A Model for Resource Assessment and Exploration/Production Production

NOT FOR QUOTATION WITHOUT P E R M I S S I O N O F THE AUTHOR

A MODEL FOR RESOURCE ASSESSMENT AND EXPLORATION/PRODUCTION

P R O C E S S E S

E . M e d o v a

A p r i l 1 9 8 0 WP-80-44

W o r k i n g P a p e r s a r e i n t e r i m r e p o r t s o n w o r k of t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s and have received o n l y l i m i t e d r e v i e w . V i e w s o r o p i n i o n s expressed h e r e i n do n o t n e c e s s a r i l y repre- s e n t those of t h e I n s t i t u t e o r of i t s N a t i o n a l Member O r g a n i z a t i o n s .

INTERNATIONAL I N S T I T U T E FOR A P P L I E D SYSTEMS A N A L Y S I S A - 2 3 6 1 L a x e n b u r g , A u s t r i a

PREFACE

Over t h e l a s t few y e a r s , many s t u d i e s (WAES, WEC, C I A , o i l companies, e t c . ) have p o p u l a r i z e d t h e i d e a t h a t w o r l d o i l pro- d u c t i o n w i l l r e a c h a maximum i n t h e 1 9 8 0 ' s o r 1 9 9 0 ' s and pro- g r e s s i v e l y d e c l i n e . I f c u m u l a t i v e p r o d u c t i o n up t o t h e maximum

i s c a l c u l a t e d and compared t o t h e r e m a i n i n g r e s o u r c e s t o be r e c o v e r e d o r produced ( t a k e n from t h e WEC D e l p h i S t u d y , f o r i n s t a n c e ) i t i s p o s s i b l e t o assume o t h e r t y p e s o f e v o l u t i o n f o r w o r l d o i l p r o d u c t i o n a s w e l l , i n p a r t i c u l a r a p l a t e a u e x t e n d i n g o v e r a few d e c a d e s . Because of t h e c o n t i n u i n g i m p o r t a n c e of o i l

i n t h e w o r l d economy, s u c h an e v o l u t i o n would b e f a r more d e s i r - a b l e t h a n a prompt d e c l i n e . But o f c o u r s e it i s i m p o r t a n t t o a s s e s s w h e t h e r t h i s i s even p o s s i b l e a n d / o r r e a l i s t i c .

The IREP model (IIASA R e s o u r c e s , E x p l o r a t i o n and P r o d u c t i o n model) h a s e s s e n t i a l l y been d e s i g n e d , i n t h e i n i t i a l v e r s i o n which i s p r e s e n t e d h e r e , t o e x p l o r e s u c h a p o s s i b i l i t y . P r e l i m -

i n a r y i d e a s f o r t h e r e s o u r c e model came from t h e Enerdym model (which was d e v e l o p e d w i t h I g o r ~ i m h ) , e s p e c i a l l y t h e c o n c e p t u a l a s p e c t s of d e s c r i b i n g t h e " l i f e " of a r e s o u r c e , from i t s i n i t i a l s t a t u s o f " s p e c u l a t i v e r e s o u r c e " t o i t s p o s s i b l e p r o d u c t i o n .

The IREP model i s composed o f a number of submodels:

r e s o u r c e a s s e s s m e n t ( t h e most d e v e l o p e d t o d a t e ) , an e x p l o - r a t i o n submodel p r i m a r i l y aimed a t o b t a i n i n g an i d e a of t h e e f f o r t n e c e s s a r y ( d r i l l i n g , i n v e s t m e n t , e t c . ) t o d i s c o v e r t h e assumed r e s o u r c e s , and a p r o d u c t i o n submodel d i r e c t l y l i n k e d t o t h e e x p l o r a t i o n submodel b u t a l l o w i n g t h e exam- i n a t i o n o r v a r i o u s s c e n a r i o s i n f l u e n c e d by p o l i t i c o - e c o n o m i c d e c i s i o n s .

I n a d d i t i o n , t h e IREP model can a l s o be u s e d a s a s e n s i - t i v i t y a n a l y s i s t o o l t o e x p l o r e how c h a n g e s i n some p a r a m e t e r s - - g e n e r a l l y l i n k e d t o t h e p r o g r e s s of e x p l o r a t i o n a n d / o r knowledge of p e t r o l e u m p r o s p e c t s o r b a s i n s - - c a n i n f l u e n c e o i l r e s o u r c e s and

-111-

t h e i r f u t u r e p r o d u c t i o n p o t e n t i a l . A s s u c h , t h i s model i s n o t o n l y a t o o l which c a n b e u s e d i n a p r e l i m i n a r y way f o r f o r e c a s t -

i n g o r a s s e s s i n g , b u t a l s o a w o r k i n g t o o l f o r e n a b l i n g a b e t t e r u n d e r s t a n d i n g o f w o r l d o i l a s s e s s m e n t .

