STUDY OF MODELING OF WATER SATURATION IN ARCHIE AND NON-ARCHIE POROUS MEDIA A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY CHANTSALMAA DALKHAA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN PETROLEUM AND NATURAL GAS ENGINEERING JULY 2005 Approval of the Graduate School of Natural and Applied Sciences Prof. Dr. Canan Özgen Director I certify that this thesis satisfies all the requirements as a thesis for the degree of Master of Sciences. Prod. Dr. Birol Demiral Head of Department This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Science. Prof. Dr. Ender Okandan Supervisor Examining Committee Members Prof. Dr. Birol Demiral (METU, PETE) Prof. Dr. Ender Okandan (METU, PETE) Prod. Dr. Mahmut Parlaktuna (METU, PETE) Prof. Dr. Nurkan Karahano(cid:1)lu (METU, GEOE) Y. Doç. Dr. Evren Özbayo(cid:1)lu (METU, PETE) I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last name: Chantsalmaa Dalkhaa Signature: iii ABSTRACT STUDY OF MODELING OF WATER SATURATION IN ARCHIE AND NON-ARCHIE POROUS MEDIA Dalkhaa, Chantsalmaa M.Sc., Department of Petroleum & Natural Gas Engineering Supervisor: Prof. Dr. Ender Okandan July 2005, 96 Pages The aim of this thesis is to study water saturation models available in the literature and to apply a proper one to a real field case. Archie equation is the most well-known water saturation model. However, it is formulated on some assumptions and is applicable to only clean sands. Archie equation cannot be used for shaly formation. There are many shaly water saturation models that account for shale effect for water saturation estimation. In this study, 3 wells, namely Well-01, Well-02 and Well-03 are studied. These wells lie in a fractured carbonate reservoir located in Southeastern part of Turkey. From well log recordings, the production formation is seen almost clean. In other words, the shale amount of the formation is so small that it can be neglected. Thus, to calculate the water saturation in those wells, the well-known Archie water saturation equation is used. Since the formation is fractured carbonate, the cementation factor (m ) and saturation exponent (n ) of conventional value of “2” each cannot be used for the water saturation iv calculation. Instead, these parameters are obtained from generalized crossplot of log-derived porosity and resistivity technique. Finally, each well is divided into zones using porosity data. Zonation is conducted based on statistical method, ANOVA (analysis of variance). Well-01 and Well-02 are both divided into two zones. On the other hand, the statistical method was initially divided Well-03 into three zones. However, Well-03 is better described as a whole zone, depending on the geological analysis and engineering judgment. After the zonation, the zones are correlated from well to well. The water saturations in significantly correlated zones are examined. Also, using the same statistical method, the water saturation zones are identified. However, these zones do not coincide with the porosity zones. This difference is attributed to pore size distribution and wettability which affect saturation distribution. Keywords: water saturation, Archie equation, statistical zonation, cementation factor and saturation exponent. v ÖZ ARCHIE VE ARCHIE OLMAYAN GÖZENEK ORTAMDAKI SU SATURASYON MODELLEMENIN CALISMASI Dalkhaa, Chantsalmaa Yüksek Lisans, Petrol ve Do(cid:1)al Gaz Mühendisli(cid:1)i Tez danı(cid:2)manı: Prof. Dr. Ender Okandan Temmuz 2005, 96 Sayfa Bu tezin amacı literatürdeki su doymu(cid:2)luk modellerini inceleyip uygun birinin gerçek sahada kullanılmasıdır. Archie denklemi en çok bilinen su doymu(cid:2)luk modelidir. Ancak, bu denklem bazı varsayım üzerine kurulmu(cid:2)tur ve sadece temiz kum tabakalarında uygulanabilir. Archie denklemi (cid:2)eylli tabakalarda kullanılamaz. Bu ara(cid:2)tırmada 3 