deep resistivity (LLD), sonic (DT), density (RHOB) and neutron porosity (NPHI), having 5 hidden neuron layers with 14 neurons per layer. It is worth noting that the transfer function of the rectified linear unit (ReLU), typical for a deep learning analysis, was implemented to replace the common sigmoidal transfer function, ensuring the successful application of DL model. Last but not least, the problem of vanishing gradient specific for a DL neural network model was also explained indetails in PVEP and FPT co-operate this paper. Key words: Deep Learning (DL), Artificial Neural Network (ANN), fracture porosity, well log analysis, fractured granite basement, Cuu Longbasin. in research and development of new technologies ...... 11
1. Introduction complex version of artificial neural networks. It is now widely used in image recognition, voice processing and language translation. The concept of soft computing was first put forward by a paper named “Possibility Artificial neural networks are used to build a connection between theory and soft data analysis” [1]. While input and output data that helps predict the outputs of a set of new NEWS hard computing needs a precisely defined inputs (Figure 1). analytical model, soft computing is tolerant Application of deep learning in petrophysics is still in its infancy of uncertainty, imprecision, approximation stage. Classic neural networks commonly use one hidden layer, whereas and partial truth. This is a method designed deep learning uses multiple hidden layers. The use of multiple hidden to model and solve real world problems, layers can cause a phenomenon called vanishing gradient problem. Negotiations on Ca Voi Xanh project to be sped up ...... 68 which cannot be modelled mathematically. Deep learning network is obtained by eliminating this problem. The concept of soft computing was designed based on the concept of human Input layer Hidden layer brain functioning. X1 Σ Soft computing consists of few principal Nhon Trach 2 Power Plant components as listed below [2]: X2 Σ - Fuzzy logic; Output layer reaches production milestone of 30 billion kWh ...... 68 X Σ Σ k - Evolutionary computation; 3 - Neural computing;
X4 Σ Activation Transfer - Probabilistic reasoning. function function Petrovietnam co-operates with potential partners ANN has been developed to simulate X5 Σ the neural structure and activity of the Activation Transfer human brain. Deep learning (DL) is a function function Figure 1. Architecture of an ANN to manufacture polyester fiber ...... 69 Date of receipt: 21/8/2017. Date of review and editing: 21/8 - 5/9/2017. Date of approval: 4/10/2017.
14 PETROVIETNAM - JOURNAL VOL 10/2017 14 Petrovietnam and PVEP sign outsourcing contract for operation of Blocks 01 & 02 ...... 70 VPI signs co-operation agreement with Industrial University of Tyumen ...... 70 Amended gas sales and purchase and transportation contracts signed for Block 06-1, Nam Con Son basin ...... 71 Proposed measures to boost production in Bir Seba project, Algeria ...... 72 Phu My Fertilizer Plant meets target 2 months ahead of schedule ...... 72 KVT meets LPG and Bach Ho condensate production targets ahead of time ...... 73 Ca Mau Gas Processing Plant supplies first LPG shipment ...... 73
30 FOCUS
Prime Minister Nguyen Xuan Phuc: PETROVIETNAM TO STAND FIRM IN THE MIDST OF DIFFICULTIES
On 12 October 2017, at the Government’s headquarters, Prime Minister Nguyen Xuan Phuc worked with key leaders of the Vietnam Oil and Gas Group to evaluate the results of implementation of the production and business plan in 2017 and the deployment of key oil and gas projects.
4 PETROVIETNAM - JOURNAL VOL 10/2017 PETROVIETNAM
Prime Minister Nguyen Xuan Phuc works with key leaders of the Vietnam Oil and Gas Group. Photo: Quang Hieu/VGP t the meeting, the Prime of the country. Especially, the Prime In addition, Petrovietnam produced Minister confi rmed that Minister highly appreciated the great 8.25 billion m3 of gas, 17.09 billion Athe oil and gas sector contribution of Petrovietnam to the kWh of electricity, 1.48 million tons of plays an important role in socio- State Budget even in the diffi cult urea (exceeding the plan by 10.6%), economic development and has period. and 5.03 million tons of petroleum made huge contributions to the products (exceeding the plan by According to Petrovietnam’s national economy. 20.7%). President and CEO Nguyen Vu Truong Throughout the development Son, the Group’s production and With average oil price reaching process, the Party and the State business targets were all overfulfi lled USD 54.3/barrel, the total revenue of have given guidance by resolutions, from 2 - 21%. the Group amounted to VND 404.2 strategies, master plans and the Prime trillion, representing an increase of In the fi rst 10 months of 2017, Minister’s decisions to orientate the 15% compared to the 10-month oil production reached 13.01 million development of the Vietnam Oil and plan and 10% compared to the same tons, exceeding the 10-month plan Gas Group. period of 2016. Petrovietnam has by 2.8% and representing 85.6% contributed VND 76.1 trillion to the In fact, the Vietnam Oil and Gas of the yearly plan. The Group has State Budget for the fi rst 10 months Group has built a united team of produced 11.39 million tons of oil of 2017, which is 2% higher than the professional and highly qualifi ed in the country (exceeding the plan yearly plan. staff to overcome challenges and by 323 thousand tons, equivalent develop the oil and gas industry into to 3%); and 1.63 million tons of oil Also at the meeting, the Prime a key economic and technical sector abroad (exceeding the plan by 1.7%). Minister listened to the proposals and
PETROVIETNAM - JOURNAL VOL 10/2017 5 FOCUS
Prime Minister Nguyen Xuan Phuc highly appreciates the great contribution of the oil and gas industry to the State Budget even in the diffi cult period. Photo: Quang Hieu/VGP
PETROVIETNAM OVERFULFILS STATE BUDGET CONTRIBUTION PLAN FOR 2017 In the fi rst 10 months of 2017, oil production reached 13.01 million tons, exceeding the 10-month plan by 2.8% and representing 85.6% of the yearly plan. The Group has produced 11.39 million tons of oil in the country (exceeding the plan by 323 thousand tons, equivalent to 3%); and 1.63 million tons of oil abroad (exceeding the plan by 1.7%). In addition, Petrovietnam produced 8.25 billion m3 of gas, 17.09 billion kWh of electricity, 1.48 million tons of urea (exceeding the plan by 10.6%), and 5.03 million tons of petroleum products (exceeding the plan by 20.7%). With average oil price reaching USD 54.3/barrel, the total revenue of the Group amounted to VND 404.2 trillion, representing an increase of 15% compared to the 10-month plan and 10% compared to the same period of 2016. Petrovietnam has contributed VND 76.1 trillion to the State Budget for the fi rst 10 months of 2017, which is 2% higher than the yearly plan. recommendations of Petrovietnam’s Prime Minister Nguyen Xuan Prime Minister Nguyen Xuan key offi cials to solve diffi culties Phuc stressed: “We are responsible to Phuc requested the Vietnam Oil and obstacles so as to enable the the country and the people”, so each and Gas Group to concentrate all its continued development of the oil person, each unit must continue resources on completing the 2017 and gas industry in the coming to unite and strive to build on past targets; review and develop the period. In particular, the Prime achievements to contribute to the 2018 production and business plan Minister wanted Petrovietnam “to development of the Vietnam Oil and in line with the country’s growth stand fi rm in the midst of diffi culties”. Gas Group. objectives; and continue with the
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Bach Ho fi eld. Photo: Minh Tri equitisation process in accordance On behalf of more than 55,000 implement the tasks assigned by the with the plan approved by the employees of the oil and gas sector, Government, contributing to the stability and further development of Prime Minister. The Group focuses Petrovietnam’s President and CEO Nguyen Vu Truong Son confi rmed the Petrovietnam. on deploying key projects such as Nguyen Hoang that the Group will continue to Ca Voi Xanh, Block B, and Dung Quat uphold the will, the responsibility, Refi nery upgrading and expansion the competences and the tradition project. of the oil and gas staff to successfully
PETROVIETNAM - JOURNAL VOL 10/2017 7 FOCUS
DDeputyeputy PrimePrime MMinisterinister TTrinhrinh DinhDinh Dung:Dung: DUNG QUAT REFINERY IS THE LEVER OF QUANG NGAI’S ECONOMY On 19 October 2017, eporting to the Deputy capacity (106 - 108% on average). Prime Minister, General BSR has focused on implementing Deputy Prime Minister Trinh RDirector of BSR Tran solutions to optimise production Dinh Dung paid a working Ngoc Nguyen said Dung Quat operation; promoting scientifi c visit to Binh Son Refining and Refi nery has always been operating research, with primary emphasis Petrochemical Co. Ltd. (BSR). stably, reaching the optimal on energy savings, and optimising
8 PETROVIETNAM - JOURNAL VOL 10/2017 PETROVIETNAM
Dung Quat Refi nery. Photo: BSR the operational conditions of Budget, and earned an after-tax strategic investors to further invest in technological processes to reduce profi t equal to 341.7% of the yearly the development of petrochemical production costs and improve plan. and deep-processing sub-sectors in order to improve its production and production and business effi ciency. BSR informed that the company business effi ciency. In the fi rst 9 months of 2017, will launch the initial public off ering BSR produced 4.4 million tons of (IPO) in the 4th quarter of 2017 BSR will work on the investors’ products, and sold nearly 4.4 million according to the plan and expects proposals in detail for the purpose tons. BSR gained a total turnover of to sell only 5 - 6% of its shares. After of launching a successful IPO and VND 54.982 billion and contributed that, BSR will continue to seek and subsequent sale of shares to strategic VND 6,522 billion to the State select institutional investors and investors, especially Petrolimex, right