The r e s o u r c e a s s e s s m e n t submodel h a s been d e v e l o p e d i n d e t a i l and t e s t e d w i t h a n a p p l i c a t i o n c a s e . R e s u l t s - - a l t h o u g h p r e l i m i n a r y - - a r e e n c o u r a g i n g , a n d it w a s t h o u g h t t h a t t h i s work c o u l d u s e f u l l y b e p r e s e n t e d and o f f e r e d f o r d i s c u s s i o n . The i n p u t d a t a f o r t h e a p p l i c a t i o n c a s e w i l l b e r e f i n e d , a n d more i m p o r t a n c e s h o u l d b e a t t a c h e d t o t h e p o t e n t i a l v a l i d i t y o f t h e a p p r o a c h t h a n t o t h e f i r s t r e s u l t s , shown h e r e i n a s a m p l e r u n .

M i c h e l Grenon

-

^{i v -}

ACKNOWLEDGEMENTS

I am v e r y much i n d e b t e d t o P r o f e s s o r Grenon f o r h i s s u p p o r t and s t i m u l a t i n g d i s c u s s i o n s . I am a l s o e x t r e m e l y g r a t e f u l t o D . Barrow f o r e d i t i n g and t y p i n g t h i s p a p e r , t o S . A r t h u r f o r c o n s u l t i n g and h e l p f u l s u g g e s t i o n s on t h e s t a t i s t i c a l a s p e c t s of t h e model and t o S. Medow f o r programming t h e s i m u l a t i o n e x p e r i m e n t s .

A MODEL FOR RESOURCE ASSESSMENT

AND EXPLORATION/PRODUCTION PROCESSES

1 . INTRODUCTION

The f o r e c a s t i n g of o i l s u p p l y , i n c l u d i n g o i l from non-OPEC s o u r c e s , i s b a s e d m a i n l y on two t y p e s of a n a l y s i s (Adelman and J a c o b y 1 9 7 9 ) . An example o f t h e f i r s t t y p e o f method i s " D i s a g - g r e g a t e d p o o l a n a l y s i s " . T h i s r e q u i r e s t h e g e o l o g i c a l i n t e r p r e - t a t i o n and s t a t i s t i c a l a n a l y s i s o f t h e e x p l o r a t o r y p r o c e s s , and t h e economic e v a l u a t i o n of t h e p o o l s found. By t h i s method a f o r e c a s t of t h e t o t a l r e c o v e r a b l e r e s e r v e s t o b e d i s c o v e r e d , and t h e d i s t r i b u t i o n o f t h e p o o l s i z e i t s e l f , and o f t h e s e q u e n c e o f d i s c o v e r i e s by s i z e , c a n b e made. T h e s e a t t r i b u t e s , t o g e t h e r w i t h c o s t f a c t o r s , d e t e r m i n e t h e economic v i a b i l i t y o f a reser- v o i r . " D i s a g g r e g a t e d p o o l a n a l y s i s " r e q u i r e s d e t a i l e d i n f o r m a - t i o n on p r e v i o u s d i s c o v e r i e s and t h e i r r e s o u r c e s . T h e r e f o r e f o r r e g i o n s where t h e e x p l o r a t i o n h a s n o t y e t begun, o r i s i n an i n i t i a l s t a g e , t h i s method c a n n o t b e u s e d .

The o t h e r method, which i s c a l l e d " a g g r e g a t e d c o u n t r y a n a l y s i s " , i s b a s e d on h i s t o r i c a l d a t a and f o r e c a s t i n g o f r i g a c t i v i t i e s and a s s u m p t i o n s made on proven r e s e r v e s added p e r r i g - y e a r . R e s e r v e a d d i t i o n s t h e n become a n i n p u t t o t h e

c a l c u l a t i o n of c a p a c i t y e x p a n s i o n and l i k e l y o i l p r o d u c t i o n . On t h i s b a s i s a n e v a l u a t i o n of new c a p a c i t y and p r o d u c t i o n p l a n s c a n b e made. " A g g r e g a t e d c o u n t r y a n a l y s i s " d o e s n o t a n a l y z e t h e main p r o p e r t y o f t h e c o u n t r y b e i n g s t u d i e d , which i s t h e a b i l i t y t o c o n t a i n o i l o r " o i l i n p l a c e " . The p r o d u c t i o n p l a n s h o u l d a l s o b e made w i t h r e g a r d t o t h e u n d i s c o v e r e d r e s o u r c e s .

The p r o p o s e d model may b e c o n s i d e r e d a n a t t e m p t t o combine t h e a t t r a c t i v e s i d e s of b o t h t h e above methods. One of t h e u s e s o f t h i s model w i l l b e t o s u g g e s t a l t e r n a t i v e p r o d u c t i o n p l a n s , b a s e d on an a s s e s s m e n t o f r e s o u r c e s i n t h e c o u n t r y and f u t u r e d i s c o v e r i e s a n d e x p l o r a t i o n .

The s e q u e n c e o f p r o c e d u r e s of t h e model i s shown i n a condensed form i n F i g u r e 1 . A s shown i n t h e d i a g r a m , t h e problem i s a n a l y z e d by a model c o n s i s t i n g of a number o f s t a g e s which a r e d e s c r i b e d i n t h e f o l l o w i n g s e c t i o n s .

