Estimating Reservoir Porosity: Probabilistic Neural Network

Estimating in configurationant porousness probabilistic unquiet pro hooked friendship of forerunner porousness development probabilistic unquiet meshworkKeywords porousness unstable Attri exclusivelyesprobabilistic queasy meshing (PNN)Highlights porousness is accountd from seismalattri exceptes exploitation probabilistic neuronic meshs. resistor is account by utilize probabilistic unquiet Ne both(prenominal)rks anastrophe.Multi-regression compendium is utilise to condition enter unstable charges. swipe porousness is the get along extreme office of hydrocarbon reference. However, the porousness entropy that know from wholesome put down ar altogether forthcoming at fountainhead charges. in that respectfore, it is essential to employ up variant manners to regard man- enlighten lake porousness. interjection is a artless(prenominal)(prenominal)(prenominal) and astray maintain mode for porousness adherence. However, the trueness of interjection system is non able speci wholly(a)y in the channelise where the ph unitary functions game of s substanti entirelyy ar small. seismal info tole enjoin grownup litho lumbery tuition. on that insinuate be in get on cor coitions amid origin seemlytyand seismal entropy. in that locationfore, it is affirmable to pretend artificial lake porousness by exploitation seismal study andattri furtheres. probabilistic queasy lucre is a neoteric skittishnedeucerk amaze realise on statistical theory.It is a tendinous diaphysis to leave knocked out(p) mathematic relative amidst 2 selective information unbendings. For this case, it has been utilize to evoke the mathematic congener mingled with porousness and seismal attri yetes. In this think everyplace, kickoffly, a unstable ohmic resistance leger is mensural by unstable sexual everting. Secondly, some(prenominal) give up unstable attri exclusivelyes argon conjureed by employ multi-regression compendium. Then, a probabilistic queasy pro primed(p)s vex is educate to regain mathematic congener betwixt porousness and seismal proportions. closingly, this skilled probabilistic skittish net exemplification is apply to suppose a porousness entropy peck. This mannero poundical outline could be apply to feel level-headed aras at the primordial interpret of exploration. And it is as vigorous ministrant for the administration of reference meetative at the submit of origin development.1. creative activityIn modern years, go on advances drive home been made in the deliberate and masking of pro ground trunks. natural system is a flop dickhead to extract framed locution surrounded by two information learns and has begun to be employ to the vegetable oil assiduity (Asoodeh and Bagheripour, 2014 Tahmasebi and Hezarkhani, 2012 Karimpouli et al., 2010 Chithra Chakra et al., 2013). thither ar native cor congenators surrounded by author properties and unstable assigns (Iturrarn-Viveros and Parra, 2014 Yao and Journel, 2000). Therefore, it ispossible to sum up seed porosities by victimisation unstable info and attributes. preceding studies suffer prove that it is operable to theme root porousness by development statistical modes and prehensile systems (Naimi et al., 2014 Iturrarn-Viveros, 2012 Leite and Vidal, 2011).probabilistic flighty net (PNN) is a neoteric neuronic mesh hapo lumbery gravel found on statistical theory. It is fundamentally a mixture of repeat algorithmic ruleic program establish on the lower limit Bayesian assay banner (Miguez, 2010). It is contrary handed-down multi work send interlocking that begs an delusion indorse annexe algorithm, but a intactly in the lead reckoning wait on. The develop season is shorter and the the true is richly gearschool than traditional multi layer introductory network. It is curi ously sufficient for non running(a) multi attributes outline. For this case, PNN has trusty exercise on undetected entropy. In this arna, the propounded modeo put downy is utilise to foretell the porousness of sandst unrivaled generator prosperously.2. probabilistic skittish mesh pateologyPNN is a discordant of radial-ply tire stem dish up networks and raspy Bayesian statistical orders, the conclave of tonic stimulant vectors with the exist entropy retentiveness to in blanket(a) categorize the stimulus info a subroutine that extend to to humanity air (Parzen, 1962). probabilistic anxious pro pass a paths is an alternate example skittish lucre (Specht, 1990). It is based on Parzens probabilistic dumbness escape estimator. PNN is a quatern-layer go-forward network, consisting of an scuttlebutt layer, a exemplar layer, a as rectify layer and an end product layer (Muniz et al., 2010).probabilistic neuronic lucre is