Recent Developments in Production Forecasting and Optimisation Methods

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1 Recent Developments in Production Forecasting and Optimisation Methods Ahmed Khamassi, Serafim Ltd Peter Cunningham, Serafim Ltd

2 Content Programme Dual Discount Rate Method for Oil & Gas Project Development Well Number Optimisation Injector Producer Optimisation C-Curves Curves Decline Curve Analysis C-Curves: Curves: Well Density and Infill Drilling Free-Gas:Liquid Ratio

3 Dual Discount Rate For Projects NPV

4 Dual Discount Rate For Projects Current Practice: NPV Assume constant discount rate Assume constant oil price Calculate NPV as (Discounted Revenues Discounted Expenditures) Carry out sensitivity analysis to estimate a range of NPVs under different senarios

5 Dual Discount Rate For Projects NPV Current Practice (Continued): Calculate Internal Rate of Return (IRR: the discount rate that leads to NPV = 0) Use a capital efficiency measure of the type NPV/NPC (Net Present Value of CAPEX)

6 Dual Discount Rate For Projects NPV Issues with current practices: Nature of the discount rate: NPV a measure of value that depends critically on discount rate. Use cost of capital (interest rate, expected shareholders return etc ) ) or opportunity cost (expected returns from alternative investments)? Do we need to discount capital investment?

7 Dual Discount Rate For Projects NPV Use of weighted average of cost of capital Assumption that post-tax tax revenues convert itself back into capital and should be discounted Uncertainty? Capital efficiency measure: When using weighted average cost of capital Generally NPV/NPC hurdle Useful for one-off off decisions: How do I allocate my capital now to maximise NPV?

8 Dual Discount Rate For Projects NPV Not so useful when trying to answer the question: How do I allocate my capital now, and next year, and the year after to maximise long-term value of my company? Example: an NPV/NPC = 0.1 is very attractive for a 2-month 2 project, but unattractive for a 20-year project. Internal Rate of Return (IRR) Discount rate at which project NPV = 0

9 Dual Discount Rate For Projects NPV Multiple IRRs if capital expenditure occurs in tranches Treatment of risk Conventional practice: calculate NPV in a deterministic way then vary NPV parameters For most parameters, it is usual to concentrate on expected NPV Risk is defined by the variance of the distribution

10 Dual Discount Rate For Projects NPV E(NPV): 3.9 NPV SD: 0.6 P(NPV)

11 Dual Discount Rate For Projects NPV E(NPV): 3.9 NPV SD: 5.7 P(NPV)

12 Dual Discount Rate For Projects NPV Oil and gas price uncertainty: Affects the entire company s s portfolio Use of screening criteria: low oil price ($10/bbl) Ignores time effects Obscures risk reduction measures

13 Dual Discount Rate For Projects NPV Capital Asset Pricing Model (CAPM): The expected rate of return on a capital asset is a linear function of its non- diversifiable risk The value of the capital asset is determined by this relationship

14 Dual Discount Rate For Projects NPV Capital Asset Pricing Model Expected return on asset Government bonds Stock market Ratio - Standard deviation of return on asset : SD of return on market portfolio

15 Dual Discount Rate For Projects NPV Advantages of the Capital Asset Pricing Model (CAPM): The value of a project depends on the uncertainty Uncertainty will be imbedded in the calculation of the NPV NPV includes all scenarios and their probabilities

16 Dual Discount Rate For Projects NPV The Dual Discount Rate NPV: Definition: NPV model that uses two discount rates: the expenditure stream is discounted at the cost of capital and the revenue stream is discounted at a rate that takes account of oil and gas price risk.

