design optimum frac jobs using virtual intelligence techniques

$: Design optimum frac jobs using virtual intelligence techniques$
Design optimum frac jobs using virtual intelligencetechniques

Shahab Mohaghegh*, Andrei Popa, Sam Ameri

Petroleum & Natural Gas Engineering, West Virginia University, PO Box 6070, Morgantown, WV 26506, USA

Received 15 March 1999; received in revised form 9 September 1999; accepted 9 September 1999

Abstract

Designing optimal frac jobs is a complex and time-consuming process. It usually involves the use of a two- orthree-dimensional computer model. For the computer models to perform as intended, a wealth of input data is

required. The input data includes wellbore con®guration and reservoir characteristics such as porosity, permeability,stress and thickness pro®les of the pay layers as well as the overburden layers. Among other essential informationrequired for the design process is fracturing ¯uid type and volume, proppant type and volume, injection rate,proppant concentration and frac job schedule.

Some of the parameters such as ¯uid and proppant types have discrete possible choices. Other parameters such as¯uid and proppant volume, on the other hand, assume values from within a range of minimum and maximumvalues. A potential frac design for a particular pay zone is a combination of all of these parameters. Finding the

optimum combination is not a trivial process. It usually requires an experienced engineer and a considerable amountof time to tune the parameters in order to achieve desirable outcome.This paper introduces a new methodology that integrates two virtual intelligence techniques, namely, arti®cial

neural networks and genetic algorithms to automate and simplify the optimum frac job design process. Thismethodology requires little input from the engineer beyond the reservoir characterizations and wellborecon®guration. The software tool that has been developed based on this methodology uses the reservoircharacteristics and an optimization criteria indicated by the engineer, for example a certain propped frac length, and

provides the detail of the optimum frac design that will result in the speci®ed criteria.An ensemble of neural networks is trained to mimic the two- or three-dimensional frac simulator. Once

successfully trained, these networks are capable of providing instantaneous results in response to any set of input

parameters. These networks will be used as the ®tness function for a genetic algorithm routine that will search forthe best combination of the design parameters for the frac job. The genetic algorithm will search through the entiresolution space and identify the optimal combination of parameters to be used in the design process. Considering the

complexity of this task this methodology converges relatively fast, providing the engineer with several near-optimumscenarios for the frac job design. These scenarios, which can be achieved in just a minute or two, can be valuableinitial points for the engineer to start his/her design job and save him/her hours of runs on the simulator. 7 2000

Elsevier Science Ltd. All rights reserved.

Keywords: Neural networks; Genetic algorithms; FRACPRO; Frac job; Treatment schedule

Computers & Geosciences 26 (2000) 927±939

0098-3004/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved.

PII: S0098-3004(00 )00029-7

* Corresponding author. Tel.: +1-304-293-7682, Ext. 3405;

fax: +1-304-293-5708.

E-mail address: [email protected] (S. Mohaghegh).

1. Introduction

As one of the major developments in petroleum and

natural gas engineering in recent decades, hydraulicfracturing is an attractive method for increasing theproductivity of oil and gas wells. Hydraulic fracturing

has become a routine practice during the completionof many gas wells producing from tight formations. Byhydraulically fracturing a formation, a highly conduc-

tive contact surface between the well and the formationis created. The fracture provides an easier path for thehydrocarbon to ¯ow into the wellbore. The extent of a

hydraulic fracture into the formation, called the frac-ture length, provides the far-reaching contact between

the original wellbore and the formation. In essence, en-gineers try to increase the `e�ective' wellbore radius bycreating a hydraulic fracture.

Hydraulic fracturing of a formation is a complexprocess that involves wellbore con®guration, reservoiras well as fracturing ¯uid and proppant characteristics.

Another factor that plays an important role in the suc-cess or failure of a frac job is the method of implemen-tation. A frac job is accomplished in several stages

that together form the treatment schedule. Design of afrac job involves selection of ¯uid and proppant typesas well as injection rates and volumes and concen-

tration in a speci®c manner (treatment schedule) thathas the highest desirable e�ect on the target formation.