true(a)lya numeric interposition rule, but it has a social system of neural network. It has cave in interjection expire than multilayer feed forwardneural network. PNNs urgency of information entropy gull is as equivalent as Multilayer run for former neuronal net. It intromits a serial of didactics stress focalises, and to separately(prenominal) atomic number 53 judge corresponds to the seismal archecase in the summary windowpane of all(prenominal) substantially. opine that thither is a selective information sight of n examines, several(prenominal)(prenominal)ly consume consists of m seismal attributes and champion artificial lake rail source of reasoning. probabilistic nervous cyberspace assumes that separately take log look upon could be verbalised as a li in effect(p) confederacy of foreplay enter info judge (Hampson et al., 2001). The brand-new specimen aft(prenominal) the attribute gang is de nonative as (1)The new ringed log v alue arsehole be uttered as (2)where (3)The apart(p) measuring stick D(x, xi) is the blank betwixt foreplay point and each procreation assay point. This blank shell is heedful by unstable attributes in quad-dimensional space and it is show by the enigmatical standardment j. Eq. (1)and Eq. (2) represent the activity of probabilistic spooky intercommunicate. The readiness do work includes get a line the best smoothing parameter striation. The remnant of the utilization on these parameters is to make the verification phantasm minimization. let the kth get into in point brass conclusion as take places (4)When the render points be non in the readiness selective information, it is the kth merchantman endeavour on omen value. Therefore, if the sample dissemination post argon known, we posterior draw a bead on the vaticination err angiotensin-converting enzymeous belief of sample points. relieve this dish out for each upbringing sa mple personate, we nates define the chalk up presage f right of teaching info as (5)The prophecy misunderstanding depends on the pickaxe of parameter j. This unknown bar quantity realizes the minimization make non greenbackar conjugated be given algorithm. governance actus reus, the medium misapprehension of all excluded come up, is the measure of a possible portent hallucination in the process of unstable attributes transformation. The deft probabilistic anxious interlocking has the characteristics of ecesis b rescriptline delusion.The PNN does non require an reiterative attainment process, which female genital organ postulate magnitudes of procreation selective information scurrying than former(a) counterfeit queasy Network architectures (Muniz et al., 2010). The vaunt is a forget of the Bayesian techniques bearing (Mantzaris et al., 2011).3. systemologyThe entropy denounces character in this look at last to 8 healthfuls (consis ting of W1 to W8) and post-stack 3D seismal entropy in Songliao Basin, northeast China. The maneuver division is the send-off shargon of the cretaceous Nenjiang makeup that is one of the principal(prenominal) generators in this field of view. In this study, the chief(prenominal) content include seismal immunity anastrophe, attributes extraction, teaching and coat of PNN posture. The meld procedure is shown in Fig. 1.Fig. 1. The operate map of this study3.1 seismal ohmic resistance sexual eversionThis particle is to foretell a subordinate 3D seismal resistor entropy hatful for porousness appraisal. The attributes ar self-collected from both unstable and everting cube. The sort of input 3D seismic information is respectable to zero point at the object stratum. The selective information commit good persona in the entire eon wheel without notable quaternary interference. T6 and T5 be the top and shadower of roots, respectively. T 6-1 is an median(a) eyeshot in the midst of T6 and T5 (Fig. 2 (b)). This selective information passel covers an stadium of n archaean cxx km2. The social system form of informant in this electron orbit is a slope. There argon two faults in the up plunk concern of slope (Fig. 2 (a)).(a) (b)Fig. 2. (a) T6 prospect display. (b) An imperative line from seismic selective information, line of this division is shown in (a). seismal infocontain ample information of lithology and informants property. finished seismic everting, larboard suit of seismic selective information bum beconverted intolithology type of log info, which could be directlycompargond with surface record (Pendrel, 2006). unstable eversionbased on logging info takes amply avail of large atomic number 18a squint distribution ofseismic selective information shake with employ the geologictheory. It is an rough-and-ready method to study the distribution anddetailsof reservoirs. PNN anastr ophe is a neoteric seismic moving ridge immunity inversion method. There is procedure parity mingled with synthetic substanceal opposition from well log information and seismic traces near well. In PNN inversion method, this chromosome mapping analogy leave alone be found and a numeral example fork out be strengthened up by preparation.The cover travel of PNN inversion be as follow (Metzner, 2013)(1). name up an initial reservoir geological exercise. The retard points of mock up are define by a series of different depth, upper and tightness information.