2 . DETERMINING THE FUTURE PRODUCTION RATE

Although it i s an u n u s u a l a p p r o a c h , w e b e g i n t h e a n a l y s i s w i t h t h e d e t e r m i n a t i o n o f t h e f u t u r e p r o d u c t i o n r a t e . T h i s g i v e s u s t h e p o s s i b i l i t y o f c h e c k i n g whether t h e d e s i r a b l e po- t e n t i a l l e v e l o f p r o d u c t i o n c a n be s u p p l i e d and, i f s o , u n d e r which c o n d i t i o n s .

The d e t e r m i n a t i o n of t h e f u t u r e p r o d u c t i o n r a t e r e l a t e s t o g e n e r a l problems of f o r e c a s t i n g and i s b a s e d on t h e e x t r a p - o l a t i o n of h i s t o r i c a l d a t a .

The i n f o r m a t i o n c o l l e c t e d on o i l p r o d u c t i o n a l l o w s u s t o draw p r o d u c t i o n c u r v e s . W e may t r e a t t h e d a t a on p r o d u c t i o n d i f f e r e n t l y d e p e n d i n g upon w h e t h e r t h e g e n e r a l t e n d e n c y i n t h e p r o d u c t i o n p r o c e s s o r a p r e c i s e p i c t u r e o f c h a n g e s i n t h e a n n u a l p r o d u c t i o n r a t e i s needed.

With r e s p e c t t o t h i s , it i s p o s s i b l e t o u s e d i f f e r e n t i n t e r - p o l a t i o n methods. A l s o t h e c h o i c e of t h e i n t e r p o l a t i o n method depends on t h e d e g r e e of a c c u r a c y o f t h e a v a i l a b l e d a t a ( i . e . i f s i g n i f i c a n t jumps i n t h e r a t e o f p r o d u c t i o n o v e r a s m a l l p e r i o d o f t i m e a r e p r e s e n t , t h e n t h e e x i s t e n c e o f e r r o r c a n b e a s s u m e d ) .

I n t h i s c a s e " p o l y n o m i a l i n t e r p o l a t i o n " i s t h e most d e s i r - a b l e and p o l y n o m i a l s of v a r i o u s d e g r e e s may b e t r i e d . A s a series o f e x p e r i m e n t s shows, a polynomial o f t h e second d e g r e e i s a p p r o p r i a t e when r e p r o d u c i n g t h e t e n d e n c y of t h e p r o d u c t i o n p r o c e s s .

The " c u b i c - s p l i n e i n t e r p o l a t i o n " method i s o p t i m a l i n t h e c a s e o f e x i s t i n g p r e c i s e d a t a on o i l p r o d u c t i o n f o r a r e l a t i v e l y l o n g p e r i o d o f t i m e ( a t l e a s t f i f t e e n t o t w e n t y y e a r s ) . Here t h e r e s u l t i n g p r o d u c t i o n c u r v e p a s s e s t h r o u g h a l l p o i n t s r e f l e c - t i n g t h e a n n u a l r a t e of p r o d u c t i o n .

S i n c e p r o d u c t i o n i s an i n e r t i a l p r o c e s s , h a v i n g a d e l a y o f f i v e t o s i x y e a r s , w e c a n e x t r a p o l a t e a p r o d u c t i o n c u r v e f o r t h a t p e r i o d o f t i m e . Delay t i m e s may b e d i f f e r e n t f o r d i f f e r e n t c o u n t r i e s ( t h e p e r i o d o f t i m e o v e r which t h e m a t h e m a t i c a l methods of e x t r a p o l a t i o n may b e a p p l i e d s h o u l d b e t h e s u b j e c t o f a d d i t i o n a l s t u d y ) .

When e x t r a p o l a t i o n i s r e q u i r e d , t h e p r o d u c t i o n c u r v e o b t a i n e d from t h e " c u b i c - s p l i n e i n t e r p o l a t i o n " method c o n t a i n s more i n f o r - m a t i o n and i s g e n e r a l l y more u s e f u l f o r p r e d i c t i o n t h a n t h e " s e c - ond d e g r e e p o l y n o m i a l i n t e r p o l a t i o n " method. P r o d u c t i o n c u r v e s o b t a i n e d by " s e c o n d d e g r e e p o l y n o m i a l i n t e r p o l a t i o n " may b e u s e d f o r t h e e x t r a p o l a t i o n o f p r o c e s s e s on t h e b a s i s o f i n a d e q u a t e o r i n a c c u r a t e i n f o r m a t i o n .

Determination o f future production rate

I

Assessment o f required reserves

m ^I

^I Resource/Exploration

submodel

I

I 1

I Resource assessment

+ ⁴

^I submodel at country

I b level

Analysis o f existing

Determination o f I

recovery methods and amount of future I

determination o f additional required discovery 1

reserves from proven reserves 4 I

I Exploration submodel

I at basin level

Decision making for facilities of a country with regard t o resources.

technology, etc.

Figure 1 . Outline of model procedures

The d e t e r m i n a t i o n of t h e p r o d u c t i o n c u r v e f o r s u b s e q u e n t p e r i o d s c a n be made on t h e b a s i s of t a b u l a r f u n c t i o n s r e f l e c t i n g t h e s u b j e c t i v e judgement of e x p e r t s .

