Reservoir simulation (april 2017)

FUNDAMENTALS OF RESERVOIR SIMULATION Dr Mai Cao Lan, GEOPET, HCMUT, Vietnam November, 2016 ABOUT THE COURSE COURSE OBJECTIVE COURSE OUTLINE REFERENCES 11/11/2019 Dr Mai Cao Lan, Faculty of Geology & Petroleum Engineering, HCMUT, Vietnam Course Objective • To review the background of petroleum reservoir simulation with an intensive focus on what and how things are done in reservoir simulations • To provide guidelines for hands-on practices with Microsoft Excel 11/11/2019 Dr Mai Cao Lan, Faculty of Geology & Petroleum Engineering, HCMUT, Vietnam COURSE OUTLINE INTRODUCTION FLOW EQUATIONS FOR PETROLEUM RESERVOIRS FINITE DIFFERENCE METHOD & NUMERICAL SOLUTION FOR FLOW EQUATIONS SINGLE-PHASE FLOW SIMULATION MULTIPHASE FLOW SIMULATION References  T Eterkin et al., 2001 Basic Applied Reservoir Simulation, SPE, Texas  J.H Abou-Kassem et al., 2005 Petroleum Reservoir Simulation – A Basic Approach, Gulf Publishing Company, Houston, Texas  C.Mattax & R Dalton, 1990 Reservoir Simulation, SPE, Texas 11/11/2019 Mai Cao Lân – Faculty of Geology & Petroleum Engineering - HCMUT INTRODUCTION NUMERICAL SIMULATION – AN OVERVIEW COMPONENTS OF A RESERVOIR SIMULATOR RESERVOIR SIMULATION BASICS 11/11/2019 Dr Mai Cao Lan, Faculty of Geology & Petroleum Engineering, HCMUT, Vietnam Numerical Simulation – An Overview 11/11/2019 Dr Mai Cao Lan, Faculty of Geology & Petroleum Engineering, HCMUT, Vietnam Mathematical Formulation 11/11/2019 Dr Mai Cao Lan, Faculty of Geology & Petroleum Engineering, HCMUT, Vietnam Numerical Methods for PDEs 11/11/2019 Dr Mai Cao Lan, Faculty of Geology & Petroleum Engineering, HCMUT, Vietnam Numerical Methods for Linear Equations 11/11/2019 Dr Mai Cao Lan, Faculty of Geology & Petroleum Engineering, HCMUT, Vietnam 10 Example of adjustment Well water simulation BT too early Possible Changes Shale or barrier? Vertical permeability between well and water? Numerical dispersion / grid effect? HISTORY MATCHING – CASE STUDY Given the history data in terms of oil, gas, water production rates, bottom hole pressure, and reservoir pressure of a waterflooding project having one injector and one producer as depicted in figure below, perform history matching by adjusting the following unknown properties: • Permeability in the horizontal direction • Permeability in the vertical direction Horizontal and vertical permeability The well bottom hole pressure (WBHP) is the function of average permeability when there is single phase flow ( See equation 1); when multi-phase flow occurs, the WBHP is a function of relative permeability and average permeability (see equation 2) When the water breakthrough has not occurred, the WBHP depends on the average permeability Assume that the oil flows in the horizontal plane, so before water breakthrough, WBHP depends on horizontal permeability (Kxx and Kyy) After water breakthrough, the water flow up ward because of up dip water injection The WBHP mainly depend on vertical permeability (Kzz) Q0  kh( PR  Pwf )  r  141.2o Bo  ln( e )  0.75  S   rw  Q0   Pwf  f (k ) kkro h( PR  Pwf )  r  141.2o Bo  ln( e )  0.75  S   rw   Pwf  f (kkro ) (1) (2) Horizontal and vertical permeability The permeability in the horizontal direction (Kxx = Kyy) was adjusted by comparison of well bottom hole pressure of producer Choose the first valve of Kxx = Kyy = 250 md and Kzz = 0.1Kxx = 25md History Simulation Figure – The result of first trail of K = K = 250 md and K = 25md Horizontal and vertical permeability Figure shows that, the WBHP of producer in case of Kxx = 200 md is smaller the base case Based on equation 2, the horizontal permeability should be increased For the second trail, Kxx = Kyy = 315 md and Kzz = 0.1Kxx = 35md History Simulation Figure The result of first trail of Kxx = Kyy = 315 md and Kzz = 35md Horizontal and vertical permeability From figure 2, the well bottom hole pressure is matched for the stage of before water breakthrough Since this is updip water injection In this matching work, well bottom hole pressure of producer is a function of vertical permeability after water breakthrough The bottom hole pressure is smaller than the base case when water breakthrough In this case, the vertical permeability should be increased and Kzz was 73md in next trail Horizontal and vertical permeability Thus, the horizontal Kxx = Kyy = 315md and Kzz = 73 md are matched with the given data History Simulation Figure The result of first trail of Kxx = Kyy = 315 md and Kzz = 73md ... Reservoir Simulation, SPE, Texas  J.H Abou-Kassem et al., 2005 Petroleum Reservoir Simulation – A Basic Approach, Gulf Publishing Company, Houston, Texas  C.Mattax & R Dalton, 1990 Reservoir Simulation, ... NUMERICAL SIMULATION – AN OVERVIEW COMPONENTS OF A RESERVOIR SIMULATOR RESERVOIR SIMULATION BASICS 11/11/2019 Dr Mai Cao Lan, Faculty of Geology & Petroleum Engineering, HCMUT, Vietnam Numerical Simulation. .. Objective • To review the background of petroleum reservoir simulation with an intensive focus on what and how things are done in reservoir simulations • To provide guidelines for hands-on practices