# US 10,767,448 B2 · Multistage oilfield design optimization under uncertainty

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- Number: US 10,767,448 B2
- Document ID: US10767448B2
- Status: Granted
- Kind: B2
- Application number: 15/109,671
- Filed: 2015-01-06
- Published: 2016-11-10
- Granted: 2020-09-08
- Earliest claimed: 2014-01-06
- Assignees: Schlumberger Technology Corporation
- Applicants: Schlumberger Technology Corporation
- Inventors: Hugues A. Djikpesse; Kashif Rashid; William J. Bailey; Michael David Prange; Benoit Couet
- Web page: https://patentgrep.com/patent/US10767448B2

## CPC

- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- E21B 41/00: Equipment or details not covered by groups E21B15/00 - E21B40/00
- E21B 43/00: Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells (applicable only to water E03B)
- E21B 43/267: reinforcing fractures by propping
- E21B 49/00: Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
- G05B 13/041: {in which a variable is automatically adjusted to optimise the performance}
- G06Q 10/06316: {Sequencing of tasks or work}
- G06Q 50/02: Agriculture; Fishing; Forestry; Mining
- E21B 43/26: by forming crevices or fractures
- G06F 30/00: Computer-aided design [CAD]
- G06F 2111/06: Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
- H04W 16/12: Fixed resource partitioning
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)
- G06Q: INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- H04W: WIRELESS COMMUNICATION NETWORKS (broadcast communication H04H; communication systems using wireless links for non-selective communication, e.g. wireless extensions H04M1/72)

## Abstract

Managing oilfield operations include obtaining a subsurface model including a fracture design model having an fracture property with an uncertain value. A set of representative values that represent uncertainty in the fracture property is obtained and used to solve an oilfield optimization problem with a control variable to obtain a solution. The solution includes an optimal value for the control variable. Based on the solution, an oilfield design is generated and stored.

## Claims

### Claim 1

A method for managing oilfield operations comprising:
obtaining a subsurface model comprising a fracture design model having a fracture property with an uncertain value;
obtaining a set of representative values that represent uncertainty in the fracture property, wherein the set of representative values comprises a plurality of model parameter samples;
solving an oilfield optimization problem with a control variable using the set of representative values of the fracture property to obtain a solution comprising an optimal value for the control variable with respect to an objective function, wherein solving the oilfield optimization problem comprises:
for each of the plurality of model parameter samples, executing a fracture forecast model with a respective value of the control variable and a respective model parameter sample of the plurality of model parameter samples to obtain a respective objective function value of the objective function; and
determining the optimal value for the control variable based on the respective objection function value obtained with each of the plurality of model parameter samples;
generating an oilfield design based on the solution; and
storing the oilfield design.

### Claim 2 (depends on 1)

The method of claim 1, further comprising:
obtaining a set of representative values for a reservoir property with an uncertain value, wherein solving the oilfield optimization problem comprises using the set of representative values for the reservoir property.

### Claim 3 (depends on 1)

The method of claim 1, wherein obtaining the set of representative values for the fracture property comprises:
obtaining a set of representative values representing uncertainty in a seismic velocity model;
obtaining microseismic event data; and
generating the set of representative values for the fracture property using the set of representative values for the seismic velocity model and the microseismic event data.

### Claim 4 (depends on 1)

The method of claim 1, further comprising:
performing an oilfield operation according to the oilfield design.

### Claim 5 (depends on 1)

The method of claim 1, further comprising:
obtaining, using a plurality of sensors located in an oilfield, oilfield data,
wherein obtaining the subsurface model comprising generating the subsurface model using the oilfield data, and
wherein obtaining the set of representative values representing the uncertainty in the fracture property comprises generating the set of representative values for the fracture property based on the oilfield data.

### Claim 6 (depends on 1)

The method of claim 1, wherein solving the oilfield optimization problem comprises:
for the plurality of model parameter samples, generating a first plurality of objective function values by, for each of the plurality of model parameter samples:
sampling the set of representative values for the fracture property to obtain a model parameter sample in the plurality of model parameter samples, and
executing the fracture forecast model with a first control variable value and the model parameter sample to obtain a first objective function value in the first plurality of objective function values;
calculating a first mean of the first plurality of objective function values; and
calculating a first variance of the first plurality of objective function values.

### Claim 7 (depends on 6)

The method of claim 6, further comprising:
determining, based on the first mean and the first variance, that the first control variable value is the optimal value for the control variable; and
setting the first control variable value in the solution based on the determining that the first control variable value is the optimal value.