kuyu, Kuyu-01, Kuyu-02 ve Kuyu -03 incelenmi(cid:2)tir. Kuyular Türkiye’de Güney AnaDoludaki çatlaklı kalker bir reservuardan üretmektedir. Kuyu loglarından, üretim formasyon tamamen temiz görünmektir, bir ba(cid:2)ka deyi(cid:2)le, üretim formasyondaki (cid:2)eyl miktarı ihmal edilebilecek kadar az bulunmaktadır. Bu yüzden, Archie denklem su doymu(cid:2)luk miktarının hesaplanmasında kullanılmı(cid:2)tır. Fakat bu hesaplamada, formasyon çatlaklı kalker oldu(cid:1)undan, çimento faktör ve su doymu(cid:2)luk katsayısı, geleneksel de(cid:1)er olan “2” olarak alınmamı(cid:2)tır. Bunun yerine, bu parametrelerin de(cid:1)erleri log resistivite ve gözeneklik krosplot teknik kullanılarak çıkartılmı(cid:2)tır. Son olarak, her kuyu kendi gözeneklik de(cid:1)erlerini kullanılarak katmanlara bölünmü(cid:2)tür. Katmanlama, istatistik metot olan ANOVA ile gerçekle(cid:2)tirilmi(cid:2)tir. Kuyu-01 ve Kuyu-02 iki(cid:2)er katmanlara ayrılmı(cid:2)tır. Di(cid:1)er taraftan, istatistik metot vi Kuyu-03’u üç katmana ayırmı(cid:2)tır. Ancak jeolojik analiz ve mühendislik kararı altında, Kuyu-03 tek bir katman olarak alınmı(cid:2)tır. Daha sonra, katmanların kuyudan kuyuya ba(cid:1)lantısı belirlenmi(cid:2)tir. Su doymu(cid:2)lu(cid:1)unun ba(cid:1)lantılı olan katmanlar boyunca benzerli(cid:1)ine bakılmı(cid:2)tır. Ayrıca aynı istatisik metot kullanılarak su doymu(cid:2)luk katmanları belirlenmi(cid:2)tir. Ancak bu katmanlar gözeneklik katmanlarıyla uyumlu bulunmamı(cid:2)tır. Anahtar kelime: su doymu(cid:1)lu(cid:2)u, Archie denklemi, istatistik zonlama, çimento faktörü ve su doymu(cid:1)lu(cid:2)u katsayısı . vii To my mother & in memory of my father viii ACKNOWLEDGMENT Firstly and foremost, I would like to express my deepest and sincere thankfulness to my thesis supervisor Prof.Dr Ender Okandan for her guidance, advice, criticism, encouragement, and precious insight throughout the research. The combination of her creativity, intellect, attention to detail and tolerance madde this undertaking possible. I would also like to thank The Production Department of TPAO for providing the necessary data for this study. Yıldız Karakece, from the Production Department of TPAO, deserves special thanks for her personal help and guidance. Also, my special thanks go to my thesis committee members for their valuable suggestions and comments. As well as, the humorous approaches and lively support of my dear friends are gratefully acknowledged. I am so lucky to have your friendship, undersatanding and love. At last, but not the least, I would like to thank my dearest family, especially, my wonderful mom for her never-ending love, faith and moral support. ix TABLE OF CONTENTS PLAGIARISM…………………………………………………………………...iii ABSTRACT……………………………………………………………………...iv ÖZ………………………………………………………………………………..vi DEDICATION………………………………………………………………….viii ACKNOWLEDGMENTS………………………………………………………..ix TABLE OF CONTENTS…………………………………………………………x LIST OF TABLES……………………………………………………………...xiii LIST OF FIGURES…………………………………………………………….xiv LIST OF SYMBOLS…………………………………………………………....xv CHAPTER 1. INTRODUCTION…………………………………………………….1 1.1 LITERATURE SURVEY ON WATER SATURATION MODELS…………………………………………………………2 1.1.1 ARCHIE EQUATION……………………………………2 1.1.2 SHALY (NON-ARCHIE) WATER SATURATION MODELS…………………………………………………3 1.1.2.1 V MODELS…………………………………………5 sh 1.1.2.2 DOUBLE LAYER MODELS………………………...6 2. THEORY……………………………………………………………...9 2.1 THOERY ON WATER SATURATION…………………………9 2.1.1 GENERALISED CROSSPLOT METHOD…………….10 2.1.2 PROCEDURE FOR DETERMINATION OF m and n…13 2.2 THEORY ON STATISTICAL ZONATION AND CORRELATION………………………………………………...14 2.2.1 PROCEDURE FOR ZONATION……………………….17 2.2.2 PROCEDURE FOR CORRELATION………………….18 3. STATEMENT OF PROBLEM……………………………………...20 4. STUDY AREA……………………………………............................21 5. CALCULATION OF WATER SATURATION (S )………………25 w x