Designing the treatment schedule that creates thedesired fracture propped length is one of the mainchallenges for an engineer. For given reservoir con-

ditions, the treatment design engineer evaluates the useof several ¯uid types and volumes, proppant type andconcentrations and several injection rates. To evaluate

all these combinations, one must perform hundreds ofruns for each treatment schedule. On most three-dimensional frac simulators, a run usually lasts from

one to several minutes. Results of each run should bestudied after the completion of each run and input par-ameters should be altered for the next run to get one

step closer to the desired outcome. Overall, designing ajob is time consuming, and the process may last fromseveral hours to a whole day. Moreover many hydrau-

lic fracture computer models are not user-friendly, andrequire a large amount of information.To address this problem an attempt was made to

build a tool that helps engineers perform optimal frac-ture treatment designs in a short time period. This tool

is based entirely on the use of virtual intelligence,namely neural networks and genetic algorithms. Neuralnetworks are tools that provide instantaneous answers

to a particular set of inputs. Therefore the neural net-works were used to replicate the functionality of ahydraulic fracture computer model. A two-step method

that integrates the neural networks with genetic algor-ithms is proposed in this study. Two main types of

neural networks were trained for the optimization pro-cess. One type was designed to create ramp treatment

schedules, whereas the second was designed to createstage treatment schedules.

2. Tools and techniques

Use of a hydraulic fracture computer model is oneof the essential parts of this study. In order to achieve

the objectives of this study, the methodology requiresdevelopment of an ensemble of neural networks thatcan replicate the frac models functionality in a fast

and convenient fashion. The hydraulic fracture compu-ter model used in this study is FRACPRO (FRAC-PRO, 1999).

2.1. Hydraulic fracture computer model

Over the years e�orts were made to develop complex

tools that simulate the propagation of the hydraulicfracture and its dimensions. The Gas Research Insti-tute (GRI) implemented a complex fracturing model(3D) called FRACPRO. This study uses the main

mode of FRACPRO, namely Fracture Simulationmode, to generate di�erent fracture dimensions corre-sponding to di�erent frac treatments.

Hydraulic fracturing is a complex process that dealswith four main domains: formation characteristics,treatment ¯uid characteristics, proppant characteristics

and treatment type. Formation characteristics refer tothe information about the formation being fractured aswell as formations above and below it. Well logs

usually provide information regarding the lithology ofthe formation. This information consists of the depthof each formation, the thickness and Poisson coe�-cient of each formation. It should be remembered that

both the pay and the overburden formation consist ofmany distinct layers. Other information about thereservoir is related to formation pressure and tempera-

ture, porosity, permeability and viscosity of the reser-voir ¯uid.FRACPRO has a Fluid and a Proppant Library

that includes several types of ¯uids and proppants andtheir characteristics. During this proof of feasibilitystudy, the methodology has been developed for a par-ticular ¯uid and proppant combination. Upon its com-

pletion, this methodology will include several popular¯uid types and proppants. The genetic algorithm op-timization routine will then search for optimum ¯uid

and proppant type as well as other parameters.The treatment design consists of total volume of

fracturing ¯uid, total quantity of proppant used and

pumping ¯ow rate. FRACPRO allows the possibilityof using di�erent types of treatment schedules. Treat-ment schedules can be classi®ed in two main types,

S. Mohaghegh et al. / Computers & Geosciences 26 (2000) 927±939928

namely ramp treatment schedule, and stage treatmentschedule. A ramp treatment consists of three mainstages, pad, slurry, and in the end, the ¯ush which

usually is slick-water and is pumped in volumes equalto the wellbore volume. During the ramp slurry stage,the proppant concentration is linearly increased from astarting concentration of 1 ppg (119.81 kg/m3) to the

®nal concentration. Table 1 shows an example of aramp treatment.Unlike the ramp treatment the stage treatment sche-

dule is composed of as many stages as the user wants.Table 2 shows an example that contains ®ve slurrystages, each one being characterized by speci®c ¯uid

volume and proppant concentration. In this case theproppant concentration is pumped in stages and keptconstant during each stage. The example treatment

also includes a pad and a ¯ush stage.