PETROVIETNAM - JOURNAL VOL 10/2017 9 FOCUS
Deputy Prime Minister Trinh Dinh Dung listens to reports on the progress of the Dung Quat Refi nery upgrading and expansion project. Photo: BSR after the plan is approved by the Deputy Prime Minister Trinh fl uctuations. At the same time, BSR Prime Minister. Dinh Dung affi rmed that the Dung needs to continue with product Quat Refi nery is the heart of Dung restructuring, investment, and With the aim of increasing Quat Economic Zone, which is the corporate governance to cut down the capacity and the fl exibility in economic lever of Quang Ngai expenditures on input and move the processing of crude oil, and province and the Central region of towards reduction of production upgrading technology to Vietnam. This is a demonstration that costs. ensure production of high- Vietnam can master the technology quality petroleum products and Emphasising the Government’s of oil refi ning and independently enhance competitiveness, BSR point of view that the State has the produce petroleum products to is implementing the project to responsibility to help businesses serve the economy. upgrade and expand Dung Quat operate eff ectively, the Deputy Refi nery to bring its capacity from Deputy Prime Minister Trinh Prime Minister affi rmed that the the current 6.5 million tons/year to Dinh Dung requested BSR to Government will support BSR to 8.5 million tons/year. The project has improve production capacity as complete its IPO as well as to upgrade been under way for 29/78 months. well as production and business and expand the Dung Quat Refi nery as scheduled. The contract for the EPC package is effi ciency in order to increase the Hong Minh expected to be signed in April 2018 competitiveness. BSR has been with the plant to be ready for start- effi cient in production but should up on 18 December 2021. not underestimate the market
10 PETROVIETNAM - JOURNAL VOL 10/2017 PETROVIETNAM PVEP and FPT co-operate in research and development of new technologies
PVEP and FPT sign a co-operation agreement on research and development of new technologies. Photo: PVEP
Petrovietnam Exploration nder this agreement, and select one of PVEP’s on-going FPT will provide support projects to pilot the application of Production Corporation Uto PVEP to digitalise new technological solutions. (PVEP) and FPT Joint Stock its operations in order to enhance FPT Chairman Truong Gia Binh Company (FPT) on 17 October the effi ciency of its oil and gas said that only industry 4.0 would 2017 signed a co-operation production, minimise downtime due help solve the specifi c problem in agreement on research to system incidents, save costs and the oil and gas sector which is how reduce risks for PVEP. and development of new to optimise production while still technologies in the fields of The two sides will promote ensuring the fi eld safety, cutting oil and gas exploration and long-term co-operation and apply costs of equipment investment and production. technological solutions on the basis shortening the exploration period. of the most advanced technologies The oil and gas sector with the such as internet of things (IoT), big application of high technologies and data, artifi cial intelligence (AI) and techniques has already been near the data science. In the coming period, optimum level, a few percentage of the two sides will meet, discuss improvement could bring signifi cant
PETROVIETNAM - JOURNAL VOL 10/2017 11 FOCUS
DR. NGO HUU HAI - PRESIDENT & CEO OF PVEP: The approach and application of 4.0 industrial technologies must be fast, neat and accurate to avoid falling behind. PVEP will pilot the application of new technologies, fi rst in wells with simple structure, then expand to other projects at home and abroad. economic benefi ts. He also asserted that in the oil and gas sector and software technology, the intellect and competences of Vietnamese people can compete in equal terms with other countries in the world. In the context where oil and gas companies are all facing diffi culties due to low oil prices, the application of advanced technological tools and solutions will facilitate more accurate data analysis, contribute to effi ciency improvement and cost optimisation in oil exploration and production.
Dr. Ngo Huu Hai, President & CEO technologies to reduce investment 6 million per day), we only need of PVEP said that as oil exploration costs and operating expenses, while an increment of 1% in output to always has risks, especially when oil increasing the continuous production decide on deployment”. Considering prices have remained at a low level time to 98 - 99%. for a long time together with other industry 4.0 as a very urgent matter, corollaries from previous unsuccessful “With the current scale of PVEP’s Dr. Ngo Huu Hai emphasised that projects, PVEP has to improve its operation (average production of the approach and application of 4.0 management level, promote the nearly 100 thousand barrels per industrial technologies must be fast, application of advanced and new day with estimated turnover of USD neat and accurate to avoid falling
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Dai Hung fi eld. Photo: PVEP behind. PVEP will pilot the application development for new technologies FPT will have the opportunity to of new technologies, fi rst in wells in oil exploration and production. access the specialised technical and with simple structure, then expand to PVEP will have an opportunity to gain technological environment of oil other projects at home and abroad. quick access to the latest trends of and gas exploration and production to test and improve the scope of By signing this agreement, industry 4.0, optimal solutions which applications, on that basis to better its are the strength of FPT, and then PVEP and FPT will strengthen services and technological solutions. their comprehensive and long- prepare resources to take advantage Manh Hoa term co-operation in research and of advanced technology. Whereas
PETROVIETNAM - JOURNAL VOL 10/2017 13 PETROLEUM EXPLORATION & PRODUCTION
APPLICATION OF DEEP LEARNING IN PREDICTING FRACTURE POROSITY Pham Huy Giao, Kushan Sandunil Geo-exploration & Petroleum Geoengineering Program, Asian Institute of Technology (AIT) Email: [email protected]
Summary
Deep learning (DL) neural network analysis is the latest development from the Artifi cial Neural Network (ANN) and it is being sedu more and more in petroleum engineering. In this study, the way to develop a new DL model for well log analysis was attempted and successfully implemented using well log data from a location in the Cuu Long basin, Vietnam. Three sets of analyses were conducted, i.e., the fi rst analysis set with a single hidden layer ANN model, the second analysis set with multiple hidden layer ANN model and the third with a DL neural network model. The DL-predicted porosity for a fractured granite basement reservoir of an oil fi eld in het Cuu Long basin was found in the range from 0.0 to 0.082, showing a good match with the conventionally-calculated values. The fi nal deeplearning model consists of 5-input layers of gamma ray (GR), deep resistivity (LLD), sonic (DT), density (RHOB) and neutron porosity (NPHI), having 5 hidden neuron layers with 14 neurons per layer. It is worth noting that the transfer function of the rectifi ed linear unit (ReLU), typical for a deep learning analysis, was implemented to replace the common sigmoidal transfer function, ensuring the successful application of DL model. Last but not least, the problem of vanishing gradient specifi c for a DL neural network model was also explained in details in this paper. Key words: Deep Learning (DL), Artifi cial Neural Network (ANN), fracture porosity, well log analysis, fractured granite basement, Cuu Long basin.
1. Introduction complex version of artifi cial neural networks. It is now widely used in image recognition, voice processing and language translation. The concept of soft computing was fi rst put forward by a paper named “Possibility Artifi cial neural networks are used to build a connection between theory and soft data analysis” [1]. While input and output data that helps predict the outputs of a set of new hard computing needs a precisely defi ned inputs (Figure 1). analytical model, soft computing is tolerant Application of deep learning in petrophysics is still in its infancy of uncertainty, imprecision, approximation stage. Classic neural networks commonly use one hidden layer, whereas and partial truth. This is a method designed deep learning uses multiple hidden layers. The use of multiple hidden to model and solve real world problems, layers can cause a phenomenon called vanishing gradient problem. which cannot be modelled mathematically. Deep learning network is obtained by eliminating this problem. The concept of soft computing was designed based on the concept of human Input layer Hidden layer brain functioning. X1 Σ Soft computing consists of few principal components as listed below [2]: X2 Σ - Fuzzy logic; Output layer X Σ Σ k - Evolutionary computation; 3 - Neural computing;
X4 Σ Activation Transfer - Probabilistic reasoning. function function
ANN has been developed to simulate X5 Σ the neural structure and activity of the Activation Transfer human brain. Deep learning (DL) is a function function Figure 1. Architecture of an ANN
Date of receipt: 21/8/2017. Date of review and editing: 21/8 - 5/9/2017. Date of approval: 4/10/2017.