17 Dual Discount Rate For Projects Equation: NPV NPV = n 1 a t.p 0 + ( ) t 1+ E(r ) ( 1+ r ) p b t f t a t, b t coefficients such that year t cash flow = a t P t + b t P 0 : starting point oil price E(r p ): expected rate of return on writing oil futures r f : risk free rate of return

18 Dual Discount Rate For Projects NPV DDR NPV vs. Conventional NPV DDR NPV is a measure of value given uncertainty DDR NPV resolves the cost of capital vs. opportunity cost of capital problem DDR NPV emphasises the fact that the IRR is an instantaneous quantity

19 Dual Discount Rate For Projects NPV We suggest the use of a NPC x Payback measure instead of NPV/NPC measure Expected returns of oil prices: Futures market indicative of value of future oil or gas Problem with longer term investments

20 Dual Discount Rate For Projects NPV Discount rate in oil futures - 7/8/2000 Discount in oil price (per annum) Mar- 00 Oct- 00 Apr- 01 Nov- 01 May- 02 Dec- 02 Jun- 03 Jan- 04 Settlement date

21 Dual Discount Rate For Projects NPV 0.4 Discount rates from IPE oil futures Discount rate over life of futures year 2 years 3 years month oil futures price ($/bbl)

22 NPV Formulas: Optimising the number of wells

23 NPV Formulas Aim Alternative to complicated spreadsheet models Provide auditable formulas Study inter-relationships relationships Effects of drilling more wells Economics: Increased CAPEX (scalable and possibly unscalable) Increased OPEX Production and recovery Speeding up field production Increased recovery

24 NPV Formulas Number of wells that maximise NPV: N Maximi sin gnpv = R. d q. L α. E q C. d C. d + E q + E α E q α. E R where α = (1+d) -Tab L.q and T ab (abandonment time)=.ln q.n E and q initial oil production per well per year, averaged over all wells, including injectors N total number of wells, including injectors R technical reserves i.e. the amount of oil that could be recovered if the field were run for a very long time L net revenue per tonne of oil (i.e. after all taxes and royalties, including profit tax) d discount rate C net capital cost per well D net capital costs not related to numbers of wells, e.g. roads and pipelines E net opex per well Note:- In this context, net means expressed in terms of effect on present value, after all taxes and royalties

25 Assumptions: NPV Formulas Technically recoverable reserves independent of number of wells Initial well rates independent of number of wells The field follows exponential decline from start

26 Interpretation: NPV Formulas Reformulate the equation Express the NPV as function of NPV maximising well number Ignore abandonment NPV Maximi sin g Well Number 1 = R. L. 1 N. C + N. q + 1 R. d E D d

27 NPV Formulas NPV Maximi sin g Well Number 1 = R. L. 1 N. C + N. q + 1 R. d E D d R.L: value of oil in the ground R. L : the value lost because of discounting N. q + 1 R. d D: value lost as net capex (C+E/d): value lost per well drilled

28 NPV Formulas Effects of changing the number of wells $500,000,000 $450,000,000 $400,000,000 $350,000,000 Present Value $300,000,000 $250,000,000 $200,000,000 $150,000,000 Value lost to time effects Opex and variable capex Sum of value lost $100,000,000 $50,000,000 $ Number of wells

29 Number of wells and NPV model Conventional NPV vs Number of Wells 1, NPV Number of Wells

30 Number of wells and NPV model Effects of changing the revenue discount rate 1, NPV ($ million) NPV with 25 wells (conventional optimal) NPV optimised with dual discount method Optimal number of wells Number of wells drilled Oil discount rate

31 Injector:Producer and NPV Assumptions Water flood Bottom whole pressure constraints Derivation Material balance Link average well rate (producers and injectors) and injector:producer ratio Feed relationship in NPV formula

32 Injector:Producer and NPV Optimal injector : producer ratio = PI. Bo.( Cp. d II. Bw.( Ci. d + Ep) + Ei) PI = productivity index of average production well II = injectivity index of average injection well Bo = oil formation volume factor Bw = water formation volume factor Cp = net capex cost per producer

33 C-Curve Curve Decline Curves Analysis

34 Summary Practical problem with decline analysis Hyperbolic decline rate converges to zero unrealistic late life production Solutions C-curve generalisation of the hyperbolic curve