### Claim 8 (depends on 6)

The method of claim 6, further comprising:
determining, based on the first mean and the first variance, that the first control variable value is not the optimal value for the control variable;
selecting a second control variable value based on the determining that the first control variable value is not the optimal value;
for the plurality of model parameter samples, generating a second plurality of objective function values by, for each of the plurality of model parameter samples:
sampling the set of representative values for the fracture property to obtain the model parameter sample in the plurality of model parameter samples, and
executing the fracture forecast model with the second control variable value and the model parameter sample to obtain a second objective function value in the second plurality of objective function values;
calculating a second mean of the second plurality of objective function values; and
calculating a second variance of the second plurality of objective function values.

### Claim 9 (depends on 8)

The method of claim 8, further comprising:
determining, based on the second mean and the second variance, that the second control variable value is the optimal value for the control variable; and
setting the second control variable value in the solution based on the determining that the second control variable value is the optimal value.

### Claim 10 (depends on 1)

The method of claim 1, wherein the objective function comprises a utility function, a loss function, or a cost function of the oilfield optimization problem.

### Claim 11

A system for oilfield management comprising:
a computer processor;
an oilfield design tool that, when executed on the computer processor:
obtains a subsurface model comprising a fracture design model having a fracture property with an uncertain value;
obtains a set of representative values that represent uncertainty in the fracture property; and
generates an oilfield design based on a solution;
an oilfield simulator that, when executed on the computer processor:
executes a fracture forecast model with a control variable value and a model parameter sample to obtain an objective function value in a plurality of objective function values; and
a solver that, when executed on the computer processor:
solves an oilfield optimization problem with a control variable using the set of representative values for the fracture property to obtain the solution comprising an optimal value for the control variable with respect to an objective function, wherein solving the oilfield optimization problem comprises:
for a plurality of model parameter samples, generating the plurality of objective function values by, for each of the plurality of model parameter samples:
sampling the set of representative values for the fracture property to obtain a respective model parameter sample in the plurality of model parameter samples, and
issuing a call to the oilfield simulator with the control variable value and the respective model parameter sample; and
calculating a mean of the plurality of objective function values.

### Claim 12 (depends on 11)

The system of claim 11, wherein obtaining the set of representative values for the fracture property comprises:
obtaining a set of representative values that represent uncertainty in a seismic velocity model;
obtaining microseismic event data; and
generating the set of representative values for the fracture property using the set of representative values for the seismic velocity model and the microseismic event data.

### Claim 13 (depends on 11)

The system of claim 11, further comprising:
an equipment controller for:
transmitting a control signal to perform an oilfield operation based on the oilfield design.

### Claim 14 (depends on 13)

The system of claim 13, further comprising:
oilfield equipment for:
receiving the control signal; and
performing the oilfield operation.

### Claim 15 (depends on 11)

The system of claim 11, further comprising:
a plurality of sensors located at an oilfield for:
obtaining oilfield data,
wherein obtaining the subsurface model comprises generating the subsurface model using the oilfield data, and
wherein obtaining the set of representative values comprises generating the set of representative values based on the oilfield data.

### Claim 16 (depends on 11)

The system of claim 11, further comprising:
a data repository configured to store a plurality of sets of representative values.

### Claim 17

A non-transitory computer readable medium for managing oilfield operations comprising computer readable program code for:
obtaining a subsurface model comprising a fracture design model having an fracture property with an uncertain value;
obtaining a set of representative values that represent uncertainty in the fracture property, wherein the set of representative values comprises a plurality of model parameter samples;
solving an oilfield optimization problem with a control variable using the set of representative values of the fracture property to obtain a solution comprising an optimal value for the control variable with respect to an objective function, wherein solving the oilfield optimization problem comprises:
for each of the plurality of model parameter samples, executing a fracture forecast model with a respective value of the control variable and a respective model parameter sample of the plurality of model parameter samples to obtain a respective objective function value of the objective function; and
determining the optimal value for the control variable based on the respective objection function value obtained with each of the plurality of model parameter samples;
generating an oilfield design based on the solution; and
storing the oilfield design.

### Claim 18 (depends on 17)

The non-transitory computer readable medium of claim 17, wherein obtaining the set of representative values for the fracture property comprises:
obtaining a set of representative values that represent uncertainty in a seismic velocity model;
obtaining microseismic event data; and
generating the set of representative values for the fracture property using the set of representative values for the seismic velocity model and the microseismic event data.

### Claim 19 (depends on 17)

The non-transitory computer readable medium of claim 17, wherein the plurality of model parameter samples comprises a plurality of model parameter samples, and wherein solving the oilfield optimization problem comprises:
for the plurality of model parameter samples, generating a first plurality of objective function values by, for each of the plurality of model parameter samples:
sampling the set of representative values for the fracture property to obtain a model parameter sample in the plurality of model parameter samples, and
executing the fracture forecast model with a first control variable value and the model parameter sample to obtain a first objective function value in the first plurality of objective function values; and
calculating a first mean of the first plurality of objective function values.

### Claim 20 (depends on 19)

The non-transitory computer readable medium of claim 19, further comprising:
calculating a first variance of the first plurality of objective function values.