We p r o p o s e t o e x p l o r e t h r e e a l t e r n a t i v e l e v e l s of p r o d u c t i o n which a r e chosen a c c o r d i n g t o t h e f o l l o w i n g c r i t e r i a :

1 . d o m e s t i c demand;

2 . a d d i t i o n a l p r o d u c t i o n f o r e x p o r t ; 3 . a d a p t a t i o n of e x p o r t s t o t h e

r e q u i r e m e n t s o f development ( i . e . t h e development p l a n ) .

I n g e n e r a l , t h e above c r i t e r i a must a p p l y t o any c o u n t r y , a l t h o u g h it i s n e c e s s a r y t o t a k e i n t o c o n s i d e r a t i o n n a t i o n a l p e c u l i a r i t i e s .

There a r e two p o s s i b l e (complementary) ways o f a c h i e v i n g t h e proposed p r o d u c t i o n l e v e l :

--

t h r o u g h t h e improvement of e x i s t i n g t e c h n o l o g i e s , i. e. a d d i t i o n a l r e c o v e r y ;

--

t h r o u g h t h e d i s c o v e r y o f new d e p o s i t s , i . e . t h e i n t e n s i f i c a t i o n o f e x p l o r a t i o n . 3 . ASSESSMENT O F REQUIRED RESERVES

The r e s o u r c e s r e q u i r e d t o a c h i e v e t h e proposed p r o d u c t i o n l e v e l can b e d e t e r m i n e d a s t h e i n t e g r a l o f t h e f u n c t i o n P ( t )

( t h e p r o d u c t i o n c u r v e s ) , t h r o u g h o u t t h e p e r i o d u n d e r c o n s i d e r a - t i o n , added t o t h e r a t e o f p r o d u c t i o n a t t h e f i n a l i n s t a n c e and m u l t i p l i e d by t h e chosen r e s e r v e t o p r o d u c t i o n r a t i o ( R P R ) , e x p r e s s e d i n number o f y e a r s . T h i s i s done i n o r d e r t o k e e p t h e l e v e l o f p r o d u c t i o n c o n s t a n t o v e r t h e p e r i o d , which depends on t h e r e s e r v e t o p r o d u c t i o n r a t i o :

Required r e s e r v e s =

I

P ( t ) d t

+

^P ( t f i n a l ) R P R t i n i t i a l

I n o r d e r t o e n s u r e t h a t t h e r e q u i r e d r e s e r v e s w i l l be a v a i l a b l e , w e have t o make a n a s s e s s m e n t of t h e c o u n t r y ' s r e s o u r c e s ( o i l i n p l a c e ) , i . e . t o s i m u l a t e t h e d i s c o v e r y p r o c e s s and t o c a l c u l a t e u n d i s c o v e r e d r e s o u r c e s .

4 . THE RESOURCE ASSESSMENT SUBMODEL

The model i s d e s i g n e d f o r t h e p u r p o s e o f a s s e s s i n g t h e u n d i s c o v e r e d r e s o u r c e s i n t h e c o u n t r y u n d e r c o n s i d e r a t i o n . According t o t h e most u s e f u l d e f i n i t i o n (USGS B u l l e t i n 1976)

,

u s i n g t h e McKelvey C l a s s i f i c a t i o n Diagram of R e s e r v e s and R e s o u r c e s , u n d i s c o v e r e d r e s o u r c e s a r e " u n s p e c i f i e d b o d i e s o f m i n e r a l - b e a r i n g m a t e r i a l s u r m i s e d t o e x i s t on t h e b a s i s o f b r o a d g e o l o g i c a l knowledge and t h e o r y " . T h e r e f o r e t h e geo- l o g i c a l c h a r a c t e r i s t i c s o f p r o s p e c t i v e a r e a s a r e t a k e n a s t h e b a s i s o f a n a l y s i s .

I n f o r m a t i o n on t h e t r a p s , r e s e r v o i r r o c k s , s o u r c e , migra- t i o n and g e n e r a t i o n o f h y d r o c a r b o n s s h o u l d b e c o l l e c t e d and a n a l y z e d t o e n a b l e d e c i s i o n s t o b e made c o n c e r n i n g t h e r i c h n e s s of t h e p r o s p e c t i v e p e t r o l e u m b a s i n s . I n a d d i t i o n , t h e s i z e and t h i c k n e s s of t h e b a s i n s s h o u l d b e d e l i n e a t e d .

Undiscovered r e s o u r c e s a r e a s s e s s e d by t h e v o l u m e t r i c method (Myer 1978 and Levorsen 1 9 6 7 ) . W e d e s i g n a t e t h e amount of r e - c o v e r a b l e o i l p e r u n i t volume of s e d i m e n t a s t h e r i c h n e s s f a c t o r

( R . F . ) . With t h i s d e s i g n a t i o n t h e amount o f u n d i s c o v e r e d r e - s o u r c e s may be c a l c u l a t e d a s f o l l o w s :

Un. R e s o u r c e s = R.F. x Area x T h i c k n e s s

I t i s o b v i o u s t h a t p a r a m e t e r s f o r t h e R.F., t h e Area and t h e T h i c k n e s s a r e v e r y u n c e r t a i n f o r a r e g i o n where d r i l l i n g h a s n o t y e t been implemented, o r h a s l e d t o no d i s c o v e r y .