14 PETROVIETNAM - JOURNAL VOL 10/2017 PETROVIETNAM
Conventional methods to estimate the primary obtained from core analysis data. Optimal porosity (or intergranular) porosity of clastic reservoirs are not prediction was given by an ANN model with one hidden helpful to estimate the fracture porosity. Therefore, layer having 15 neurons. Optimal permeability prediction petrophysicists keep trying to fi nd new techniques for was found by an ANN model having one hidden layer with fracture porosity estimation. 9 neurons. Nakapraves [8] carried out a research, using two ANN models to predict reservoir porosity for a clastic oil Kohli and Arora [3] did a research on application of fi eld in the northern Pattani basin, Gulf of Thailand. In the artifi cial neural networks for well log analysis. They used fi rst model, GR, LLD, RHOB, NPHI and DT logs were used as data from three wells including gamma ray (GR), resistivity input data. In the second model, the seismic attributes such (RES), density (RHOB), neutron porosity logs (NPHI) as the as dip, azimuth, instantaneous phase and relative acoustic input data and the core permeability as the target data for impedance were used as input parameters. Core porosity the ANN analysis. Kohli and Arora also concluded that ANN was used as the target values in both models. It was found could be relied upon for determination of characteristics that the ANN model trained using seismic attributes gave even in areas where cores are not available. The estimation far better results than the model trained using well log was completely data-driven and did not require any prior data. Foongthoncharoen [9] did a research on prediction of assumption. More than that the method was cost eff ective permeability and water saturation using neuron networks since it did not require labourious core analysis. and fuzzy logic for a clastic reservoir in the Gulf of Thailand. Korjani et al. [4] carried out a research on a new Permeability and water saturation were predicted for two approach of reservoir characterisation using deep wells. Well log data of gamma ray, deep resistivity, medium learning neural networks for Kern River fi eld located in resistivity, density and neutron porosity were used as San Joaquin valley, California. The fi eld consists of nine input parameters. Core permeability and water saturation production formations. The study was carried out using calculated by using Indonesian model were used as target data from 473 wells. Well log data such as deep resistivity, values. Between the two models of ANN and fuzzy logic, medium resistivity, and neutron porosity were used as the latter one gave better results. Sakulluangaram [10] did input parameters. The authors came to conclude that a research on petrophysical modelling for the Miocene deep learning is an eff ective method for characterisation Sand in the South Fang basin, northern Thailand, where of a reservoir with large volumes of data. he predicted porosity distribution of a well (well A) using the data from a nearby well (well B). GR, RHOB, NPHI and Guler et al. [5] carried out a study on predicting DT logs were used as the input parameters. Porosity values relative permeability of a hydrocarbon reservoir using an predicted were similar to the porosity obtained from well artifi cial neural network. First, they found what should be logs. Thanh [11] did an ANN prediction of porosity using the key input data, i.e., common fl uid and rock properties the integrated well log and seismic attribute data including were selected as the input data set. In addition, when refl ection amplitude, instantaneous amplitude, its 1st and selecting these data, they focused on parameters that 2nd derivative, as well as instantaneous phase, frequency, could be measured in laboratories and/or easily obtained dominant frequency and refl ectivity as the input for from literature. Based on the results of their study, the an ANN model. The fi nal porosity output determined authors concluded that with the increase in the number using a Bayesian Regulation training algorithm gave the of property-based input parameters, the effi ciency of the best match with the highest R-value of 0.86. Kano [12] ANN model was enhanced. predicted porosity for a fractured basement reservoir In the last decade, researchers from the Asian Institute with well log data from two wells using a conventional of Technology (AIT) had conducted a number of studies method proposed by Elkewidy and Tiab [13] and fi ve soft on application of soft computing in well log analysis computing techniques, including ANN, Fuzzy Inference using fuzzy logic and neural computing [6]. For example, System with Mamdani’s style, Fuzzy Inference System with Witthayapradit [7] carried out a research on an integrated Sugeno’s style, Fuzzy Subtractive Clustering and Adaptive petrophysical study using well logging data for enhancing Neuro-Fuzzy Inference System (ANFIS). These Artifi cial a gas fi eld in the Gulf of Thailand. He originally used gamma Neural Networks gave the best prediction. Duangngern ray (GR), deep resistivity (LLD), density (RHOB), neutron [14] did a fuzzy analysis to predict the eff ective porosity of porosity (NPHI) and sonic log (DT) as the input parameters a clastic reservoir in the Pattani basin, Thailand. He applied to predict porosity and permeability. Target values were various Fuzzy logic techniques, using well logging and
PETROVIETNAM - JOURNAL VOL 10/2017 15 PETROLEUM EXPLORATION & PRODUCTION
core data of two wells. Among three fuzzy techniques Deep learning is a machine learning algorithm which used, the fuzzy subtractive clustering was found the best could learn complex functions. The learning process of for prediction of eff ective porosity with low value of root deep learning algorithm fi lters important information mean square error, high value of R2 and R-value. Wang from raw data in a systematic way. [15] carried out a research on ANN-based prediction of Deep learning architecture consists of multiple fractured rock mass hydraulic conductivity for the Frieda hidden layers comparing to shallow neural networks River copper-gold mine in Papua New Guinea. In this that used to have one hidden layer. With multiple hidden study, the backpropagation neural network (BPNN) was layers, a problem called vanishing gradient occurs during trained to successfully map the relationship between back propagation, thus any deep learning network should indicative rock parameters and hydraulic conductivity be able to overcome this problem. using a variety of rock data sets collected in the site Deep learning networks, like other ANN’s, have a investigation of a feasibility study for the study mine. Input predicted and an expected (target) value. The intention data were selected for ANN analysis included lithology, of learning is to make the diff erence between the target weathering, fracturing, unconfi ned compressive strength and the expected values as small as possible (which (UCS), defect angle and rock quality designation (RQD). we assign as the goal). To understand how vanishing Diff erent numbers of input parameters (4, 5 and 6) were gradient occurs, a simple deep neural network to predict used to build the ANN model. Wang [15] also investigated a cost function with single neuron in each hidden layer is the eff ect of various transfer functions on the ANN model considered as shown in Figure 2, where x is the input, W , by using log-sigmoid, tan-sigmoid and purelin. 1 W2, W3, and W4 are the weights, b1, b2, b3, and b4 are the 2. Vanishing gradient problem of multiple deep biases, and J is the cost function of the network. learning neural network analysis In Figure 3, J represents the cost function, which is a function of the diff erence between predicted and W W W W expected values. Artifi cial neural networks usually make X 1 b 2 b 3 b 4 b J 1 2 3 4 use of the following sigmoid function as the activation Figure 2. Simple multi-layer ANN model after introducing the cost function function or transfer function: (1) Where: S(n): The sigmoid function n is variable One of the reasons for popular use of the sigmoid function is that its derivative can be easily calculated by the very value of sigmoid function as follows: ‘ (2) Where: Figure 3. Graphical representation of sigmoid function [12] S' (n): The derivative of sigmoid function
W Vanishing gradient problem 1 (a) X b1 J
One hidden layer b 1 W W 1 2 b (b) X b1 2 J
Two hidden layers W W W 1 2 b 3 X b1 2 b3 J (c)
Three hidden layers Figure 4. Diff erent ANN modes: (a) ANN model with one hidden layer; (b) ANN model with two hidden layers; and (c) ANN model with three hidden layers Figure 5. Graphical representation of the derivative of sigmoid function [12]
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The derivative of sigmoidal function is plotted in Where: Figure 5 which shows it lies between 0 and 0.25. S: Sigmoid function; By the chain rule, the derivative of the error (J) with z2: Input to the second hidden layer; respect to the fi rst weight (W1), can be written as: z3: Input to the third hidden layer; (3a) z4: Input to the output layer.
(3b) (5a)
(3c) (5b) (3d)
(3e) (5c) Where: The maximum value that the derivative of the aout: Output of the ANN network; sigmoid function can take is 0.25 (and the minimum is 0). a : Output from the fi rst hidden layer; 1 The weights are selected based on Gaussian distribution,
a2: Output from the second hidden layer; thus the value of weights always lies between -1 and 1.
a3: Output from the third hidden layer; When the values of each derivative are multiplied by each other, the resultant will give a small value less W : Weights of the input layer; 1 than 1. Imagine if the number of hidden layers increased,
W2: Weights of the fi rst hidden layer; becoming deeper and deeper, the number of derivative terms will increase as well as the number of terms to be W3: Weights of the second hidden layer; multiplied (Equations 5a-c), making the resulting value of W : Weights of the third hidden layer; 4 smaller and smaller. This shows how early layers x: Inputs of the ANN; learn slower with the increase of the number of hidden S: Sigmoid function. layers. A similar approach can be implemented to show Considering the following derivative components in that latter layers learn faster by obtaining the derivation of cost function with respect to W . Equation 3a 3 Vanishing gradient occurs because of using the sigmoid function. To overcome the problem, an alternative activation function known as rectifi ed linear unit (ReLU) was introduced in deep learning. In Figure 2, by denoting the inputs to the 4th, 3rd, 2nd hidden layers as z4, z3, z2 respectively, one can write the 3. Methodology of this study following relationships: The well log data were collected from a well drilled (4a) into a fractured granite basement (FGB) reservoir in an oil (4b) fi eld of Cuu Long basin for a depth range from 2,525m to 3,015m including gamma ray (GR), deep resistivity (LLD), (4c) shallow resistivity (LLS), interval transit time (DT), bulk density (RHOB), neutron porosity (NPHI), photoelectric (4d) factor (PEF), and caliper (CAL). Figure 6 shows the general (4e) workfl ow of this study.