2.2. Virtual intelligence techniques

Arti®cial neural networks and genetic algorithms arethe two virtual intelligence techniques being used in

this study. Background information on neural net-works has been covered in previous papers (Moha-ghegh et al., 1994a,b) and will not be repeated in this

paper. A general background on genetic algorithmswill follow.Many problems in life are solved through some kind

of search process. In a world of almost unlimited com-binations, we need to ®nd the best time to schedulemeetings, the best mix of chemicals, the best way to

frac a well, the best stocks to buy, or the best way tostack boxes. The most popular way we solve simple

problems is the `trial and error' method. The problemis that search spaces are frequently too large for us toexamine every possible combination.

The model being investigated in this study has fourparameters, which have been encoded into a 36-bit-

long `chromosome'. A chromosome is the binary rep-resentation of all parameters concatenated to form one

member of the genetic population. All the possiblecombinations of genes within this chromosome give

this problem 107 distinct possible solutions. If wecould examine one solution per second (about 100times faster than making a simple run on FRACPRO

Ð not counting the time it takes to input data into theprogram) Ð it would take 116 days to search exhaus-

tively the model space for a single problem. In thepast, people would solve problems like this by making

intelligent guesses about the values of the parameters,using whatever trial and error as they could a�ord,

time-wise. This way, one could obtain a solution, butnot necessarily a good one.

In 1975 John Holland proposed an optimizationtechnique that exploited an analogy between functionoptimization and the biological process of evolutionary

adaptation. Genetic algorithms maintain a populationof individuals (potential solutions) and act in a way

that favors the creation and `survival' of better individ-uals. This innovative technique solves complex pro-

blems by imitating Darwinian theories of evolution ona computer. In nature, organisms evolve as they adapt

Table 1

Example of ramp treatment schedule

No Stage Volume

(gal)

Rate

(bbl/min)

Starting proppant concentration

(ppg)

Final proppant concentration

(ppg)

Fluid type

1 Pad 21,598 20 ± ± HL_HYB_30_1

2 Slurry 39,458 20 1 7.5 HL_HYB_30_1

3 Flush 2150 20 ± ± SLICKWATER

Table 2

Example of stage treatment schedule

No Stage Volume

(gal)

Rate

(bbl/min)

Starting proppant concentration

(ppg)

Final proppant concentration

(ppg)

Fluid type

1 Pad 21,598 20 ± ± HL_HYB_30_1

2 Slurry 4773 20 1.5 1.5 HL_HYB_30_1

3 Slurry 4773 20 3 3 HL_HYB_30_1

4 Slurry 9546 20 4.5 4.5 HL_HYB_30_1

5 Slurry 11,932 20 6 6 HL_HYB_30_1

6 Slurry 14,318 20 7.5 7.5 HL_HYB_30_1

7 Flush 2150 20 ± ± SLICKWATER

S. Mohaghegh et al. / Computers & Geosciences 26 (2000) 927±939 929

to dynamic environments. The `®tter' an organism is,the longer it will live, and the more chance it has to

reproduce and pass along those `®t' genes to anothergeneration. New organisms are generated throughreproduction, and each organism essentially gets `eval-

uated' by proving how long it can live in a harshworld. In biological evolution, only the winners surviveto continue the evolutionary process. Note that one

does not need to know what aspect of the organismmakes it a winner, nature just assumes that if it lives,it must be doing something right. A genetic algorithm

uses the same evolutionary technique and has beenapplied to a wide variety of real-world problems likewire routing, scheduling, adaptive control, optimalcontrol, game playing, transportation problems, travel-

ing salesman problem, database query optimization,gas pipeline operation, and inverse modeling in geo-physics, to name a few.

By setting the parameters randomly throughout thesearch space a population of chromosomes Ð eachrepresenting a potential frac design Ð is created. This

is the ®rst step in implementation of a genetic algor-ithm. From this population of solutions, the worst arediscarded and the best solutions are then `bred' with

each other by mixing the parameters (genes) from themost successful organisms, thus creating a new popu-lation. During reproduction, the chromosomesundergo di�erent genetic operation such as selection,

crossover, mutation and inversion (Michalewicz, 1992).The selection operator is responsible for choosing twoorganisms to become parents. Selection routines can be

thought of as professional breeders, with a biastowards selecting only the best individuals in the popu-lation.

