Determining multilayer formation properties from transient temperature and pressure measurements PDF
Preview Determining multilayer formation properties from transient temperature and pressure measurements
DETERMINING MULTILAYER FORMATION PROPERTIES FROM TRANSIENT TEMPERATURE AND PRESSURE MEASUREMENTS A Dissertation by WEIBO SUI Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY August 2009 Major Subject: Petroleum Engineering DETERMINING MULTILAYER FORMATION PROPERTIES FROM TRANSIENT TEMPERATURE AND PRESSURE MEASUREMENTS A Dissertation by WEIBO SUI Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Approved by: Co-Chairs of Committee, Christine Ehlig-Economides Ding Zhu Committee Members, A. Daniel Hill Yalchin Efendiev Head of Department, Stephen A. Holditch August 2009 Major Subject: Petroleum Engineering iii ABSTRACT Determining Multilayer Formation Properties from Transient Temperature and Pressure Measurements. (August 2009) Weibo Sui, B.S., China University of Petroleum (Beijing); M.S., China University of Petroleum (Beijing) Co-Chairs of Advisory Committee: Dr. Christine Ehlig-Economides Dr. Ding Zhu The Multilayer Transient Test is a well-testing technique designed to determine formation properties in multiple layers, and it has been proved effective during the past two decades. To apply the Multilayer Transient Test, a combination of rate profiles from production logs and transient rate and pressure measurements are required at multiple surface rates. Therefore, this method can be time consuming and may involve significant errors due to inaccurate transient flow rate measurements. A new testing approach is proposed after realizing the limitations of the Multilayer Transient Test. The new testing approach replaces the transient flow rate measurement with transient temperature measurement by using multiple temperature sensors. This research shows that formation properties can be quantified in multiple layers by analyzing measured transient temperature and pressure data. A single-phase wellbore/reservoir coupled thermal model is developed as the forward model. The forward model is used to simulate the temperature and pressure response along the wellbore during the transient test. With the forward model, this work proves that the transient temperature and pressure are sufficiently sensitive to formation properties and can be used for multilayer reservoir characterization. The inverse model is formulated by incorporating the forward model to solve formation properties using nonlinear least-square regression. For the hypothetical cases, the proposed new multilayer testing method has successfully been applied for investigating formation properties in commingled multilayer reservoirs. Layer iv permeability, damaged permeability, and damaged radius can be uniquely determined using single-point transient pressure data and multipoint transient temperature data at appropriate locations. Due to the proposed data acquisition scheme, only one surface flow rate change is needed to implement this testing approach, which significantly reduces the test duration compared to the standard multilayer transient testing approach using a series of flow rate changes. Of special interest, this is the first test design that shows promise for determination of the damaged radius, which can be useful for well stimulation design. In addition, temperature resolution, data noise, and data rate impacts have been studied along with a data filtering approach that enable selection of suitable pressure and temperature sensor technologies for applying the new testing method. v DEDICATION This dissertation is dedicated to my beloved parents Changfu Sui and Yaqin Zhang for their unconditional support and encouragement while I pursued my dream. This dissertation is also dedicated to my husband Jianye who has been being there assisting and understanding me during every step of my doctorate program, and to my wonderful son Jiarui. vi ACKNOWLEDGEMENTS I would like to express my gratitude to my co-advisors, Drs. Ehlig-Economides and Zhu, for their support, patience, and encouragement throughout my graduate studies. They also gave me innumerable lessons and insights on the workings of academic research in general, which will benefits my future research and work. I also thank my committee members, Dr. Hill and Dr. Efendiev, for spending time in discussion with me and every precious advice throughout the course of this research. Thanks also go to my friends and colleagues and the department faculty and staff for making my time at Texas A&M University a great experience. vii NOMENCLATURE A coefficient defined in Eq. 2.112 j a logarithmic spatial transform coefficient lg a logarithmic temporal transform coefficient lgt B coefficient defined in Eq. 2.102 j b coefficient for outer boundary condition j C wellbore storage coefficient C dimensionless wellbore storage coefficient D C reservoir rock compressibility f C heat capacity of fluid p C heat capacity of formation rock pr C weight matrix for observations n c total system compressibility t D bottom depth of reservoir d observation data dqˆ normalized layer flow rate change i E energy E kinetic energy KE E viscous shear energy term VS e intermediate vector f friction factor f objective function G sensitivity matrix g predicted data viii g gravity acceleration g geothermal gradient T H Hessian matrix H enthalpy h thickness h heat convection coefficient a I identity matrix J Jacobian matrix I ,K zero order modified Bessel function of the first and second kind 0 0 I ,K first order modified Bessel function of the first and second kind 1 1 K thermal conductivity T K Joule-Thomson coefficient JT k permeability k damage permeability s M number of time points used for regression ( ) m p pseudo-pressure function N number of producing layers in reservoir system N cumulative production rate p NT number of time step during a transient flow test n number of layers in reservoir system p pressure p reservoir initial pressure i p flowing bottomhole pressure wf p reservoir pressure in layer j j p dimensionless reservoir pressure in Layer j jD p pressure under standard condition sc ix q conductive heat flux q surface production rate q flow rate before surface rate change in Layer j bc,j q flow rate for Layer j j q dimensionless flow rate for Layer j jD q last production rate before rate change last R wellbore radius r radial coordinate r dimensionless radial distance D r reservoir outer radius e r dimensionless reservoir outer radius eD r damage radius s r tubing inner radius ti r wellbore radius wb s skin factor s skin factor in Layer j j T temperature T temperature at external boundary of reservoir e T geothermal temperature Ge T inflow temperature I T temperature under standard condition sc t time t dimensionless time reference to Layer j D t total time length of the transient test N t pseudoproducing time pH x U internal energy U overall heat transfer coefficient T V volume v velocity vector v velocity x parameter vector w derivative vector z vertical coordinate Greek β thermal expansion coefficient γ pipe open ratio δx upgrading parameter θ wellbore inclination ι Laplace space variable κ permeability-thickness fraction λ Marquardt parameter µ viscosity π total molecular stress tensor ρ density ™ shear stress tensor φ porosity ω porosity-thickness fraction Superscripts n time step index T matrix transform
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