FUNDAMENTALS OF RESERVOIR SIMULATION Dr  Mai  Cao  Lan,   GEOPET,  HCMUT,  Vietnam Jan,  2014 ABOUT THE COURSE COURSE OBJECTIVE COURSE OUTLINE REFERENCES 9/11/16 Dr  Mai  Cao  Lan,  F aculty  of  G eology  &  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 9/11/16 Dr  Mai  Cao  Lan,  F aculty  of  G eology  &  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   9/11/16 Mai Cao Lân – Faculty of Geology & Petroleum Engineering - HCMUT INTRODUCTION NUMERICAL SIMULATION – AN OVERVIEW COMPONENTS OF A  RESERVOIR SIMULATOR RESERVOIR SIMULATION BASICS 9/11/16 Dr  Mai  Cao  Lan,  F aculty  of  G eology  &  Petroleum  Engineering,  HCMUT,   Vietnam Numerical  Simulation  – An  Overview 9/11/16 Dr  Mai  Cao  Lan,  F aculty  of  G eology  &  Petroleum  Engineering,  HCMUT,   Vietnam Mathematical  Formulation 9/11/16 Dr  Mai  Cao  Lan,  F aculty  of  G eology  &  Petroleum  Engineering,  HCMUT,   Vietnam Numerical  Methods  for  PDEs 9/11/16 Dr  Mai  Cao  Lan,  F aculty  of  G eology  &  Petroleum  Engineering,  HCMUT,   Vietnam Numerical  Methods  for   Linear  Equations 9/11/16 Dr  Mai  Cao  Lan,  F aculty  of  G eology  &  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 ⎞ 141.2µo Bo ⎜ ln( e ) − 0.75 + S ⎟ ⎝ rw ⎠ Q0 = ⇒ Pwf = f (k ) kkro h( PR − Pwf ) ⎛ r ⎞ 141.2 µo 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  3  The  result  of  first  trail  of  Kxx  =  Kyy =  315  md  and  Kzz =  73md