As in real life, this type of continuous adaptationcreates robust individuals. The whole process continuesthrough many `generations', with the best genes beinghanded down to future generations. The result is typi-

cally a good solution to the problem. By continuallycycling these operators, we have a surprisingly power-ful search engine, which inherently preserves the criti-

cal balance needed with any search: the balancebetween exploitation (taking advantage of informationalready obtained) and exploration (searching new

areas). Although simplistic from a biologist's view-

point, these algorithms are su�ciently complex to pro-vide robust and powerful search mechanisms.

Table 3 presents the list of four parameters beingoptimized in this study. These parameters can bedivided into two general categories. First are par-

ameters that have distinct and discrete values or mem-bers such as contractor, ¯uid type, and sand mesh size.Therefore selecting one member for each parameter in

this category requires a random roulette selection. Par-ameters in the second category on the other hand,have continuous values such as average injection rate,

¯uid amount and proppant concentration. Any valuebetween some designated minimum and maximum canbe chosen for these parameters.A potential solution to the hydraulic fracture optim-

ization problem includes a combination of values ofthese four parameters. A gene represents each par-ameter and when combined together the four genes

form a chromosome. Each chromosome is a potentialsolution.As mentioned earlier one of the keys to a successful

genetic algorithm is having a method to rank solutions.This is done using a `®tness function'. A ®tness func-tion in any problem is the model or the function that

is being optimized. In this study the neural networksreplicating FRACPRO are the ®tness functions.

3. Methodology

The objective of the methodology developed in thisstudy is to create the desired propped length by design-ing a treatment schedule. Moreover, the methodology

calls for minimum input data and interaction by theengineer. Also note that at this stage of the develop-ment the entire process is data driven. Addition ofexpert knowledge or `rules of thumb' for online and

real time decision making may enhance this process.The only required information at this point to com-plete the design process is the formation character-

istics. The objective is to ®nd the optimum treatmentschedule (either ramp or stage scheduling) as well asamount of ¯uid, proppant and the pumping rate for

each stage for the treatment. The outcome of the pro-cess is a detailed treatment schedule as seen in Tables1 and 2. This is exactly the inverse problem of the frac-turing simulation. This methodology is coded into a

software application that is described later.Fig. 1 is the ¯ow chart of this methodology. Devel-

opment of the software application started with con-

struction and training of the neural networks thatwould replicate the hydraulic fracture computer modelwithin acceptable accuracy.

Input to the neural networks includes reservoircharacteristics, well con®guration, and frac job design.The optimization process only operates on the frac job

Table 3

List of parameters used in genetic algorithm for optimization

Parameters being optimized Unit

Total ¯uid volume gal

Pad volume gal

Final proppant concentration ppg (lb/gal)

Flow pumping rate bbl/min


design parameters. The reservoir characteristics arepreprocessed before being used in the neural networks.The preprocessing tasks are covered next.

3.1. Preprocessing reservoir characteristics data

Most of the three-dimensional hydraulic fracturingcomputer models require a wealth of data about for-

mation characteristics. These data include thickness,stress, and permeability for every individual layerinvolved. Usually the formation to be fractured is not

bounded by only one layer at the top and one layer atthe bottom. Moreover, the productive formationincludes intercalation of several nonproductive layers.

In order to model the shape of the fracture accurately,characteristics of all the layers must be known. Table 4presents an example of reservoir lithology for a for-

mation in Oklahoma, each row representing an inde-pendent layer. This formation includes 13 overburdenshale layers, 19 layers in the pay zone from which 10are productive layers (Redfork formation) and nine are

non-productive. This table contains the layer descrip-tion in the ®rst column, followed by three columnsde®ning the depth to the top of the layer, the depth to

the bottom of the layer and the thickness of the layer.The next columns de®ne the permeability, with valuesonly for the productive layers, the Poisson coe�cient

(calculated from Gamma-Ray logs) and then closure-stress gradient and the closure stress. A graphical rep-resentation of this formation's closure stress is pre-sented in Fig. 2.