For u n e x p l o r e d b a s i n s t h e s e v a l u e s a r e g i v e n by g e o l o g i s t s a s t h e d e s c r i p t i o n of t h e p o t e n t i a l s e d i m e n t a r y volume and d e p t h of b u r i a l . T h i s i n f o r m a t i o n i s used t o c o n s t r u c t t h e p r o b a b i l i t y d i s t r i b u t i o n o f t h e Area and t h e T h i c k n e s s p a r a m e t e r s .

The R.F. may b e d e f i n e d by a n a l o g i e s t o s i m i l a r , m a t u r e p r o d u c i n g b a s i n s and w e t h e r e f o r e need t o have some b a s i n c l a s s i f i c a t i o n scheme.

One b a s i n c l a s s i f i c a t i o n scheme h a s been proposed by Klemme ( 1 9 7 5 ) . K l e m m e examined t h e o i l r e c o v e r y ( o r i t s g a s e q u i v a l e n t ) i n t e r m s o f b a r r e l s p e r c u b i c m i l e of s e d i m e n t and s u g g e s t e d

a " y a r d s t i c k " , which, i n c o n j u n c t i o n w i t h t h e r a t i n g o f t h e main g e o l o g i c a l p a r a m e t e r s , c o u l d a s s i s t i n t h e d e t e r m i n a t i o n o f t h e

K.F. f o r a g e n e r a l t y p e of g e o l o g i c a l b a s i n '(Table 1 )

.

The R.F. o f a n u n e x p l o r e d b a s i n w i l l l i e w i t h i n a r a n g e o f v a l u e s , which f o r s i m i l a r t y p e s of b a s i n c a n be d e f i n e d , and t h e p r o b a b i l i t y d i s t r i b u t i o n of t h e R.F. c a n b e c o n s t r u c t e d .

Thus t h e g e o l o g i c a l a n a l y s i s o f t h e a r e a under c o n s i d e r a t i o n p r o v i d e s u s w i t h t h e c r i t i c a l d a t a f o r i n p u t t o t h e model, a s shown i n F i g u r e 2 . The a r e a o f c o u n t r y i s d i v i d e d i n t o a number of p o t e n t i a l p e t r o l e u m b a s i n s , i d e n t i f i e d by K ( K = 1 ,

...

^{N ) .}

Each b a s i n i s d e s c r i b e d by t h e d i s t r i b u t i o n of t h e main p a r a - m e t e r s : t h e A r e a , t h e T h i c k n e s s and t h e R.F., which a r e i n d e x e d by t h e a p p r o p r i a t e K s u b s c r i p t . The t y p e o f d i s t r i b u t i o n depends on o n e ' s knowledge a b o u t t h e b e h a v i o u r of a p a r a m e t e r .

For example, t h e R.F. c a n be r e p r e s e n t e d by t h e l o g n o r m a l d i s t r i b u t i o n f o r a g i v e n p r o d u c i n g f o r m a t i o n by a common reser- v o i r mechanism. However, i n t h e c a s e of a n u n e x p l o r e d b a s i n t h e R.F. i s a v e r y d i f f i c u l t p a r a m e t e r t o d e f i n e and w e c a n s i m p l i f y t h e R.F. d i s t r i b u t i o n a s t r i a n g u l a r w i t h minimum, maxi- mum and m o s t l i k e l y v a l u e s of t h e random v a r i a b l e R.F.

T a b l e 1 . " Y a r d s t i c k " f o r b a s i n e v a l u a t i o n

"Yardstick" for Basin Evaluation

Richness factor Chance of

bbl per cubic Commercial Presence Basin type mile of sediments production of giants

1. Cratonic 35,000 High 30% 20%

interior 18,000 Average

3.500 Low

2. Cratonic 250,000 80% 65%

multicycle 120,000

( Large) 25,000

(Small) 75,000 50% 30%

40,000 7,500 3. Cratonic r i f t

4. Intermediate 600,000" 50% 50%

extracontinental 150,000

4A Closed 10,000

48 Foredeep 60.000 40% 10%

25,000 1,000

4C Open 300,000

160,000 3,000

5. Pull-apart ? 30% 20%

Presently average 40.000

6.-7. 4,000,000 20% 40%

Intermontane 1 80,000 5,000

8. Delta 220,000 50% Few giants

1 90,000

?

Average a l l basins 50,000 to 100.000 50% 50%

Field size' largest field ( 1 0th largest field)

'Based on ultimate recovery of total basin reserves.

'*Middle East

F i g u r e 2. H y p o t h e t i c a l map of a c o u n t r y showing b a s i n s and d i s t r i b u t i o n of main param- e t e r s

The s i m u l a t i o n model i s p r e s e n t e d i n t h e f l o w c h a r t F i g u r e 3 , where "A" i s t h e s e t ' o f d i s t r i b u t i o n s o f t h e A r e a , T h i c k n e s s and t h e R.F. The e x p e c t e d v a l u e o f t h e u n d i s c o v e r e d

r e s o u r c e s i s c a l c u l a t e d u s i n g Monte-Carlo t e c h n i q u e s .