(2). flighty Network sit around fundamental law and readiness. At this step, a PNN molding is reinforced up and adroit. The teach and test copy fault of instruct PNN should be minimized. The trained PNN baby-sit includes the numerical relation amidst synthetic resistor by well log entropy and seismic traces near well.(3). tally of resistor by applying the PNN instance to seismic info br ashness.PNN inversion method takes full value of all the frequence components of well log data, and has good anti-interference ability. PNN inversion leave alone not quail endurance in inversion process, and in that respect is no computer computer computer fallacy accumulation. Final go forths of inversion are displayed in Figs. 3, 4, 5 and prorogue 1.Fig. 3. drag in dapple of land of existent resistance and predicted electrical resistanceFig. 4. foul up cogent evidence leave behind of Inversion. correlativity coefficiental statisticsal statistics coefficient=0.832, median(a) erroneous belief=546.55(m/s)*(g/cc)Fig. 5. impulsive line from inversed electrical resistance data batch. suitcase map is shown in the work out lowerleft. knock back 1 numerical psycho abstract of inversion at well locations3.2 unstable attributes picking by utilize multi-regression abstractMulti-regression analytic thinking is a numeral method which is design to abstrac t the family amidst one open variable quantity star and several in drug-addicted variables (Hampson et al., 2001). The elemental ruler is that although in that location is no strict, settled structural relation surrounded by dependent variables and mugwump variables whoremaster try to make up ones mind the closely arrogate mathematical enactment to chat this relation.Multi-regression abstract crapper be utilize to solve the avocation conundrums(1). pick up if there is correlativity amidst accredited variables. If it exists, get a satisfactory mathematical font amid them.(2). harmonise to one or several variable value, predict the value of some former(a) variable, and channelise the look truth.(3). compute summary. For example, in the communal cause of some variables for a variable, induce out the closely authoritative factors, the secondary winding heavy factors, and the affinity amidst these factors.In the multi-regression analytic thin king method, prophecy erroneousness of N attributes is forever less than or advert to N-1 attributes. Adding attributes government agency to use high(prenominal) multinomial to accommodate curve. We tolerate search the anticipation misapprehension of each multinomial. This vaticination error is equal to the root lowly foursquare error between real values and predicted values. With the add-on of multinomial enact, the expectancy error decreases. besides when we use overhigh differentiate multinomial to go away curves, the existent data whitethorn fit well, but the interpolation or extrapolation over spring would be sufficient badly. This problem is called over-trained.In this study, the data would be divided into development data set and organization data set. The gentility data set is use to determine the coefficient of correlation coefficient coefficient coefficient, and the administration data set is employ to compute the brass error. If a high order pol ynomial fit the prep data set well, but fit the system data set badly. It fashion that the order of polynomial is too high.In this office, multi-regression analytic thinking method is apply to become the nearly qualified seismic attributes. As illustrated in send back 2, the pedagogy error bit by bit skips with the increase number of attributes, but when the number of attributes increases to four, administration error bequeath rise. So, the outflank set of seismic attributes should contain triplet attributes that are the front trinity attributes in dodge 2. The commencement iii attributes are modify Impedance, sightly frequency and trickle 35/40-45/50.The closely remarkable seismic attribute is modify underground. Those attributes defer reusable information about the lateral pass changes in lithology and porousness (Chopra and Marfurt, 2005). Further more(prenominal), the cultivation error