In Fig. 2 the thin line represents the original layersof the reservoir and the thick line is a representationof the same formation after being preprocessed using

an algorithm speci®cally developed for this method-ology. The objective of this algorithm is to represent amulti-layer formation with four distinct layers while

maintaining the main characteristics of the zones.These characteristics are the major driving forcebehind the hydraulic fracture that will be initiated and

propagated in the formation. Many di�erent methodsand algorithms were tested. The algorithm presentedhere has been found to be able to maintain the main

characteristics of the hydraulic fracture including itsshape.This algorithm was rigorously tested for formations

with up to 26 distinct layers. It was observed that

this method of preprocessing of the reservoir charac-teristics is representative, and approximates thecharacteristics of the hydraulic fractures modeled by

FRACPRO with reasonable accuracy. In this algor-ithm, the overburden layer with highest closure stressis placed immediately above the pay zone. The rest of

Fig. 1. Flow chart of optimization process.

Fig. 2. Graphical representation of closure stress of formation

in Oklahoma.


the overburden layers are combined into one overbur-

den layer. One layer represents all the layers withinthe pay zone and the last layer is the zone below the

pay zone (Fig. 2).This algorithm was tested using 72 di�erent

examples. The actual formation characteristics wereused in FRACPRO and a hydraulic fracture was gen-

erated. The reservoir characteristics were then prepro-cessed using the proposed algorithm and the

formation layers were reduced to only four layers.Using the same hydraulic fracture design FRACPRO

was run on the preprocessed reservoir characteristics.The results (hydraulic fracture characteristics) were

compared for all 72 examples and the average errorwas about 8%.

To determine the characteristics of the proposed

layers, an averaging technique was used. The represen-

tative layer's thickness equals the sum of all the layers'thickness and the closure stress, seq, of the representa-

tive layer is de®ned by the following relationship:

seq � Ssi � hiShi

�1�

where si is the closure stress of the i-th layer and hi isthe thickness of the i-th layer.

The equivalent permeability, keq, of the productiveformation was determined using a similar relationship:

keq � Ski � hiShi

�2�

where ki is the permeability of the i-th layer.

Using this algorithm the characteristics of the entire

Table 4

Example of reservoir lithology

Layer

description

Upper

depth

Lower

depth

Layer

thickness

Layer

permeability

Poisson's

ratio

Closure stress

gradient

Closure stress

Shale 1 10800 10920 120 0 0.23 0.69 7521.07

Shale 2 10920 10944 24 0 0.25 0.71 7747.24

Shale 3 10944 10960 16 0 0.29 0.74 8141.81

Shale 1 10960 10984 24 0 0.23 0.69 7598.63

Shale 2 10984 10994 10 0 0.25 0.71 7787.64

Shale 3 10994 11004 10 0 0.29 0.74 8176.75

Shale 4 11004 11011 7 0 0.22 0.68 7487.15

Shale 5 11011 11017 6 0 0.30 0.76 8394.24

Shale 1 11017 11032 15 0 0.23 0.69 7634.99

Shale 6 11032 11102 70 0 0.28 0.73 8127.56

Shale 7 11102 11113 11 0 0.34 0.80 8916.29

Shale 6 11113 11132 19 0 0.28 0.73 8168.32

Shale 4 11132 11140 8 0 0.22 0.68 7574.56

Redfork 1 11140 11143 3 0.01182 0.21 0.67 7511.35

Shale 2 11143 11148 5 0 0.25 0.71 7898.55

Redfork 1 11148 11150 2 0.01182 0.21 0.67 7516.40

Shale 2 11150 11156 6 0 0.25 0.71 7903.86

Redfork 1 11156 11158 2 0.01182 0.21 0.67 7521.80

Shale 2 11158 11162 4 0 0.25 0.71 7908.82

Redfork 2 11162 11165 3 0.01182 0.20 0.67 7444.05

Shale 1 11165 11168 3 0 0.23 0.69 7733.33

Redfork 2 11168 11171 3 0.01182 0.20 0.67 7448.05

Shale 1 11171 11175 4 0 0.23 0.69 7737.83

Redfork 2 11175 11182 7 0.01182 0.20 0.67 7454.05

Shale 4 11182 11190 8 0 0.22 0.68 7608.57

Redfork 2 11190 11197 7 0.01182 0.20 0.67 7464.05

Shale 1 11197 11201 4 0 0.23 0.69 7755.84

Redfork 3 11201 11230 29 0.01182 0.19 0.66 7398.08

Shale 1 11230 11234 4 0 0.23 0.69 7778.69

Redfork 2 11234 11236 2 0.01182 0.20 0.67 7491.73

Shale 2 11236 11238 2 0 0.25 0.71 7963.39

Redfork 3 11238 11247 9 0.01182 0.19 0.66 7415.89

Shale 1 11247 11254 7 0 0.23 0.69 7791.51

Shale 8 11254 11500 246 0 0.26 0.72 8157.74


formation can be presented to the neural networkusing only eight parameters:

. thickness of the top layer;

. closure-stress gradient of the top layer;

. thickness of the overburden layer;

. closure-gradient stress of the overburden layer;

. thickness of the pay zone;

. closure-gradient stress of the pay zone;

. permeability of the pay zone; and

. closure-gradient stress of the bottom layer.

4. Results and discussions

Results of three stages of development will be dis-cussed in this section. First the construction, trainingand veri®cation of the neural networks will be pre-

sented followed by the genetic algorithm optimizationprocess. The section will conclude by introducing thesoftware that was developed to carry out this process.

4.1. Building neural models

Two neural networks were constructed and trained.

The networks were trained to represent ramp treat-ment schedule and stage treatment schedule. About600 hydraulic fracture designs were generated using the

computer simulator (FRACPRO) for each treatmentschedule. The networks were trained and veri®ed usingthe 600 cases for each treatment schedule. Table 5 pre-

sents some detail about the input and output of theneural networks.Neural networks include two categories of input

data, namely, reservoir characteristics, and hydraulicfracture design parameters. The reservoir character-istics include the eight parameters discussed in the pre-

vious section plus depth of the pay zone and thereservoir pressure. The hydraulic fracture design par-ameters include total ¯uid volume and pad volumealong with proppant concentration and injection rates.

It should be noted that Table 5 shows the input par-ameters for the ramp treatment schedule. Input par-ameters for stage treatment schedule are slightly

Table 5

Input and output parameters used in ramp treatment schedule network

Number Parameter Type Range interval Units

1 Total ¯uid volume Input 10,000±200,000 gal

2 Pad volume Input 3500±90,000 gal

3 Final proppant concentration Input 6±16 ppg

4 Flow pumping rate Input 15±40 bbl/min

5 Depth to the `pay zone' Input 5000±15,000 ft

6 Reservoir pressure Input 1500±7000 psia

7 Permeability Input 0.001±0.1 md

8 Top layer thickness Input 170±250 ft

9 Top layer closure stress gradient Input 0.72±0.85 psi/ft

10 Overburdon layer thickness Input 10±50 ft

11 Overburdon layer closure stress gradient Input 0.74±0.85 psi/ft

12 Pay zone thickness Input 50±130 ft

13 Pay zone closure stress gradient Input 0.64±0.72 psi/ft

14 Bottom layer closure stress gradient Input 0.71±0.81 psi/ft

1 Fracture e�ciency Output 0.2±0.97 ±

2 Fracture propped length Output 170±900 ft

3 Fracture total height Output 220±600 ft

4 Fracture proppant concentration Output 0.4±2.0 lb/ft2

5 Fracture maximum width Output 0.14±1.5 in

Fig. 3. Neural network's prediction vs FRACPRO results for

ramp treatment (fracture e�ciency).


di�erent from the parameters presented in this table.Each network has ®ve outputs as shown in Table 5.

Figs. 3±7 show the accuracy of the neural networkdeveloped for the ramp treatment schedule. In theseFigures, the neural network's predictions are plotted

against FRACPRO results.The result of neural model building for both ramp

and stage treatment procedures is summarized inTable 6. The veri®cation data set represents the 40%

of the data that were not used during the training pro-cess and therefore are new to the neural network.Results in this table show that the neural networks

trained for this purpose are capable of replicating theFRACPRO functionality with acceptable accuracy.

4.2. Optimization using genetic algorithms

To test the capabilities of the methodology ahydraulic fracture for a speci®c formation designed by

an expert engineer was chosen. This design had alreadybeen implemented in the ®eld. This design is termed

the `original job'. The methodology presented in this

paper was used to design a similar frac job for the

same formation without consultation with an expert

engineer.