(4f) The total and fracture porosity for the target data set was calculated using the approach suggested by Elkewidy
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The formation factor (F): R a Well log data collec on Deep learning model with 5 F (7a) R (GR, LLD, LLS, RHOB, DT, input parameters and 150 NPHI, PEF, CAL) training examples having rec fied linear unit (ReLU) and fracture intensity index (FII): as the transfer func on (7b)
Single hidden layer model By rearranging Equation 7b, the matrix porosity is: with 5 input parameters and (7c) 150 training examples Single hidden layer, having log-sigmoid as the mul ple hidden layer and As fracture porosity ( f) is: transfer func on deep learning models for 500, 1000, 2000 and 3000 (7d) training examples by replacing m in 7d with 7c, one has: (7e) Using different combina ons of input parameters on the For a double porosity fractured reservoir with single layer model to find the 100% formation fl uid saturation one can write: best input Results comparision (7f)
Where Rma is the resistivity of 100% fl uid
saturated matrix and Ro is the resistivity of the total Mul ple hidden layer model system (matrix voids + fracture voids) being 100% with 5, 6, 7, 8 input fl uid saturated. parameters with 150 training Rearranging Equation 7f and combining with examples having log-sigmoid as the transfer func on Equation 7a one gets:
(7g) Figure 6. Flow chart of the study’s methodology and Tiab [13] as shown in Equations 6a and 6b below. Matrix (7h) density was assumed as 2.71g/cc since formation density and porosity were measured in limestone scale. Assuming a = 1 and with further rearranging Equation 7h one has: (6a)
(7i) (6b) In case, one can neglect water resistivity (R ) in Where: w Equation 7i since Rma >> Rw, the porosity partitioning coeffi cient can be expressed as: Øt: Total porosity (fraction); NPHI : Neutron porosity (fraction); (7j) By replacing 7j with 7b one has: PHID: Porosity calculated from bulk density (fraction); (7k) RHOB: Bulk density of formation (g/cc); Further replacing Equation 7k with 7c and 7e one
ρma: Matrix density, assumed to be 2.71g/cc (since gets: measured in limestone scale); (7l) ρ : Fluid density, assumed to be 1g/cc (water). f Hence the target (fracture porosity) will be: An equation to calculate fracture porosity of a fractured (7m) reservoir can be derived by using the following steps:
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Where: method proposed by Elkewidy and Tiab [13] as explained above in detail (Equation 7f). Øf: Fracture porosity (fraction); 4. Results and discussion Øma: Matrix porosity (fraction); m: Cementation exponent. In Analysis I, ANN models with a single hidden layer were analysed. Firstly, 16 models numbered from MI1 to MI16 (Table 1) were tested with Partitioning coeffi cient (ν), matrix 150 training examples to fi nd out the best combination of fi ve input porosity (Ø ), and fracture porosity (Ø ) ma f parameters out of 8 well log data used (GR, LLD, LLS, DT, RHOB, NPHI, PEF are calculated by Equations 7j, 7l and 7m, and CAL). It was found that the model with the basic 5-input sets (GR, LLD, respectively [13]: RHOB, NPHI and DT), 12 neurons of the hidden layer and running for 150 Data from the depth interval of 2,515 training examples (Figure 7) gave the best prediction of fracture porosity - 3,015m were selected and analysed for with the least prediction error (Table 2). Four more models in Analysis each 0.125m interval. Three conducted I, numbered from MI17 to 20 (Table 1), were tested with the number analyses are summarised in Table 1 and of training examples increased from 150 to 500; 1,000; 2,000 and 3,000 named as I, II and III. In analysis I, only respectively, and with diff erent number of neurons in the hidden layer. fi ve inputs out of the eight well log However, prediction of fracture porosity did not improve (Figure 7). parameters were investigated. A total of In Analysis II, various multiple hidden layer ANN models (Table 1) 16 combinations, denoted as MI1 to 16 were tested to see if the prediction of fracture porosity would increase (Table 1), will be done to fi nd out the best with the increasing number of hidden layers using the basic set of fi ve combination of 5. Based on the criteria proposed by Guller et al. [5], the combination of fi ve selected input parameters having the least prediction error at 150 training examples will be further tested for training examples of 500; 1,000; 2,000 and 3,000, respectively. In analysis II, with multiple hidden layer ANN model, the fi rst issue to be studied is what would happen if one uses more than 5 input parameters, for example 6, 7 and 8 input parameters. After that, the eff ect of the number of training examples will be also Figure 7. Fracture porosity calculated by single hidden layer ANN models, Analysis I, with 150; 500; 1,000; 2,000 investigated. In analysis III, a deep learning and 3,000 training examples as seen from left to right model will be developed from the best multiple hidden layer model found in Analysis II by replacing the sigmoidal transfer functions with the rectifi ed linear units (RELU). The deep learning (DL) models will also be investigated for various number of hidden layers as well as number of training examples, i.e., 50; 500; 1,000; 2,000 and 3,000. The fracture porosity values predicted by all of the ANN and DL models in analyses I, II and III will be plotted and compared between them as well with the Figure 8. Fracture porosity calculated by multiple hidden layer ANN models, Analysis II, with 150; 500; 1,000; fracture porosity values calculated by the 2,000 and 3,000 training examples as seen from left to right
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input parameters as found in Analysis I. It was found that model MII1 In Analysis III, deep learning models with 4 hidden layers and 12 neurons per layer gave the least prediction were developed using the ReLU transfer error of 16.46% after 150 training examples. When the number of training function and tested. A total of fi ve models examples increased from 150 to 500; 1,000; 2,000 and 3,000 respectively, numbered from MIII1 - MIII5 as seen in the prediction of fracture porosity was not improved either (Figure 8). Table 1 were run with the basic set of fi ve input parameters (GR, LLD, RHOB, NPHI and DT) and with training examples of 150; 500; 1,000; 2,000 and 3,000. The MIII5 model was found as the best with 5 hidden layers and 14 neurons per layer for the case of 3,000 training examples. The deep learning predicted fracture porosity in the range from 0 - 0.082, which matched with those calculated by the conventional method by Elkewidy and Tiab [13]. 5. Some concluding remarks Figure 9. Fracture porosity calculated by deep learning models, Analysis III, with 150; 500; 1,000; 2,000 and 3,000 training examples In this study, a three-step approach Table 1. Summary of ANN and deep learning models in this study Type of Neural Number of training Input Parameters Transfer function Networks (NN) examples Analysis Model Model Single Multiple Modifi Increased Deep Basic Rectified Remarks No. No. Code hidden hidden ed number 150 500 1,000 2,000 3,000 Log- learning five Linear layer layer five of inputs sigmoid (DLNN) inputs Unit (ANN) (ANN) inputs 6 7 8
Five basic inputs 1 MI1 V V V V GR, LLD, RHOB,
NPHI, DT MI2- Each parameter 2-6 V V V V MI6 replaced by a CAL MI7- Each parameter 7-11 V V V V I MI11 replaced by a LLS MI12- Each parameter 12-16 V V V V MI16 replaced by a PEF 17 MI17 V V V V Five basic inputs
18 MI18 V V V V Five basic inputs 19 MI19 V V V V Five basic inputs 20 MI20 V V V V Five basic inputs 21 MII1 V V V Five basic inputs
CAL, LLS, and PEF MII2- 22-24 V V V V added to basic 5- MII4 inputs CAL and LLS, CAL MII5- and PEF and LLS 25-27 V V V V MII7 and CAL added to II basic 5-inputs All 8 parameters 28 MII8 V V V V used 29 MII9 V V V Five basic inputs
30 MII10 V V V Five basic inputs 31 MII11 V V V Five basic inputs
32 MII12 V V V Five basic inputs 33 MIII1 V V V Five basic inputs
34 MIII2 V V V Five basic inputs
III 35 MIII3 V V V Five basicinputs 36 MIII4 V V V Five basic inputs
37 MIII5 V V V Five basic inputs
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Table 2. Average prediction error for diff erent number of neurons in single hidden layer ANN models, Analysis I, with 150; 500; 1,000; ,0002 and 3,000 training examples Neurons No. Number of hidden layers Model Model in the Training No. code hidden examples 3 4 5 6 7 8 9 10 11 12 13 14 15 layer 150 1 MI1 13 36 17 20 20 21 19 21 17 10 32 20 20 12 500 17 MI17 1,284 1,305 817 1,665 1,345 2,504 2,326 2,301 2,123 1,568 1,996 4,168 1,973 5 1,000 18 MI18 1,152 799 879 702 932 876 635 1,088 870 738 2,914 909 1,713 9 2,000 19 MI19 1,302 20,642 1,284 5,767 7,078 5,782 5,622 5,203 3,240 22,832 3,972 4,025 16,131 5 3,000 20 MI20 1,050 2,173 694 712 3,360 1,576 1,476 2,186 9,003 6,397 1,655 818 4,537 14