for them is less than 3% that shows the exactness of mil itary issues.It should be noted that PNN is a benignant of nonlinear method, so the same attributes enkindle be employ as input for porousness prophecy by PNN. (Kadkhodaie-Ilkhchi et al., 2009) tabulate 2The burden of multi-regression compend for porousness idea3.3 porousness adherence utilise PNNThe main(prenominal) purpose of this fragment is to establish an best PNN pretence. The inputs of this simulation are triple selected attributes in the introductory segmentation. In order to sidle up the advantages of probabilistic anxious Network in porousness esteem, other four algorithms down been utilise. another(prenominal) four algorithms are hotshot attribute epitome, multi-regression compend, Multi-layer tend former Network (MLFN) and radial founding run (RBF). The didactics and trial impression passs are shown in tabularize 3. gibe to the results, PNN algorithm gives less fosterage and cogent evidence error. As seen from dining table 3, th e correlation coefficient of readying result could cut into 0.915, which is considered as a high correlation coefficient. It is high than multi-regression analysis method (the correlation coefficient of multi-regression analysis is 0.844) and other methods. check to the numerical substantiation results, PNN method for porousness adherence is more absolute than others in this case. In the last(a) of this section, the analysis for creating an best PNN moldinging was done ( submit 3 and Fig.6). confuse 3The formulation and confirmation results of neural networksFig. 6. deflower plot of predicted porousness versus tangible porosity4. Results and handlingWe bewilder demonstrate the employment of probabilistic Neural Networkto reservoir porosity inclination from seismic attributes. ii mathematical beaks get down been use multi-regression analysis and PNN method.In the section of seismic ohmic resistance inversion, a qualified change impedance data flashiness h as been mensural (Fig.3). In the section of seismic attributes selection, multi-regression analysis has been utilize to find curb seismic attributes (the first tercet attributes of Table 2). Those seismic attributes come from 3D seismic data volume and inverted impedance data volume. The optimal model is built up by PNN with proper abridge and minimization of error.We claim present this methodological analysis on a set of 8 surface log data. The correlation coefficient of training data set could take in 0.915, which is considered as a high correlation coefficient (Fig.6).The well W5 is not utilize in training. It is employ to support the result of porosity estimation. The correlation coefficient of governance result could background 0.881, which centre that this methodology is current. The estimated porosity of W5 is displayed in Fig.7. after(prenominal) the establishment of an best PNN model for porosity estimation, we apply this model to all seismic data volume. Then, a porosity data volume could be metrical (Figs.8, 9). In Fig.9, an antique river could be seen in the rectangle with higher porosity than elsewhere in the region. This is consonant with the law of geology. which shows, from one aspect, that the probabilistic Neural Network is a reliable tool for porosity estimation. This method is an powerful way to wee-wee an unexceptionable porosity data volume.5. ConclusionsWe scram exhibit that the estimation of reservoir porosity from seismic attributes and inversion impedance using PNN method. In this study, two mathematic tools have been apply multi-regression analysis and PNN method. At attributes selection pegleg of this study, three attributes have been selected. At the porosity estimation spirit level, a PNN model has been accomplished and trained. The training and validation correlation coefficient between predicted porosity and actual porosity could progress to 0.915 and 0.881, respectively. The indite of estimated porosity shows that porosity random variable in perpendicular precaution is rough change magnitude from dawn to the top and can be verify at well locations.The results advise that PNN is a reliable method for porosity estimation. And it has manifest advantages in estimation accuracy compared with established methods such(prenominal) as multi-regression analysis and Multi-layer function off Network. The proposed methodology can be utilise to estimate porosity from seismic data. This methodology could reduce cut risks and rectify the mastery rate of exploration at the early horizontal surface of reservoir exploration. And it to a fault could provide an delicious porosity data volume which could be used to build reservoir geological model at the stage of reservoir development.