Probabilistic Modelling

Jerry S. Blinten Torben Riis

Probabilistic Development Modeling The oil industry is getting better at quantifying reservoir and production risks, but it still struggles to determine their economic impact. New software integrates development planning, economic modeling and risk analysis and provides the missing link to the bottom line.

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isk analysis via Monte Carlo simulation is conceptually simple, accounting for it's wide-spread acceptance. Three key components are required for any type of Monte Carlo analysis: n Probability distribution functions describing the uncertainty in important assumptions. n Results that measure important project risks. n A model to calculate these results. Armed with these three components, Monte Carlo simulation is a brute force technique. At each iteration of the simulation, a value is sampled from the distribution function for each assumption. Results are calculated from the model and saved. After sufficient iterations, the distribution of all possible results emerges. This process is basically an extension of traditional petroleum project decision making. In the past, common inputs to decision making were a high, low, and expected case (HLE). In a sense, a Monte Carlo simulation simply fills in the rest of the curve. In addition to providing an insight to the probability of possible results, the shape of the result distribution curves provides the decision maker additional information and offers additional methods of comparing projects. One of the most useful results of a Monte Carlo analysis is the measurement of the sensitivity of the results to the input assumptions. This sensitivity analysis is most often presented as a tornado chart. Quality control of Monte Carlo results is not much different than quality control for traditional HLE case analysis. The new twist is the requirement for the important assumptions’ probability distribution functions. The ideal situation is to have actual data to build the distributions. However, it rare to have such information and most often they are estimated with simple triangular, normal or lognormal shapes. The accuracy of the model and its representation of the real world business problem are critical. Monte Carlo simulations impose new requirements on oilfield development models. In general, they must be more dynamic

than in the past and be able to handle a broader range of inputs. With the focus on profitability, most development models are attempting to calculate financial measures such as rate of return or present value. Typically, the exploration, appraisal, and development phases of a petroleum project are modeled in a spreadsheet. The spreadsheet generates a forecast of capital and operating expenses (cash flow) and production. These profiles are then linked to an economic analysis program or sheet, which applies a tax and deal structure. This structure of spreadsheets and financial analysis programs is useful for simple types of Monte Carlo problems. However, the combination is often difficult to generalize. Without significant programming effort, spreadsheets are relatively static. For instance, well spacing might be an important input assumption. If it is, the spreadsheet must be able to calculate the number of wells required and build a drilling schedule at each iteration. Most often, time (either starting dates or elapsed time) will be an important variable. It is not trivial for a spreadsheet to adjust spending and production profiles at each iteration. Petroleum Ventures And Risk To overcome the limitations of Monte Carlo analysis with spreadsheets and financial programs, a new software program called PetroVR was developed by Caesar Petroleum Systems. PetroVR begins with a rigorous deterministic model of petroleum projects from conception through abandonment. The key components of the model are: n Descriptions of reservoir, well and facility resources. n Process flow diagrams describing the development system and fluid flow. n Timelines describing key events in the exploration, appraisal and development schedule. n Constraints on rig schedules and facility capacities.

Caesar Petroleum Systems 2500 City West, Suite 300 @1998 - All Rights Reserved Houston, Tx 77042 Originally Published in Hart's Petroleum Engineer - Feb 1998

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Jerry S. Blinten Torben Riis

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Dimensionless Simulation Results Single Well 1

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Based on this information PetroVR will automatically adjust the exploration, appraisal and development schedules. It will then generate cash flow and production profiles. These profiles are routed to PetroVR’s economic system. The program includes a financial modeling language capable of modeling any fiscal regime and deal structure. In its probabilistic mode, PetroVRTM allows any exploration, engineering or financial variable to be a risked input. At each iteration of a Monte Carlo simulation, the full development model is executed and financial measurements calculated. This allows each discipline to directly measure the effect of their uncertainty on fullcycle economics. Evaluating An FSU Oil & Gas Project A major western oil company was considering bidding on a license in the Former Soviet Union (FSU) containing two discoveries. The major risks associated with projects in the FSU are often different from traditional exploration risks. In the west, volumetric and recovery risks generally overshadow risks associated with production and export, whereas in the FSU drilling and production costs are often the biggest unknown. PetroVR was selected for its capability to model and perform integrated risk analysis on the entire exploration, production and abandonment cycle. Discovery A, of Devonian age, had been explored by 15 wells drilled by a non-western operator. And although the well data were sparse and of poor quality, the discovery was fairly well delineated. Discovery A consisted of one reservoir zone. Interpretation of porosity logs was questionable, but showed consistently low porosities