The original job is a ramp treatment schedule, per-

formed at a depth of 3524 m (11,440 ft) in a tight gas

reservoir. The job is designed to create a propped frac-

ture length of 138.6 m (450 ft). Table 7 presents other

characteristics of the treatment, such as ¯uid volumes,

proppant concentration and pumping rate. Table 7

also shows the results of the neural network integrated

with genetic algorithms for the same formation.

Remember that far less information was used as input

to the method presented in this paper.

The neural network and genetic algorithm method-

ology proposed four di�erent designs. These designs

were implemented using FRACPRO. The results of

FRACPRO runs for these designs are also presented

in this Table.

The process generates four di�erent near optimum

designs that have propped length close to the desired

value of 138.6 m (450 ft). As a future addition to this

methodology, an economic evaluation module will be

added to the software to identify the most economic of

the proposed designs. The largest di�erence between

the desired propped length and those proposed by this

methodology is 4.62 m (15 ft) or 3%.

According to the material-balance equation, the lar-

ger the ¯uid volume pumped the longer the length of

the fracture. Consequently, the third treatment design

should have provided the longest fracture. However

the proppant concentration controls the fracture prop-

pant concentration. So, the higher the fracture prop-

pant concentration, the higher the quantity of

proppant needed to be pumped. This results in higher

values of ®nal proppant concentration in the treatment

schedule and more ¯uid to transport the proppant in

the fracture.


ramp treatment (fracture total height).


ramp treatment (fracture propped length).


ramp treatment (fracture proppant concentration).


All four proposed treatment designs create thedesired propped length but at the same time the prop-

pant concentration in the fracture is di�erent. Thiscould provide a good starting point for those engineersthat are experts in the hydraulic fracturing or have lit-

tle or no experience using sophisticated three-dimen-sional computer models such as FRACPRO.

4.3. Software developed for this methodology

The process of designing treatment schedules thatcreates desired hydraulic fractures consists of the fol-lowing stages:

4.3.1. Stage one: de®ning the inputsThis stage deals with the formation characteristics

(Fig. 8). All the information related to the formation

characteristics is imported in a data grid control froman input ®le. The information imported from the ®leconsists of a depth for each layer, the closure-stress

gradient, and the permeability for each individuallayer. Automatically, the formation stress and thick-

ness are calculated. Setting up the margins in this win-dow identi®es the top and the bottom of overburdenand the pay zone. By clicking on the `calculate' button

on the bottom of the form, the properties of the fourrepresentative layers are calculated using the algor-ithms that were explained in the previous sections.

4.3.2. Stage two: rapid screeningThis stage presents a one-step treatment design pro-

cess as shown in Fig. 9. In this form other input par-

ameters such as reservoir pressure and depth to themiddle of the perforation are identi®ed. The target ordesired fracture propped length is also provided in this

form.The rapid screening consists of a random generation

of 100 treatment schedules. These treatments are auto-matically sent to the neural network, which generates

the corresponding, output±fracture propped length.The treatments are then ranked and sorted based ontheir proximity to the desired propped length (the tar-

get). All 100 ranked treatments are displayed in a datagrid control. The user can choose any of the designs toperform more detailed analysis on the treatment by

changing each parameter and observing the impact ofthe change on the outcome.Fig. 10 shows the form that provides the facility for

the user to change the treatment parameters to seetheir in¯uence on the output. Changing the values ofthe treatment parameters in this form is the same ascreating a new design. The example presented in

Fig. 10 deals with the stage treatment schedule. Simi-larly activities can be performed for a ramp treatmentschedule.


ramp treatment (fracture maxim width).

Table 6

Results of neural network for both ramp and stage treatments

Parameter name Training data set (60%) Veri®cation data set (40%)

Correlation coe�cient R 2 Correlation coe�cient R 2

Ramp treatment schedule

Fracture e�ciency 0.942 0.886 0.974 0.947

Fracture propped length 0.957 0.917 0.967 0.919

Total fracture height 0.974 0.946 0.978 0.942

Fracture conductivity 0.952 0.902 0.921 0.798

Maximum fracture width 0.933 0.868 0.888 0.684

Stage treatment schedule

Fracture e�ciency 0.929 0.844 0.948 0.885

Fracture propped length 0.948 0.898 0.966 0.931

Total fracture height 0.941 0.877 0.953 0.888

Fracture conductivity 0.917 0.839 0.929 0.852

Maximum fracture width 0.968 0.937 0.959 0.920


Fig. 9. More data input and rapid screening.