35 Introduction (Simple decline analysis = calculation of oil-cut or oil-rate from cumulative production) Production forecasts for existing wells/fields Approximate production profiles for new wells/fields (from initial rates and ultimate recovery)

36 Exponential Hyperbolic Li-Horne Main formulations q ( t ) = α. ( UR Np ) b ( UR Np) ( ) 1 q( t) = α. q ( t ) = α Np β Shapes of the different decline equations (idealised example) Oil production rate (stb/day) Cumulative production (MM stb) Exponential Hyperbolic; b=0.3 Hyperbolic; b=0.7 Li-Horne

37 Typical decline in simulation run 1.2 Decline in Ebughu North-East sector simulation model Oil-cut Cumulative oil (k stb)

38 Generalisation of exponential to hyperbolic dq dt oil q oil = a dq dt oil q oil = a. q b oil

39 Generalisation of exponential to C-C curve dq dt oil ( ) = a R Q oil dq dt oil ( ) = ( a + β ( R Q ) oil ) R Q oil b

40 Integrating the C-curve C equation = R. 1 Q oil b a. b. Q a a 1+ e Oil R

41 C (cumulatives)) curve q( t) = α. ( ) ( ) b+ UR Np + β. UR Np 1 C-curve and hyperbolic match to well simulation profile (Alba Field) dr/dx r P10 eclipse results P50 eclipse results C-curve - a=0.263; b = 8 C-curve - a=0.081; b =20 Hyperbolic with fixed reserves - b = 0.79

42 C-Curves Curves and Number of Wells From basic C-curve C equation and the derivation work dr 2 = βr dx Where: x is the number of wells drilled and r the fraction of removable oil remaining Gives a good approximation of the effect of increasing the number of wells

43 C-Curves Curves and Number of Wells AXS area - Effects of well density on recovery Ultimate recovery in 2020 (mm b) UR Calibration to simulation Validation to additional simulation runs Additional rec per well Additional recovery per 1000 ft (mmb) Well footage (1000 ft)

44 Free Gas:Liquid Ratio

45 Free Gas:Liquid Ratio Problems with Muskat material balance method: Depends on field relative permeabilities, but no information on these Core plug relative permeabilities do not include main mechanism at play - gravity Result relative permeabilities adjusted until profiles are no longer obviously wrong But Not obviously wrong correct

46 North Oron I-2 Material balance (Muskat method) calculation Jan-05 Jan-06 Jan-07 Rates (bbl or Mscf per day) Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 Jan-16 Jan-17 Jan-18 Jan-19 Oil Rate Total Gas Rate Water Rate

47 NOR I-1 (North Oron simulation run) Jan-04 Jan-05 Jan-06 Rates (bbl or Mscf per day) Jan-07 Jan-08 Oil Rate Produced Gas Rate Water Rate

48 FGLR (Free-gas:liquid ratio) equilibrium method Gas much more mobile than oil or water Once gas cone reaches well, then can produce very high levels of gas Result cone does not easily move further down i.e. gas-liquid contact reaches equilibrium position Easy to calculate equilibrium FGLR (= (Gas expansion + injection) / (Liquid expansion + injection))

49 FGLR equation ( ) QL a FGLR FGLR. e FGLR FGLRinitial + equilibrium initial 1 = where Q L = cumulative liquid production a = gas breakthrough parameter, a measure of the speed of convergence to equilibrium.

50 NOR (North Oron FGLR profile) Rates (bbl or Mscf per day) Jan-05 Jan-06 Jan-07 Jan-08 Oil Rate Produced Gas Rate Water Rate

51 Thank you For more information visit:

Total 100 All learning outcomes must be evidenced; a 10% aggregate variance is allowed.

Total 100 All learning outcomes must be evidenced; a 10% aggregate variance is allowed. Prescription: 603 Business Finance Elective prescription Level 6 Credit 20 Version 3 Aim Prerequisites Recommended prior knowledge Students will apply financial management knowledge and skills to small