One s i m u l a t i o n p a s s b e g i n s w i t h t h e t e s t t o see w h e t h e r o i l e x i s t s i n b a s i n K and g o e s on t o t h e n e x t b a s i n . Each

t e s t i s p e r f o r m e d by a c o m p a r i s o n o f t h e i n d i v i d u a l p r o b a b i l i t y P ( B k ) o f o i l o c c u r r e n c e i n t h e ~ t h b a s i n w i t h t h e random number

and g o e s on t o t h e n e x t b a s i n . I£

t h e n b a s i n K h a s o i l . I f

t h e n b a s i n K h a s n o o i l .

The i n d i v i d u a l p r o b a b i l i t y P ( B ) i s a s s i g n e d t o e a c h b a s i n b a s e d on p a s t e x p e r i e n c e o f e x p l o r a t i o n o r , i f e x p l o r a t i o n h a s n o t y e t been s t a r t e d , on p a s t e x p e r i e n c e i n a r e a s w i t h s i m i l a r g e o l o g y . One s e t o f p a s t e x p e r i e n c e i s r e a d i l y a v a i l a b l e i n t h e form o f n a t i o n a l d r i l l i n g s t a t i s t i c s ( n a t i o n a l s u c c e s s r a t i o ) which have been s y s t e m a t i c a l l y r e c o r d e d f o r many y e a r s . Unfor- t u n a t e l y , most g e o l o g i s t s f e e l t h a t t h e n a t i o n a l s t a t i s t i c s a r e o f l i t t l e u s e i n c o n s i d e r i n g a p a r t i c u l a r v e n t u r e a n d t h e y a r e more w i l l i n g t o r e g a r d t h e l o c a l p a s t e x p e r i e n c e i n o r d e r t o make a d e c i s i o n on a p a r t i c u l a r v e n t u r e . Thus a s s i g n i n g proba- b i l i t i e s i s o n e o f t h e c r i t i c a l p a r t s o f r e s o u r c e a s s e s s m e n t .

R e s o u r c e s o f t h e K~~ b a s i n a r e a s s e s s e d o n l y a f t e r t h e t e s t h a s been c o m p l e t e d s u c c e s s f u l l y by s a m p l i n g t h e v a l u e o f t h e A r e a , T h i c k n e s s a n d R.F. and c o m p u t i n g t h e i r p r o d u c t .

Each i t e r a t i o n y i e l d s a v a l u e f o r t o t a l r e s o u r c e s i n t h e c o u n t r y . T h i s s i m u l a t i o n p r o c e s s i s r e p e a t e d i t i m e s , where i = 1 ,

...

^I-

- t h e number o f i t e r a t i o n s . The mean, v a r i a n c e , e t c . o f t o t a l r e s o u r c e s c a n t h e n e a s i l y b e c a l c u l a t e d . A l s o , t h e f r e q u e n c y d i s t r i b u t i o n a n d c u m u l a t i v e d i s t r i b u t i o n g r a p h s c a n b e p l o t t e d t o r e p r e s e n t t h e r e s u l t o f t h e m o d e l l i n g .

5. THE EXPLORATION MODEL

The e x p l o r a t i o n submodel p e r f o r m s t h e c a l c u l a t i o n s o f r e s o u r c e s a t b a s i n l e v e l by i n t r o d u c i n g o i l s t r u c t u r e s o r t a r g e t s .

I

^-- Do 1 iterations

i s 0

I

f

Set to initial conditions

TOTRESOURCE = TOTRESOURCEZERO;

N; p l ; p2;

...

^{; pN}

I

^Yes

No b

TOTRESOU RCE = TOTRESOU RCE +

RESOURCE K Sample the area thickness, richness factor

compute RESOURCE of K basin

End of ith passtore

TOTRESOURCE

I

I Yes

Simulation run is finished. Print means, variance. Plot distributions

F i g u r e 3 . Flow c h a r t o f t h e r e s o u r c e submodel

An example o f a s i m i l a r s i m u l a t i o n a n a l y s i s i s d e s c r i b e d by Newendorf ( 1 9 7 5 ) . The p r o p o s e d model i s an a p p l i c a t i o n o f t h i s example t o r e s o u r c e a s s e s s m e n t i n t h e b a s i n a n d t h e d e t e r - m i n a t i o n o f t h e amount o f e x p l o r a t o r y d r i l l i n g r e q u i r e d t o f i n d t h e e x p e c t e d v a l u e o f r e s o u r c e s i n t h e b a s i n . T h i s e x p e c t e d v a l u e i s d e f i n e d by t h e p a r a m e t e r CONT--the number o f s t r u c t u r e s which a r e h y p o t h e s i z e d t o c o n t a i n o i l :

CONT = NZERO X pZERO,

w h e r e , NZERO i s t h e number o f s t r u c t u r e s which h a v e t o b e t e s t e d a n d pZERO i s t h e p r o b a b i l i t y o f s u c c e s s ( a s s i g n e d a c c o r d i n g t o t h e e x p l o r a t o r y s u c c e s s r a t i o i n a g i v e n o r s i m i l a r b a s i n ) . I n d e x ZERO r e f l e c t s t h e i n i t i a l c o n d i t i o n s o f s i m u l a t i o n .