Table 3. Average prediction error for diff erent number of neurons in multiple hidden layer ANN models, Analysis II, with 150; 500; 1,000; 2,000 and 3,000 training examples Number of hidden layers Neurons No. Model Model Hidden in the Training No. code layers hidden examples 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 layer 150 21 MII1 19 22 16 34 22 31 18 47 29 38 23 33 40 23 48 31 44 70 66 4 12 500 29 MII9 1,503 3,355 2,313 1,882 1,499 1,222 452 994 3,123 2,842 2,079 8,410 595 1,927 475 1,106 1,752 450 1,236 19 5 1,000 30 MII10 1,045 948 477 841 735 559 566 605 493 267 545 480 556 534 513 380 627 1,012 356 11 9 2,000 31 MII11 1,045 4,016 462 961 46,535 5,058 3,127 803 4,983 2,427 3,512 606 1,683 2,691 2,307 1,530 4,548 3,558 833 4 5 3,000 32 MII12 3,804 882 405 387 2,717 2,197 1,503 1,223 429 1,304 1,691 290 417 1,244 762 700 573 1,280 1,315 5 14
Table 4. Average prediction error for diff erent number of neurons in deep learning model References with 150; 500; 1,000; 2,000 and 3,000 training examples Number of Number of 1. Lotfi A.Zadeh. Fuzzy logic, neural networks, and Model Training neurons per hidden soft computing. Communications of the ACM. 1994; 37(3): code examples hidden layer layers p. 77 - 84. MIII1 150 12 4 2. R.C.Chakraboty. Fundamentals of neural network. MIII2 500 5 19 Artifi cial Intelligence. 2010. MIII3 1,000 9 11 3. A.Kohli, P.Arora. Application of artifi cial neural MIII4 2,000 5 4 networks for well logs. International Petroleum Technology MIII5 3,000 14 5 Conference. 19 - 22 January, 2014. 4. M.Korjani, Andrei Popa, Eli Grijalva, Steve Cassidy, was successfully conducted to develop deep learning I.Ershaghi. A new approach to reservoir characterization models to predict the fracture porosity of a fractured using deep learning neural networks. SPE Western Regional granite basement (FGB) reservoir in the Cuu Long basin Meeting, Anchorage, Alaska, USA. 23 - 26 May 2016. for the depth interval from 2,515m to 3,015m. The facture porosity was found in a range from 0.0 to 0.084, which 5. B.Guler, T.Ertekin, A.S.Grader. An artifi cial neural is matching quite well with the values calculated using network based relative permeability predictor. Journal of the conventional method by Elkewidy and Tiab [13]. The Canadian Petroleum Technology. 2003; 42(4). results of this study showed that for the large volumes 6. P.H.Giao. Application of ANN in petrophysics. of well data (number of training examples) the more Lecture notes, Asian Institute of Technology, Bangkok, traditional ANN models with a single hidden layer could Thailand. 2008. not work well, but the DL model could. Thus, to apply 7. T.Witthayapradit. Formation evaluation using more eff ectively the neural network analyses in analysis of integrated well logging data for a gas fi eld in the Gulf of well log data at the industrial scale, one may try to employ Thailand. Master thesis, Asian Institute of Technology, the DL models with multiple hidden neuron layers and Bangkok, Thailand. 2009. ReLU transfer function instead of one-hidden layer ANN models. 8. N.Nakapraves. Application of ANN analysis in prediction of reservoir porosity for an oil fi eld in the Northern
PETROVIETNAM - JOURNAL VOL 10/2017 21 PETROLEUM EXPLORATION & PRODUCTION
Pattani basin. Master thesis, Asian Institute of Technology, thesis, Asian Institute of Technology, Bangkok, Thailand. Bangkok, Thailand. 2011. 2014. 9. T.Foongthoncharoen. Prediction of permeability 13. T.I.Elkewidy, D.Tiab. An application of conventional and water saturation using neuron networks and fuzzy well logs to characterize naturally fractured reservoirs with logics for a clastic reservoir in the Gulf of Thailand. Master their hydraulic (fl ow) units; a novel approach. SPE Gas thesis, Asian Institute of Technology, Bangkok, Thailand. Technology Symposium, Calgary, Canada. 1998. 2012. 14. D.Duangngern. Application of Fuzzy Analysis to 10. C.Sakulluangaram. Petrophysical modelling for the predict the eff ective porosity in a clastic reservoir, Pattani Miocene sand in the South Fang basin. Master thesis, Asian basin. Master thesis, Asian Institute of Technology, Institute of Technology, Bangkok, Thailand. 2013. Bangkok, Thailand. 2015. 11. D.V.Thanh. Prediction of porosity by ANN analysis 15. Y.Wang. ANN-based prediction of fractured rock integrating well log and seismic attribute data for an oil mass hydraulic conductivity for the Frieda river copper-gold fi eld in the Cuu Long basin, off shore Vietnam. Professional mine in Papua New Guinea. Master thesis, Asian Institute of Master Research Study, Asian Institute of Technology, Technology, Bangkok, Thailand. 2016. Bangkok, Thailand. 2013. 16. R.Kapur. The vanishing gradient problem. A Year 12. N.Kano. Soft computing - Based prediction of of Artifi cial Intelligence. 2016. porosity for a fractured granite basement reservoir. Master
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DIFFERENT FORMS OF GASSMANN EQUATION AND IMPLICATIONS FOR THE ESTIMATION OF ROCK PROPERTIES Tran Trung Dung1, Carl H.Sondergeld2, Jean-Claude Roegiers2 1Phu Quoc POC 2University of Oklahoma Email: [email protected]
Summary
Three new equivalent forms of Gassmann equation are presented that are useful when the unknown parameters are the Biot- Willis coeffi cient, the dry bulk modulus, and/or the grain matrix bulk modulus. We apply these equations to several sets of laboratory measurements to determine the profi les of grain matrix bulk modulus and Biot-Willis coeffi cient as functions of applied pressure, and perform a Monte Carlo simulation to examine the eff ect of uncertainty and/or measurement errors on the calculated grain matrix bulk modulus and Biot-Willis coeffi cient. The results show that the calculated grain matrix bulk modulus is relatively constant with applied diff erential pressure (up to 50MPa). However, it is very sensitive to the uncertainty of dry and saturated bulk modulus values. Thus, the presented new forms of Gassmann equation can be used to eff ectively quantify the uncertainty of dry and saturated bulk modulus (and subsequently, the seismic velocities) in fl uid identifi cation, fl uid substitution, or reservoir monitoring applications. Key words: Gassmann equation, bulk moduli, Biot-Willis coeffi cient, sensitivity analysis.
1. Introduction Berryman [5] gave a concise derivation of Gassmann equations for an isotropic and homogeneous medium The Gassmann equations [1] have been used using the quasi-static poroelastic theory. Other extensively in the oil and gas industry for fl uid identifi cation forms of Equation (1) can be found in Mavko et al. [6]. and reservoir monitoring applications, despite its various Zimmerman [7] presented an equivalent form in terms assumptions [2, 3]. The fi rst Gassmann equation provides of compressibility. However, Equation (1) is probably the the relationship between the saturated bulk modulus most intuitive in describing the eff ect of fl uid presence on of a rock and its dry frame bulk modulus, porosity, bulk the bulk modulus. modulus of the mineral matrix, and bulk modulus of the pore-fi lling fl uid. Whereas, the second Gassmann White and Castagna [8] argued that, since all input equation simply states that the shear modulus of the rock parameters for Gassmann equations carry some degrees is independent of the presence of the saturating fl uid: of uncertainty, a fl uid modulus inversion should be performed using a probabilistic approach. Artola and K α 2 f Alvarado [9] evaluated the eff ect of uncertainty of K = K + (1) sat dry K diff erent input parameters and showed that the computed f φ + ()α − φ compressional velocity of a saturated rock is most sensitive K m to uncertainties in the rock bulk density and the dry bulk G=G sat dry (2) and shear moduli, while other parameters (porosity, the grain matrix and fl uid bulk moduli) have negligible eff ects. Where α is the Biot-Willis coeffi cient [4]: K Note that the three parameters: dry frame modulus dry (3) α =1− (Kdry), Biot-Willis coeffi cient (α), and grain matrix bulk K m modulus (Km) are related by Equation (3); in many instances The moduli are related to the seismic velocities and they are unknown. The fl uid saturated bulk modulus (Ksat) density by: and fl uid bulk modulus (Kf) can also be unknown (e.g. in ⎛ 2 4 2 ⎞ fl uid substitution problem). As a result, ad-hoc and empirical K = ρ ⎜V − Vs ⎟ (4) ⎝ p 3 ⎠ correlations have been proposed to address this problem. There are many instances Biot-Willis coeffi cient is assumed G = ρV 2 s (5) to be 1 due to the lack of a better estimate. For sandstone
Date of receipt: 20/9/2017. Date of review and editing: 20/9 - 5/10/2017. Date of approval: 5/10/2017.