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degrading with depth. The majority of the well tests were shorter than one hour, and never produced oil to the surface. Less information was available for the smaller Devonian Discovery B. It appeared to have reservoir characteristics similar to Discovery A. However, regional erosion had reduced the pay thickness relative to Discovery A. Nine wells had been drilled and logged, and only two short well tests had been conducted. The well test data indicated rates comparable to Discovery A, however, API gravity was measured at about 40o, compared to 30o for Discovery A. A 160-acre five-spot reservoir sector model of Discovery A was built to evaluate the range of production profiles to be expected. The lack of rate history to tie down the initial rates forced the engineers to essentially run the model unconstrained. It was assumed that injection wells would initially produce 10% of the reserves contained in their drainage area and then be converted to injectors. Fig. 1 shows the range of oil and water simulation output obtained by varying reservoir parameters such as permeability, net pay and saturation curves (Fig 1). PetroVR includes an option for production profiles to be expressed in a dimensionless format as a function of dimensionless cumulative production. Fig. 2 demonstrates that the transformed simulation output curves have similar characteristics, and the average dimensionless curve shown in red was assumed to represent the average well performance in dimensionless terms. PetroVR allows well reserves, initial rate, and initial GOR to be risked variables. This enables a probabilistic assessment based on reservoir model results. Discovery

Caesar Petroleum Systems 2500 City West, Suite 300 @1998 - All Rights Reserved Houston, Tx 77042 Originally Published in Hart's Petroleum Engineer - Feb 1998

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Water Cut

Devonian Waterflood Simulation Results Single Well

Jerry S. Blinten Torben Riis

PC

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Process Facility Auto Water Processing Expansion 1

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Fig. 3 - This schematic shows the initial process system considered for the project. B was also expected to be developed by a five-spot waterflood. But rather than building a simulation model for Discovery B, it was decided to use the dimensionless curve already created for A and only change initial rate and reserves per well. Discovery B injectors would not produce any of their reserves, but be immediately placed on injection. The surface facilities consisted of a single process train with a total fluid capacity of 80,000 b/d at a central location on Discovery A. A pump would be installed on Discovery B, feeding a 10-mile, 3-phase pipeline to Discovery A. A return line piped injection water to Discovery B. Drilling would take place from gravel pads hold97

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ing 20 wells each. Initial water processing capacity was 10,000 b/d. PetroVR was allowed to automatically add additional water processing capacity of 50,000 b/d when needed. High water cut wells would be shut in, as needed, following the water processing expansion. The company was hoping to negotiate a tie-in to an existing oil pipeline and expected to re-inject produced gas. After entering reservoir, production, drilling and facility data in PetroVR, the process flow system and the initial development schedule was created (Fig 3 and Fig 4). PetroVR calculated that 132 wells were required to 02

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Signature Bonus Central Production Facilities Build Infrastructure (roads, camps etc) Engineer and Build Process Facility Build Gas Re-injection Build Water Injection System Build Export Facilities Lay and hook-up Export Pipeline Mobilize Development Rigs Construct and Drill from A Pad Construct and Drill from A Pad V1 Construct and Drill from A Pad V2 Construct and Drill from A Pad V3 Build Discovery B 3-phase Pump Station Construct and Drill Wells on B Pad Construct and Drill Wells on B Pad V1 Construct and Drill Wells on B Pad V2 Auto Water Processing Expansion 1

Fig. 4 - This timeline shows the initial sequence of key events considered for the project .

Caesar Petroleum Systems 2500 City West, Suite 300 @1998 - All Rights Reserved Houston, Tx 77042 Originally Published in Hart's Petroleum Engineer - Feb 1998

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Jerry S. Blinten Torben Riis

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Values in Ten Millions

economic model for a Production Sharing Agreement previously created in PetroVR was modified and used Fig. 6 - This bar chart show the distribution for this project. of NPV @ 20% for initial system considered. Initial production rate, porosity, recovery factor, net develop both reservoirs. It then automatically built well pay, drilling time and process facility costs were considpads, laid out the drilling schedule and calculated the oil, ered the major uncertainties. The values for these pagas and water production. The rig schedules were con- rameters were entered as triangular distributions in Petstrained by having three rigs on A and two rigs on B. roVR. Subsequently, full cycle risk analysis was perThe oil rate was automatically constrained by choking formed on the model. Full cycle risk analysis is based on back production. Water processing capacity was ex- Monte Carlo simulation of the entire development panded and high watercut wells were temporally shut in. schedule. Production profiles and economic model reBlending calculations were also made at the process fa- sults are re-calculated in each iteration cycle (Fig 6 and Fig 7). Results for the net present value of the project, cility (Fig 5). To handle the cost and production profiles generated discounted at 20%, and the sensitivity of the risked inby the development planning section of PetroVR , an puts on NPV are shown in Table 1. Noting the sensitivity of DiscovRegression Sensitivity for NPV @ 20% ery A's volumetric parameters Discovery A: Net Pay helped convince the operator to run Discovery A: Rec Factor 3-D seismic over the structure before Devonian Drilling: Drilling Time Discovery A: Reservoir Area making any development decisions. Discovery B: Reservoir Area To reduce risks even further, apProcessing Plant: Cap Ex Discovery B: Rec Factor praisal wells would also be drilled Discovery B: Net Pay Development Pad: Cap Ex on both structures. -6.00E-01 -4.00E-01 -2.00E-01 0.00E+00 2.00E-01 4.00E-01 6.00E-01 8.00E-01 1.00E+00 Well productivity and viability of Std b coefficient water injection remained a major concern due to the lack of reliable Fig. 7 - This column chart shows the sensitivity of the risked inputs on NPV @ 20% results. Caesar Petroleum Systems 2500 City West, Suite 300 @1998 - All Rights Reserved Houston, Tx 77042 Originally Published in Hart's Petroleum Engineer - Feb 1998