When s e a r c h i n g f o r o i l , s u c c e s s and f a i l u r e a r e c o n s i d e r e d a s random t r i a l s , s o t h e t e s t f o r e a c h k s t r u c t u r e i s made by t h e c o m p a r i s o n o f a random number w i t h t h e p r o b a b i l i t y o f s u c c e s s p. I n t h i s model t h e o c c u r r e n c e s o f o i l i n e a c h s t r u c t u r e a r e t h e d e p e n d e n t e v e n t , and a f t e r e a c h t e s t t h e N , t h e p and t h e CONT p a r a m e t e r s a r e r e v i s e d . Each i t e r a t i o n i s p e r f o r m e d u n t i l a l l h y p o t h e s i z e d o i l - c o n t a i n i n g s t r u c t u r e s h a v e been f o u n d .

The s i m u l a t i o n model i s p r e s e n t e d i n t h e f l o w c h a r t F i g u r e 4 , where "B" i s t h e s e t o f i n p u t d i s t r i b u t i o n s o f t h e A r e a , T h i c k n e s s and t h e R.F. f o r e a c h s t r u c t u r e .

The r e s u l t o f m o d e l l i n g g i v e s t h e amount of r e s o u r c e s i n t h e b a s i n i n t h e f o r m o f a c u m u l a t i v e p r o b a b i l i t y g r a p h w i t h t h e means and s t a n d a r d d e v i a t i o n and t h e d i s t r i b u t i o n o f t h e random v a l u e k . T h i s v a l u e r e p r e s e n t s t h e number o f s t r u c t u r e s t h a t had been d r i l l e d on e a c h i t e r a t i o n p a s s b e f o r e d i s c o v e r i n g a l l t h e CONT = NZERO x pZERO e x p e c t e d o i l - c o n t a i n i n g s t r u c t u r e s . The minimum v a l u e o f t h i s d i s t r i b u t i o n would b e k = CONT--the c a s e i n which n o d r y s t r u c t u r e s w e r e d r i l l e d . The maximum

v a l u e o f t h e d i s t r i b u t i o n would b e k = NZERO--the c a s e i n which t h e l a s t o i l - c o n t a i n i n g s t r u c t u r e was n o t f o u n d u n t i l t h e v e r y l a s t s t r u c t u r e had been d r i l l e d .

With t h e d i s t r i b u t i o n o f k v a l u e s w e c o u l d g a i n i n s i g h t i n t o t h e amount o f e x p l o r a t o r y d r i l l i n g r e q u i r e d t o f i n d a l l t h e r e s o u r c e s i n t h e b a s i n .

6 . MAKING DECISIONS CONCERNING THE FACILITIES OF

A COUNTRY WITH REGARD TO RESOURCES, TECHNOLOGY, ETC.

T h i s p a r t o f t h e model p r o d u c e s t h e f o r e c a s t o f f u t u r e p r o d u c t i o n , a n d d e p e n d s on t h e r e s u l t s o f t h e e x p l o r a t i o n model.

I n g e n e r a l , t h e submodel a t t e m p t s t o r e s t o r e t h e b a l a n c e between p r o d u c i n g f a c i l i t i e s a n d r e s o u r c e s u p p l y . The mean v a l u e o f p r o s p e c t i v e r e s o u r c e s i s compared w i t h t h e amount o f r e q u i r e d r e s e r v e s o b t a i n e d f r o m t h e e x t r a p o l a t i o n o f t h e i n i t i a l l y

a c c e p t e d p r o d u c t i o n r a t e s . The i m p a c t o f economic, t e c h n o l o g i c a l and p o l i t i c a l f a c t o r s must b e t a k e n i n t o a c c o u n t . W i t h o u t d o u b t

I

^{Do I} number of iterations

I

Set to initial conditions

TOTRESOURCE = TOTRESOURCEZERO N p = pZERO,

-

^NZERO,

CONT = NZEROXPZERO

Compute new P for (K + 1) structure

N o

TOTR ESOU RCE = TOTRESOU RCE + + RESOURCE K

Sample the area, thickness, richness factor compute RESOURCE of

~t~ structure

End of one passtore K

Q

,

L

Yes Yes

N = N - 1 CONT = CONT

-

1

4 Yes

-

1

Simulation run is finished

-

Print distributions of TOTRESOURCE and K, means, variances

w v

End of one passtore TOTRESOURCE

Figure 4 . Flow c h a r t o f t h e e x p l o r a t i o n submodel

t h e s e f a c t o r s a r e q u i t e u n p r e d i c t a b l e - - a l s o t h e comparison of p r o s p e c t i v e r e s o u r c e s w i t h v a r i o u s p r o b a b i l i t i e s may be made.

A l l t h i s l e a d s t o some c o r r e c t i o n of t h e p r o d u c t i o n c u r v e

o b t a i n e d t h r o u g h t h e s e l e c t e d c r i t e r i a of e x p e r t s i n t h e f i r s t p a r t of t h e model. S e v e r a l r e v i s e d a l t e r n a t i v e c u r v e s c o u l d be t a k e n i n t o a c c o u n t f o r t h e e s t a b l i s h m e n t of t h e p r o d u c t i o n p o l i c y .