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at high diff erential pressure (40MPa), Han and Batzle [10] Therefore, instead of having two non-linear equations proposed α to be a polynomial function of porosity: for two unknowns (α and Km), we reduce the problem to α = 3.206φ − 3.349φ 2 + 1.143φ 3 (6) one simple quadratic equation, Equation (7), that always gives one physically realistic solution. In this study, we present 3 new equivalent forms of This provides an independent methodology to Gassmann equation that are useful for diff erent scenarios calculate the grain matrix bulk modulus of a rock from SCAL of available data. We apply these equations to several laboratory acoustic measurements of dry and saturated sets of laboratory measurements. A stochastic simulation rock samples. Traditionally, the grain matrix bulk moduli is performed to examine the eff ect of uncertainty and/ are estimated from averages of the rock mineralogical or measurement errors on calculated grain matrix bulk composition (e.g. Voigt-Reuss-Hill average or Hashin- modulus and Biot-Willis coeffi cient. Shtrikman bounds). These bounds may carry large 2. The new equivalent Gassmann equations uncertainties since many minerals, especially clays, have a high variance in their bulk modulus values depending 2.1. When (K , K , K , and φ) are known dry sat f on the measurement conditions [12, 13]. We can further This is generally the case for laboratory measurements postulate that: (a) the grain matrix calculated from on dry and wet rock samples (e.g. dry and brine saturated Gassmann equation (using Equations (8) to (12)) must lie acoustic velocities are measured as functions of diff erential between the two bounds obtained from mixture theory, pressure along with rock porosity). In this case we can and (b) the calculated grain matrix values are insensitive rewrite Equation (1) as a function of Biot-Willis coeffi cient to the fi rst order to the applied pressure. Equations (7) to α (see Appendix A for a detailed derivation): (11) can also be used to verify the applicability of existing empirical or ad-hoc correlations (such as Equation (6) to ⎛ K ⎞ ⎛ K ⎞⎛ K ⎞ 2 dry dry ⎜ dry ⎟ α − (φ + 1)⎜1− ⎟α +φ⎜1− ⎟ 1− = 0 (7) estimate Biot-Willis coeffi cient) for diff erent rocks. ⎜ K ⎟ ⎜ K ⎟⎜ K ⎟ ⎝ sat ⎠ ⎝ sat ⎠⎝ f ⎠ 2.2. When (Ksat1, Ksat2, Kf1, Kf2, and φ) are known Equation (7) is a quadratic equation A2 + B + C = 0, This case can be encountered in the fi eld. The same where all coeffi cients can be readily calculated. rock can be fully saturated with brine in one well while A = 1 (8) having oil or gas in another well; or it can have varying ⎛ K ⎞ dry saturations in the same well. Acoustic logs, and density B1= −(φ + 1)⎜ − ⎟ (9) ⎜ K ⎟ - porosity logs are available. In this case, Kdry, Km, and α ⎝ sat ⎠ are unknown in a system of three non-linear equations ⎛ K ⎞⎛ K ⎞ dry dry (two Equations (1) for two diff erent saturation fl uids and C1= φ ⎜1− ⎟⎜ − ⎟ (10) ⎜ ⎟⎜ ⎟ Equation (3)). Starting from Equation (7) instead, we end Ksat K f ⎝ ⎠⎝ ⎠ up with (see Appendix B for detailed derivations): This simple quadratic equation has two solutions: ⎛ 1 1 ⎞ ⎛ 1 1 ⎞ φ ⎜ − ⎟K =φ⎜ − ⎟ − − B ± ∆ 2 ⎜ K K K K ⎟ dry ⎜ K K ⎟ α = , where ∆ = B4− AC (11) ⎝ sat 1 f1 sat2 f 2 ⎠ ⎝ f1 f 2 ⎠ 1,2 2A (13) ⎛ 1 1 ⎞ ⎜ ⎟ However, Berryman and Milton [11] showed that α is []α ()φ+1 −φ ⎜ − ⎟ ⎝ Ksat1 Ksat2 ⎠ physically bounded between 0 and 1. Equations (9) and We can write Equation (13) in a more convenient form (10) show that B is negative since Kdry < Ksat, and C is also for numerical calculations: negative since Kf < Kdry for consolidated rocks. This means − B + ∆ Δ = B2 - 4AC > B2 and thus, α = is the only 1 2A ⎛ K K ⎞ ⎛ ⎞ ⎜ sat2 sat1 ⎟ ⎜ 1 1 ⎟ possible solution since α is negative. φ − K = φ − K K 2 ⎜ K K ⎟ dry ⎜ K K ⎟ sat1 sat2 ⎝ f 1 f 2 ⎠ ⎝ f 1 f 2 ⎠ The corresponding grain matrix bulk modulus then (14) can be calculated from Equation (3): + ()K − K []α (φ+ 1) − φ K sat1 sat2 dry Km = (12) 1− α Kdry, α, and Km can now be calculated very quickly
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using a simple iteration using Equation (14) and Equation And applying this α to Equation (3) gives Kdry. This is
(7) as follows: equivalent to the Kdry solution of Zhu and McMechan [14]. - Step 1: Make an initial guess, for example: 3. Numerical applications K×dry = 0.5 min{}Ksat1, Ksat2 3.1. Han and Batzle’s sandstone data - Step 2: Use guessed Kdry value in Equation (7) to fi nd two Biot-Willis coeffi cients αf1 and αf2 (for two saturations): We applied Equation (7) to the pressure dependent dry and brine saturated velocities and moduli of a porous ⎛ K ⎞ ⎛ K ⎞⎛ K ⎞ α 2 − (φ +1)⎜1− dry ⎟α +φ⎜1− dry ⎟⎜1− dry⎟ = 0 sandstone sample published by Han and Batzle [10] (Figure ⎜ K ⎟ ⎜ K ⎟⎜ K ⎟ ⎝ sat1⎠ ⎝ sat1⎠⎝ f1 ⎠ 1). The wet and dry densities are back-calculated from ⎛ K ⎞ ⎛ K ⎞⎛ K ⎞ Equations (4) and (5). The porosity values are calculated α 2 − (φ+1)⎜1− dry ⎟α +φ ⎜1− dry ⎟⎜1− dry ⎟ = 0 ⎜ K ⎟ ⎜ K ⎟⎜ K ⎟ using the density relationship: ⎝ sat2 ⎠ ⎝ sat2 ⎠⎝ f2 ⎠ ρ = ρ + φρ sat dry f (16) - Step 3: Take the average for a new Biot-Willis coeffi cient: The calculated Biot-Willis coeffi cient and grain matrix modulus as functions of pressure are plotted in Figure 1. α = ()α + α /2 f1f2 The relatively constant value of the grain bulk modulus - Step 4: Use this new α in Equation (14) to fi nd new (39GPa) as a function of pressure is a good indicator that Gassmann equation is applicable for this rock. The Kdry. variation of grain bulk modulus at low confi ning pressure - Step 5: Repeat steps 2 to 4 until K converges: dry (< 10MPa) is possibly due to higher uncertainty in input K − K values (i.e. higher noise-to-signal ratio from velocity dry,new dry,old < ε signals). Kdry,new The Biot-Willis coeffi cient profi le is remarkably similar - Step 6: Use Equations (7) and (12) to fi nd to the result measured on a 26% porosity Boise sandstone corresponding α and K . m sample by Fatt [15]. Note that Gassmann equation gave Note that we have assumed there are no softening a higher value (0.73 at 40MPa) than Han and Batzle’s or hardening eff ects caused by the saturating fl uids on Equation (6) (0.63). the grain bulk modulus (K is constant). The second m 3.2. Coyner’s limestone data assumption is that the rock dry frame is stiff er than both fl uids, K>dry max {}K f 1, Kf 2 , so that Equation We employed the iteration procedure using Equations (7) still gives only one positive (physically realistic) root. (7) to (14) on water and benzene saturated Bedford This assumption is generally valid for consolidated limestone sample published by Coyner [16] (Figure 2). sedimentary rocks. In his experiment at room temperature, the fl uid pore pressure in both saturation cases was maintained at 2.3. When (K , K , K , and φ) are known m sat f 10MPa. The porosity of the rock is 11.9%. The shear modulus profi le is almost identical for all vacuum dry, In this case K and α are unknown. An instance for dry water saturated, and benzene saturated cases, suggesting this case is that fl uid data, fl uid saturation, acoustic log that Gassmann equation is valid for this rock. At 10MPa (V , V ) and density-porosity log are available while K is p s m pore pressure, K = 2.24GPa, and K = 1.21GPa. estimated from the mineralogical composition of the rock water benzene (FTIR, XRD, thin section of rock cuttings, or mineralogy The back-calculated dry bulk modulus is also log). The Biot-Willis coeffi cient can be estimated directly plotted (as a dashed line) against the various measured from the following equivalent Gassmann equation (see moduli in Figure 2. The profi le is consistently higher Appendix C for detailed derivations): than the measured vacuum dry bulk modulus profi le by approximately 2.5GPa (or 5 - 9%). This is another ⎡ ⎛ K ⎞⎤ ⎡ ⎛ K ⎞⎤ ⎢φ()K1−K −K ⎜1− sat ⎟⎥α =φ ⎢()K −K −K ⎜ − f ⎟⎥ evidence supporting the argument that the vacuum m f f ⎜ K ⎟ m f sat ⎜ K ⎟ (15) ⎣ ⎝ m ⎠⎦ ⎣ ⎝ m ⎠⎦ dry measured bulk modulus is too dry and should not
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be used in Gassmann equation [6, 17]. We could have 80 1.0 applied the measured vacuum dry and either water- or benzene-saturated moduli values on Equation (7), but 70 0.8 α that approach would give unrealistically high grain matrix 60 bulk modulus. 0.6 50 The grain matrix bulk modulus and Biot-Willis 0.4 coeffi cient profi les obtained from the rock water- and
40 coefficient -Willis benzene-saturated moduli are shown in Figure 3. While the Biot