Fig. 8. Data input form.


Fig. 11. Form for optimization of frac job.

Fig. 10. Form for analysing speci®c design in detail.


4.3.3. Stage three: genetic optimizationReferring to Fig. 11, this stage is accomplished in

the following steps:

1. Set the parameters for:1.1. type of selection process,

1.2. type of crossover,1.3. population size,1.4. number of chromosomes chosen to breed, and

1.5. number of generations.

2. The cases are sent to the ®tness function neural net-

work.3. The outcome (fracture propped length) is then com-

pared to the desired propped length and, based on

the error between the two, the treatments areranked.

4. The top-ranked treatment schedules are selected tocreate the new generation and the rest are dis-

carded.5. A new generation of frac designs are generated

using crossover and mutation processes performed

on the selected designs of Step 4.6. The procedure is repeated from Step 2.

The convergence of the solution to the optimum design

can be followed in real time as shown in Fig. 11. Thebest solution in each generation is also displayed in adata grid control at the right side of the form.

The top ranked treatments are the optimized sol-utions to the problem. Even an optimized solution canbe analyzed separately. A double click on its currentranked number calls the detailed treatment design

form presented in Fig. 10.

5. Conclusions

A new methodology is introduced that assists engin-eers in designing optimum hydraulic fracture jobs. Asoftware program is developed that implements the

introduced methodology. This methodology integratesthe power of arti®cial neural networks and genetic al-gorithms in order to achieve its objectives. The process

includes replication of a sophisticated three-dimen-sional hydraulic fracturing computer model (FRAC-PRO) using an ensemble of neural networks. Themethodology uses genetic algorithms to search through

the entire solution space for a particular well treatmentand ®nds the best combination of the parameters thatprovide the hydraulic fracture propped length that is

desired. This paper presents this methodology as aproof of feasibility and shows that a complete workingmodel based on this methodology can be built. It also

shows that sophisticated numerical models can bereplicated using an ensemble of neural networks thatcan be implemented in a parallel fashion.T

able

7

ResultsofmethodologycomparedwithdesignbyexpertengineerusingFRACPRO

Treatm

entcharacteristics

NN

&GA

predictions

FRACPRO

results

Total¯uid

volume(gal)

Pad¯uid

volume(gal)

Startingproppant

concentration

(ppg)

Finalproppant

concentration

(ppg)

Pump

rate

(bpm)

Proppant

length

(ft)

Fracproppant

concentration(lb/

ft2)

Proppant

length

(ft)

Fracproppant

concentration(lb/

ft2)

Originaljob

59,929

21,504

17.5

20

451.6

0.5

Designed

jobs

72,491

29,169

17.2

28

450.6

0.56

451.01

0.47

65,155

22,666

16.5

22

450.4

0.5

465.38

0.45

78,684

34,034

110.5

25

450.4

0.78

459.24

0.69

61,800

21,864

16.5

20

448.6

0.5

457.56

0.46


References

FRACPRO, 1999. Hydraulic Fracture Treatment Design and

Analysis. User Manual version 8.1. Resources Engineering

Systems Inc (RES).

Michalewicz, Z., 1992. Genetic Algorithms+Data

Structure=Evolution Programs. Springer-Verlag, New

York, 387 pp.

Mohaghegh, S., Are®, R., Ameri, S., 1994a. Design and devel-

opment of an arti®cial neural network for estimation of

formation permeability. In: SPE 28237, Proceedings of the

SPE Petroleum Computer Conference, 31 July±3 August,

1994, Dallas, Texas.

Mohaghegh, S., Are®, R., Ameri, S., Hefner, H., 1994b. A

methodological approach for reservoir heterogeneity

characterization using arti®cial neural networks. In: SPE

28394, Proceedings of the SPE 69th Annual Technical

Conference, 25±28 September 1994, New Orleans,

Louisiana.


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