7 . THE TEST CASE

The f i r s t r u n of t h e model was made f o r Mexico. The d e t e r m i n a t i o n of t h e f u t u r e p r o d u c t i o n r a t e was based on

i n f o r m a t i o n from t h e ENERTREE Data Base R e t r i e v a l System u s i n g d a t a from t h e IIASA O i l D a t a Base. Our s o u r c e s of i n f o r m a t i o n f o r t h e r e s o u r c e a s s e s s m e n t submodel a r e p u b l i s h e d d a t a , i n p a r t i c - u l a r "Development i n Mexican Petroleum" by Meyerhoff and Morvis.

G e o l o g i c a l a n a l y s i s was accomplished f o r t h e d e t e r m i n a t i o n of t h e r i c h n e s s f a c t o r by u s i n g K l e m m e ' s c l a s s i f i c a t i o n scheme

( 1 975) --see T a b l e 1 . W e c o n s i d e r e d 1 9 p r o s p e c t i v e b a s i n s

i n Mexico. For e a c h b a s i n t h e g e o l o g i c a l a n a l y s i s was performed and t h e d i s t r i b u t i o n of t h e main p a r a m e t e r s was c o n s t r u c t e d . The i n d i v i d u a l p r o b a b i l i t y i s a s s i g n e d u s i n g Meyer's d e s c r i p t i o n of g e o l o g i c a l f e a t u r e s ( 1 978)

.

The r e s u l t s of t h e d e t e r m i n a t i o n of f u t u r e p r o d u c t i o n r a t e s and of t h e r e q u i r e d r e s o u r c e s t o s u p p l y t h e s e r a t e s a r e p r e s e n t e d i n Appendix 1 . T a b l e Al. 1 shows t h e i n p u t d a t a and r e s u l t s f o r

polynomial e x t r a p o l a t i o n . F i g u r e A l . l shows t h e p r o d u c t i o n c u r v e d e r i v e d from t h i s method. 25,549 b i l l i o n b a r r e l s of r e s o u r c e s a r e r e q u i r e d t o s u p p l y t h i s form o f o i l p r o d u c t i o n c u r v e .

T a b l e A 1 . 2 shows t h e i n p u t d a t a and r e s u l t s f o r c u b i c - s p l i n e i n t e r p o l a t i o n . The p r o d u c t i o n c u r v e d e r i v e d from t h e c u b i c - s p l i n e method i s p r e s e n t e d i n F i g u r e A 1 . 2 . 49,9229 b i l l i o n b a r r e l s of r e s o u r c e s a r e r e q u i r e d f o r t h e s e r a t e s o f p r o d u c t i o n .

The i n p u t d a t a , some i n t e r m e d i a t e s t a t i s t i c s and t h e o u t p u t of t h e r e s o u r c e a s s e s s m e n t submodel a r e p r e s e n t e d i n Appendix 2 . The r e s u l t s show t h e r e s o u r c e s i n Mexico i n t h e form of t h e p r o b a b i l i t y d i s t r i b u t i o n s . Frequency d i s t r i b u t i o n i s shown i n F i g u r e A 2 . 1 and c u m u l a t i v e d i s t r i b u t i o n i n F i g u r e A 2 . 2 . The minimum v a l u e i s 8,0934 b i l l i o n b a r r e l s and t h e maximum v a l u e

i s 140,34 b i l l i o n b a r r e l s . The mean v a l u e of r e s o u r c e s i n Mexico i s 58,3726 b i l l i o n b a r r e l s . On t h e c u m u l a t i v e g r a p h t h e v a l u e 11,574 b i l l i o n b a r r e l s w i t h a p r o b a b i l i t y of 1 may be i n t e r p r e t e d a s proven r e s e r v e s .

The comparison of r e s u l t s of t h e r e s o u r c e a s s e s s m e n t sub- model w i t h t h e amount of r e s o u r c e s d e r i v e d from t h e e x t r a p o l a -

t i o n of t h e p r o d u c t i o n c u r v e (25,5490 o r 42,9229) shows t h a t w i t h t h e p r o b a b i l i t y 0.98 o r 0.7 t h i s amount of r e q u i r a b l e r e s o u r c e s can be s u p p l i e d from f u t u r e d i s c o v e r i e s .

I t i s n e c e s s a r y t o mention h e r e t h a t some o f t h e d a t a used i n t h e t e s t c a s e a r e n o t v e r i f i e d and a r e sometimes " s p e c u l a t i v e . "

D e t a i l e d work on i n p u t d a t a c o u l d g r e a t l y improve t h e r e s u l t o f m o d e l l i n g .

APPENDIX 1

I E I I I I I I a Q a a a 0 0 0 0 a Q 0 0 a a a * 3 a a 0 Q I

o e a e e o 8 ~ ' o e o ~ ~ o o o o

1 l, 1

8 ~ ~ ~ g 8 ~ g ~ 8 1 C 3 8 p I S ~ Q E 4 4

^maeco8 1 I L ( e l ?

. . . cc,j

.?,,?=.=?==.=

;

IZI-l---I

I I W I I

1 - 1 3 1 I

I l l I

'

i s ;

I ^{I - ,}

I a I

-

^{+ -.-.-.-. +}

I I C I I

I L. I I - P l r ) T I

I I I I