Grain bulk modulus, GPa 0.2 30 Grain bulk modulus K m grain matrix bulk modulus is similar to Coyner’s reported Biot-Willis coefficientα value of 65GPa, the back-calculated Biot-Willis coeffi cient 20 0 0 1020304050 profi le decreases from 0.6 to 0.53, signifi cantly lower than Pressure, MPa the commonly assumed value of 1 while signifi cantly higher than the estimated value of 0.34 obtained from Figure 1. Grain bulk modulus and Biot-Willis coeffi cient of a sandstone sample as a func- tion of pressure calculated from its dry and brine saturated moduli [10] using Gassmann Han and Batzle’s 2004 correlation. equation. 3.3. Eff ects of input data errors on calculated grain bulk modulus 40 Measured values always have some associated errors. Velocities, especially shear wave velocities may carry 30 signifi cant uncertainties. We would like to determine the
eff ects of uncertainties from porosity, Kdry, Ksat, and Kf to the uncertainty of the predicted K . Since the relationship 20 m in Equation (7) is not linear, a Monte Carlo (stochastic)
Modulus, GPa K vacuum dry - measured simulation was used. 10 K water saturated K benzene saturated G (all saturation cases) Table 1 summarises the input parameter values K dry Gassmann [18] and their estimated ranges of uncertainties. The 0 rock sample is a Berea sandstone sample with Voigt- 0 1020304050 Differential pressure, MPa Reuss-Hill average grain bulk modulus of 39.6GPa from its mineralogical composition. All parameters were
Figure 2. Bulk and shear moduli as a function of diff erential pressure for Bedford lime- assumed to have a normal distribution with means being stone [6]. The dashed line is the dry bulk modulus calculated from Gassmann equation, the measured values and the errors represent the 95% consistently higher than the vacuum dry measured data. confi dence interval. Thus, the relative error (uncertainty) of each parameter is defi ned as: 2s 80 1.0 % error = × 100 % (17) mean
70 0.8 α Where s is the standard deviation of the parameter’s 60 sample. 0.6 50 For each set of perturbed errors, 10,000 sets of 0.4 (porosity, dry bulk modulus, wet bulk modulus, and fl uid 40 modulus) values were generated to compute 10,000 grain Biot-Willis coefficient coefficient Biot-Willis
Grain bulk modulus, GPa 0.2 30 Grain bulk modulus Km bulk moduli, which are then analysed for the mean value α Biot-Willis coefficient and standard deviation. 20 0 0 1020304050 In our base case, porosity is assigned a 1% error, Pressure, MPa Kdry and Ksat are each assigned a 3% error, and Kf carries a 10% uncertainty. The resulting K is also a Gaussian Figure 3. Calculated grain matrix bulk modulus and Biot-Willis coeffi cient of Bedford m limestone sample as a function of pressure using Gassmann equation from its water - and distribution with a mean of 44.6GPa and a standard benzene - saturated moduli [16]. deviation of 3.45GPa. The 95% confi dence interval is,
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Table 1. Mean (measured) values of a Berea sandstone sample [18] and ranges of uncertainties used in Monte Carlo simulations Parameters Mean values (measured) % error Standard deviation Porosity 17.6% ±1 - 15% ±0.09 - 1.3% Effective dry bulk modulus 16.8GPa ±1 - 15% ±0.25 - 1.26GPa Effective wet bulk modulus 21.1GPa ±1 - 15% ±0.32 - 1.58GPa Fluid bulk modulus (water) 2.2GPa ±0 - 30% ±0 - 0.33GPa
stochastic simulation was also performed to examine
K K effect f the eff ect of uncertainty and/or measurement errors on 60 sat φ K dry calculated grain matrix bulk modulus. The results showed K sat m
K base case that the calculated grain matrix bulk modulus is relatively constant with applied diff erential pressure (up to 50MPa) 40 Kdry effect for sedimentary rocks. However, the estimation is very K effect f sensitive to the uncertainty of dry and saturated bulk
bulk modulusbulk φ 20 effect modulus values. Our new forms of Gassmann equation can be used to eff ectively quantify the uncertainty of base case: 1% φ error, 3% Kdry & K errors, 10% K error % error% in calculated grain matrix sat f dry and saturated bulk modulus (and subsequently, the 0 0 5 10 15 20 25 30 35 seismic velocities) in fl uid identifi cation, fl uid substitution, % error of input parameters (K f /φ /Kdry/K sat) or reservoir monitoring applications. The uncertainty of the computed grain matrix bulk modulus K using Gassmann Figure 4. m NOMENCLATURE equation as functions of percent error in one input parameter (Kf, α, Kdry, or Ksat), while the remaining input parameters carry the same errors as the base case. Errors from Ksat and K: bulk modulus (GPa or psi)
Kdry have the largest impacts on the uncertainty of calculated Km. Porosity and fl uid bulk modulus, on the other hand, show negligible eff ects. Ksat: saturated bulk modulus (GPa or psi)
Kdry: dry (frame) bulk modulus (GPa or psi) therefore, from 37.7GPa to 51.5GPa (or 16% error). The K : grain (matrix) bulk modulus (GPa or psi) Biot-Willis coeffi cient α is also a Gaussian distribution with m K : fl uid bulk modulus (GPa or psi) a mean of 0.62 and a standard deviation of 0.03. The 95% f confi dence interval is from 0.56 to 0.68 (or 10% error). G: shear modulus (GPa or psi) Figure 4 shows the uncertainty of the computed grain Gsat: saturated shear modulus (GPa or psi) matrix bulk modulus Km as functions of percent error in Gdry: dry (frame) shear modulus (GPa or psi) one input parameter (Kf, φ, Kdry, or Ksat), while the remaining input parameters carry the same uncertainties as of the : Biot-Willis coeffi cient (dimensionless) base case. Errors from Ksat and Kdry have the largest eff ects φ: porosity (dimensionless) on the uncertainty of K . Minus errors in K and K (even m dry sat : density (g/cc) within laboratory measurement standard) can result in V : compressional wave velocity (km/s) a large error in the estimated value of Km. Porosity and p fl uid bulk modulus, on the other hand, show negligible Vs: shear wave velocity (km/s) infl uence. This result is not surprising, as K , φ and K f m APPENDIX A: Derivation of Equation (7) should be uncorrelated parameters. From Equation (3) we can write: 4. Conclusions
K f K f Three equivalent forms of Gassmann equation were = (1 − α ) (A.1) Km Kdry presented that can be useful for the determination of Biot-Willis coeffi cient, dry bulk modulus, and/or grain Rewriting Equation (1) as a function of gives: matrix bulk modulus of a rock. We demonstrated the ⎡ K ⎤ applicability of these equations using several sets of f 2 (K=sat − Kdry)⎢φ + (1−α ) (α −φ)⎥ K f α (A.2) published laboratory measurements and the implications ⎣⎢ K dry ⎦⎥ of the results for other estimations of rock properties. A
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⎡ K ⎤ K equation and rearrange Equation (1) as a function of , α 2 K + f (K − K ) − (φ+1) f (K − K )α ⎢ f sat dry ⎥ sat dry the Biot-Willis coeffi cient only: ⎣⎢ Kdry ⎦⎥ Kdry ⎡ K ⎤ (A.3) f 2 ⎛ K ⎞ []K=sat − (1−α )K m ⎢φ + (α −φ)⎥ Kf α (C.1) +φ(K − K )⎜ f −1⎟ = 0 K sat dry ⎜ ⎟ ⎣ m ⎦ ⎝ Kdry ⎠ Expanding LHS and subtracting K 2 both sides, we ⎡ ⎤ f Kf Ksat 2 K f α − ⎢(φ+1) (Ksat − Kdry)⎥α have: Kdry ⎣⎢ Kdry ⎦⎥ ⎡K K ⎤ ⎡ K K ⎤ (A.4) α sat f +K φ − (=φ+1)K +φ ()K −K + K − f sat 0 ⎛ ⎞ ⎢ m f⎥ ⎢ sat m f ⎥ K f K K +φ(K − K )⎜ −1⎟ = 0 ⎣ m ⎦ ⎣ m ⎦(C.2) sat dry ⎜ ⎟ ⎝ Kdry ⎠ or equivalently, K Multiplying both sides with dry gives ⎡ ⎛ K ⎞⎤ ⎡ ⎛ K ⎞⎤ ⎜ sat ⎟ ⎜ f ⎟ K f Ksat ⎢φ()K1m−Kf − Kf ⎜1− ⎟⎥α = φ⎢()Km− Kf − Ksat⎜ − ⎟⎥ ⎣ ⎝ K m ⎠⎦ ⎣ ⎝ K m ⎠⎦ ⎛ K ⎞ ⎛ K ⎞⎛ K ⎞ α 2 − (φ+1)⎜1− dry ⎟α +φ ⎜1− dry ⎟⎜1− dry ⎟ = 0, ⎜ ⎟ ⎜ ⎟⎜ ⎟ which is Equation (15). ⎝ K sat ⎠ ⎝ K sat ⎠⎝ K f ⎠ References which is Equation (7). APPENDIX B: Derivation of Equation (13) 1. Fritz Gassmann. Uber die Elastizität Poröser Medien. Vierteljahrschrift der Naturforschenden Gesellschaftin If the same rock is subjected to two diff erent Zürich. 1951; 96: p. 1 - 23. saturation fl uids, then we have two equations in the form of Equation (7): 2. Tad M.Smith, Carl H.Sondergeld, Chandra S.Rai. ⎛ K ⎞ ⎛ K ⎞⎛ K ⎞ Gassmann fl uid substitutions: A tutorial. Geophysics. 2003; α 2 − (φ+1)⎜1− dry ⎟α +φ⎜1− dry ⎟⎜1− dry ⎟ = 0 ⎜ ⎟ ⎜ ⎟⎜ ⎟ (B.1) 68(2): p. 430 - 440. ⎝ Ksat1⎠ ⎝ Ksat1⎠⎝ K f1 ⎠ 3. Ludmila Adam, Michael Batzle, Ivar Brevik. ⎛ K ⎞ ⎛ K ⎞⎛ K ⎞ α 2 − (φ+1)⎜1− dry ⎟α +φ⎜1− dry ⎟⎜1− dry ⎟ = 0 Gassmann fl uid substitution and shear modulus variability in ⎜ ⎟ ⎜ ⎟⎜ ⎟ (B.2) ⎝ Ksat2⎠ ⎝ Ksat2⎠⎝ K f 2 ⎠ carbonates at laboratory seismic and ultrasonic frequencies. Geophysics. 2006; 71(6): p. F173 - F183. Subtracting Equation (B.2) from (B.1) gives: 4. Maurice Anthony Biot, David G.Willis. The elastic ⎛ 1 1 ⎞ ⎡⎛ 1 1 ⎞ ()φ +1 ⎜ − ⎟K α =φK ⎢⎜ − ⎟ coeffi cients of the theory of consolidation. Journal of ⎜ K K ⎟ dry dry ⎜ K K ⎟ ⎝ sat1 sat2⎠ ⎣⎢⎝ f1 f2 ⎠ Applied Mechanics. 1957; 24: p. 594 - 601. (B.3) ⎛ 1 1 ⎞ ⎛ 1 1 ⎞⎤ 5. James G.Berryman. Origin of Gassmann’s equations. + ⎜ − ⎟ − K ⎜ − ⎟⎥ ⎜ K K ⎟ dry⎜ K K K K ⎟ ⎝ sat1 sat2⎠ ⎝ sat1 f1 sat2 f 2 ⎠⎦⎥ Geophysics. 1999; 64(5): p. 1627 - 1629. 6. Gary Mavko, Tapan Mukerji, Jack Dvorkin. The rock Canceling Kdry both sides and rearranging Equation (B.3) leads to: physics handbook: Tools for seismic analysis in porous media. Cambridge University Press, Cambridge. 1998. ⎛ 1 1 ⎞ ⎛ 1 1 ⎞ φ⎜ − ⎟K =φ ⎜ − ⎟ − ⎜ K K K K ⎟ dry ⎜ K K ⎟ 7. Robert W.Zimmerman. Compressibility of ⎝ sat1 f 1 sat2 f 2⎠ ⎝ f 1 f2 ⎠ sandstones. Elsevier Science. 1991. ⎛ 1 1 ⎞ []α ()φ +1 −φ ⎜ − ⎟ 8. Luther White, John Castagna. Stochastic fl uid ⎝ Ksat1 Ksat2 ⎠ modulus inversion. Geophysics. 2002; 67(6): p. 1835 - 1843. which is Equation (13). Equation (14) then can be 9. Fredy A.V.Artola, Vladimir Alvarado. Sensitivity readily obtained by multiplying both sides by (K × K ). sat1 sat2 analysis of Gassmann's fl uid substitution equations: Some APPENDIX C: Derivation of Equation (15) implications in feasibility studies of time-lapse seismic reservoir monitoring. Journal of Applied Geophysics. 2006; If K value can be obtained (e.g. using mixture theory), m 59(1): p. 47 - 62. then one can substitute K)dry = (1 − α Km into Gassmann
