Recent Developments in Production Forecasting and Optimisation Methods Ahmed Khamassi, Serafim Ltd Peter Cunningham, Serafim Ltd
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
Dual Discount Rate For Projects NPV
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
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)
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?
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?
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
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
Dual Discount Rate For Projects NPV E(NPV): 3.9 NPV SD: 0.6 P(NPV)
Dual Discount Rate For Projects NPV E(NPV): 3.9 NPV SD: 5.7 P(NPV)
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
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
Dual Discount Rate For Projects NPV Capital Asset Pricing Model 0.18 0.16 Expected return on asset 0.14 0.12 0.1 0.08 0.06 0.04 0.02 Government bonds Stock market 0 0 1 Ratio - Standard deviation of return on asset : SD of return on market portfolio
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
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.
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
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
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
Dual Discount Rate For Projects NPV Discount rate in oil futures - 7/8/2000 Discount in oil price (per annum) 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 Mar- 00 Oct- 00 Apr- 01 Nov- 01 May- 02 Dec- 02 Jun- 03 Jan- 04 Settlement date
Dual Discount Rate For Projects NPV 0.4 Discount rates from IPE oil futures 1998-2000 Discount rate over life of futures 0.3 0.2 0.1 0 20 21 22 23 24 25 26 27 28 29 30-0.1-0.2-0.3 1 year 2 years 3 years -0.4 1 month oil futures price ($/bbl)
NPV Formulas: Optimising the number of wells
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
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
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
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
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
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 $0 0 5 10 15 20 25 30 35 40 Number of wells
Number of wells and NPV model Conventional NPV vs Number of Wells 1,000 800 600 400 NPV 200 0-200 -400-600 -800 0 10 20 30 40 50 60 Number of Wells
Number of wells and NPV model Effects of changing the revenue discount rate 1,000 40 NPV ($ million) 900 800 700 600 500 400 300 200 100 NPV with 25 wells (conventional optimal) NPV optimised with dual discount method Optimal number of wells 35 30 25 20 15 10 5 Number of wells drilled 0 0 0.1 0.12 0.14 0.16 0.18 0.2 Oil discount rate
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
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
C-Curve Curve Decline Curves Analysis
Summary Practical problem with decline analysis Hyperbolic decline rate converges to zero unrealistic late life production Solutions C-curve generalisation of the hyperbolic curve
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)
Exponential Hyperbolic Li-Horne Main formulations q ( t ) = α. ( UR Np ) b ( UR Np) ( ) 1 q( t) = α. q ( t ) = α Np β 12000 Shapes of the different decline equations (idealised example) Oil production rate (stb/day) 10000 8000 6000 4000 2000 0 0 1 2 3 4 5 6 Cumulative production (MM stb) Exponential Hyperbolic; b=0.3 Hyperbolic; b=0.7 Li-Horne
Typical decline in simulation run 1.2 Decline in Ebughu North-East sector simulation model 1 0.8 Oil-cut 0.6 0.4 0.2 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Cumulative oil (k stb)
Generalisation of exponential to hyperbolic dq dt oil q oil = a dq dt oil q oil = a. q b oil
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
Integrating the C-curve C equation = R. 1 Q oil b a. b. Q a a 1+ e Oil R
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 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 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
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
C-Curves Curves and Number of Wells AXS area - Effects of well density on recovery Ultimate recovery in 2020 (mm b) 250 200 150 100 50 UR Calibration to simulation Validation to additional simulation runs Additional rec per well 18 16 14 12 10 8 6 4 2 Additional recovery per 1000 ft (mmb) 0 0 0 20 40 60 80 100 120 Well footage (1000 ft)
Free Gas:Liquid Ratio
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
North Oron I-2 Material balance (Muskat method) calculation 60000 50000 40000 30000 20000 10000 0 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
NOR I-1 (North Oron simulation run) 12000 10000 8000 6000 4000 2000 0 Jan-04 Jan-05 Jan-06 Rates (bbl or Mscf per day) Jan-07 Jan-08 Oil Rate Produced Gas Rate Water Rate
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))
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.
NOR (North Oron FGLR profile) 14000 12000 Rates (bbl or Mscf per day) 10000 8000 6000 4000 2000 0 Jan-05 Jan-06 Jan-07 Jan-08 Oil Rate Produced Gas Rate Water Rate
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