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Jerry S. Blinten Torben Riis 97

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Signature Bonus Shoot 3D Seismic on Discovery A & B Build Discovery A Appraisal Pad Mobilize 1st Rig on Discovery A Drill Devonian A Appraisal Well Drill 3 Discovery A Pilot Wells Mobilize Pilot Test Equipment Conduct 6 month Pilot Injection Test Mobilize Discovery B Rig Drill Discovery B Appraisal Well Drill 3 Discovery B Appraisal Wells Prepare Declaration of Commerciality Declare Commerciality Central Production Facilities Mobilize 2nd Discovery A Rig Construct and Drill from Discovery A Well Pads Construct and Drill from Discovery A Well Pads V1 Construct and Drill from Discovery A Well Pads V2 Construct and Drill from Discovery A Well Pads V3

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Engineer and Construct Discovery B 3-phase Pump Station Construct and Drill Wells on Discovery B Pads Construct and Drill Wells on Discovery B Pads V1 Construct and Drill Wells on Discovery B Pads V2

Fig. 8 - This timeline shows the key events required to implement an appraisal program and pilot waterflood. It was therefore decided to investigate the economical well test data. An injection pilot consisting of one injector and three producers was therefore considered. Simu- implications of constructing the injection pilot, followed lations showed that 6 months of injection would be suf- by the creation of a development schedule in PetroVR ficient to estimate sweep efficiency. However, the costs (Fig 8). associated with the pilot were high, since new wells had The major objective of a water injection pilot is to to be drilled. Also, due to the high cost of any type of reduce the risk that field-wide water injection might fail export system, re-injection of the oil was required. to achieve the desired recovery and production perform-

Pilot Success? 35.2 $ MM Develop w ith Pilot Development Decision 67.0 $ MM

Waterflood Success? 68.5 $ MM Yes 70.0%

Yes 90.0%

Develop w ith pilot (Rf 35%) NPV at 20: 78.0 $ MM

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Develop w ith pilot (Rf 15%) NPV at 20: -17.1 $ MM Pilot Fails NPV at 20: -42.5 $ MM

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Waterflood Success? 67.0 $ MM

Yes 63.0%

Develop w ithout pilot (Rf 35%) NPV at 20: 108.2 $ MM

No 37.0%

Develop w ithout pilot (Rf 15%) NPV at 20: -3.2 $ MM

Develop w ithout Pilot

Fig. 9 - This decision tree shows the economic results of the project with and without a waterflood pilot. Caesar Petroleum Systems 2500 City West, Suite 300 @1998 - All Rights Reserved Houston, Tx 77042 Originally Published in Hart's Petroleum Engineer - Feb 1998

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Jerry S. Blinten Torben Riis ance. Pilots can be quite expensive, particularly if the produced oil cannot be sold. Additional downsides of pilots normally include delaying the project start date and oil revenues. A relatively simple decision tree was created in PetroVR to resolve the whether the injection pilot should be built (Fig 9). The end “value” on each result node is a full project model. The failure branches were simply created from the success cases by reducing the recovery factor to 15 %. Fig. 9 shows the large negative financial impact of the pilot and fairly small exposure on the waterflood failure case. This tree, along with the additional information which will be gained during the appraisal program, helped convince the operator to forgo the pilot. The operator considers the production risk analysis process and PetroVR software essential in presenting the winning bid for these properties with confidence in the project's profitability. The process and software helped the operator focus on reducing the key risks through the

appraisal program and ignore the additional waterflood pilot expense. This example demonstrates the importance of measuring all key risks, with their impact on the development plan, against full cycle economics. ABOUT THE AUTHORS Torben Riis is vice president of engineering at Caesar Petroleum Systems. Prior to joining Caesar, he held positions with Timan Pechora Co., Norsk Hydro and Maersk Oil & Gas. Torben holds a MS in mechanical engineering from the Technical University of Denmark and an MBA from INSEAD. Torben is a member of SPE. His e-mail address is: [email protected]. Jerry S. Blinten is president of Caesar Petroleum Systems. Prior to joining Caesar, he worked with Amoco Production Co. and Schlumberger. Jerry holds BS degrees in physics and mathematics from North Carolina State University. He is a member of SPE and SPWLA. His e-mail address is: [email protected].

Caesar Petroleum Systems 2500 City West, Suite 300 @1998 - All Rights Reserved Houston, Tx 77042 Originally Published in Hart's Petroleum Engineer - Feb 1998

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