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10. De-Hua Han, Michael L.Batzle. Gassmann’s 15. I.Fatt. The Biot-Willis elastic coeffi cients for a equation and fl uid-saturation eff ects on seismic velocities. sandstone. Journal of Applied Mechanics. 1959; 26: p. 296 Geophysics. 2004; 69(2): p. 398 - 405. - 297. 11. James G.Berryman, Graeme W.Milton. Exact 16. Karl B.Coyner. Eff ects of stress, pore pressure, and results for generalized Gassmann’s equations in composite pore fl uids on bulk strain, velocity, and permeability in rocks. porous media with two constituents. Geophysics. 1991; 56: Ph.D. dissertation, Massachusetts Institute of Technology, p. 1950 - 1960. Cambridge, Massachusetts. 1984. 12. Keith W.Katahara. Clay mineral elastic properties. 17. Virginia A.Clark, Bernhard R.Tittmann, SEG Technical Program Expanded Abstracts. 1996: p. 1691 Terry W.Spencer. Eff ect of volatiles on attenuation - 1694. (Q-1) and velocity in sedimentary rocks. Journal of Geophysical Research. 1980; 85(B10): 13. Zhijing Jee Wang, Hui Wang, Michael E.Cates. p. 5190 - 5198. Elastic properties of solid clays. SEG Technical Program Expanded Abstracts. 1998: p. 1045 - 1048. 18. Tran Trung Dung, Chandra S.Rai, Carl H.Sondergeld. Changes in crack aspect-ratio concentration 14. Xianhuai Zhu, George A.McMechan. Direct from heat treatment: A comparison between velocity estimation of the bulk modulus of the frame in fl uid saturated inversion and experimental data. Geophysics. 2008; 73(4): elastic medium by Biot theory. SEG Technical Program p. E123 - E132. Expanded Abstracts. 1990: p. 787 - 790.
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MERGING OF 3D SEISMIC DATA Ta Quang Minh, Nguyen Thanh Tung, Mai Thi Lua, Bui Thi Hanh, Do The Nam, Nguyen Ngoc Huy Vietnam Petroleum Institute Email: [email protected]
Summary
Merging of individual seismic datasets into a single uniform dataset is useful for structure analysis, geological modelling, and seismic attribute analysis for a large area. However, many challenges are met, both from the acquisition aspect to processing of data before merging. The authors investigate in detail the technical diffi culties of merging data, and discuss methods to accomplish the goal with an emphasis on post stack seismic merging, as well as merging results from our processing of fi eld seismic datasets. Key words: Merging seismic data, seismic data processing, special seismic techniques.
1. Introduction structures’ orientation. A more feasible alternative is to merge available “small” overlapping 3D vintage seismic data into a single Seismic survey data has the pioneering role dataset with uniform amplitude, frequency, and phase. A merged in laterally extending the geological study area. seismic dataset should provide a reasonable approximation to A regional-scale seismic study, such as the study full area acquired/processed data at a much economical cost and of a basin, may face a stiff challenge where the shorter operation/processing time. area is so vast that it might not be coverable by a single seismic survey. In order to do so, the In fact, seismic data merging has been performed regularly ability to combine and blend information from on many foreign projects [1 - 3] and the results have been very individual surveys becomes necessary. encouraging. Figure 1 shows an example map of several overlapping surveys in India [1] subjected to the merging process. Nowadays, a number of 3D seismic surveys has been carried out each year on the There are several important applications of merged seismic continental shelf of Vietnam with a typical data. The subsurface image of regions near the edges of a local coverage area ranging from about 100km2 to survey is usually distorted from the migration due to the defi ciency 3,500km2, usually within a study block. The of input seismic data, which eventually can be compensated by division of the continental shelf into blocks and another overlapped survey data [1]. The most important application assignment to diff erent operation companies is probably the ability to carry out the interpretation of structures also implies that each 3D seismic survey is continuously and seamlessly on the merged seismic data from one limited to the block operated by a company. A local region to another, and hence enable many geological analyses regional-scale geological assessment, therefore, for a large area such as the structural analysis, sequence stratigraphy will be very diffi cult since the data is a collection analysis, etc. Moreover, many attribute extraction applications can of patchy seismic surveys that often have also be performed on the merged dataset such as various seismic diff erent acquisition characteristics and thus attribute analyses, PaleoScan software, etc. distinctive recorded seismic data characteristics. Certainly, reacquiring seismic data for the whole region and processing the data as a large single seismic dataset may solve part of the problem of patchy data. However, this is unrealistic and prohibitive due to expensive costs and long computation time, not to mention the regional administrative problems (a) (b) as well as diffi culties with the survey design Figure 1. (a) Display all fi ve surveys acquisition grids (b) Display data acquisition superimposed on phase to comprehensively cover various local Bathymetry [1]
Date of receipt: 7/9/2017. Date of review and editing: 7/9 - 21/9/2017. Date of approval: 4/10/2017.
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2. Technical diffi culties with merging seismic data The most obvious diff erences are due to the acquisition confi guration on the survey boat such as The process of merging seismic data is basically related to the source confi guration, including the types of the the compensation for the diff erences in seismic characteristics source - air gun, vibroseis, dynamite, the geometry of of various overlapping datasets. The variation in seismic the source array, and the volumes of individual guns, characteristics between datasets can broadly be categorised etc. In addition, the variation in the confi guration of as coming from 2 major sources: the widely varying seismic the receiver side may include the number and length acquisition confi gurations and the diff erences in processing of the streamer cables, the interval of the receivers, technologies. We will discuss the eff ect of each type of the type of receivers such as hydrophones, velocity variations on the seismic characteristics as follow. phones, the recording and sampling intervals, the 2.1. Eff ect of variations in acquisition schemes frequency of anti-aliasing fi lter, etc. Those diff erences provide decisive impacts on the amplitude and Each seismic survey is usually designed with a specifi c goal frequency content of the acquired seismic data, the suitable for a particular local region. Thus, diff erent seismic signal to noise ratio (SNR), as well as the fold density surveys in nearby regions may have diff erent acquisition at local common middle points. Drastic amplitude parameters. We concentrate on a few important acquisition diff erences between two overlapping surveys can be parameters. seen in Figure 2. The frequency content diff erences may come from another source. Nearby surveys may have diff erent source depths and receiver depths that can aff ect the ghost frequencies. Typically, the ghost notch frequency is related to the source or receiver depth by the formula [4]