Patent Application: US-201514685249-A

Abstract:
the present disclosure describes the use of growth models and data driven models that are combined for quickly and efficiently modeling sagd reservoir oil production . growth function surrogate models are used for efficient and reliable reservoir modeling and production forecasting as opposed to cpu intensive simulations based on finite difference models . a data - driven technique can then compare the growth function surrogate model with real field data to find discrepancies and inconsistencies between the two , allowing for an updates and improvements of the growth function model .

Description:
the present invention is exemplified with respect to the figures and the following discussion regarding sagd . however , this is exemplary only , and the invention can be broadly applied to any hydrocarbon or hydrocarbon recovery process . the following discussion and figures are intended to be illustrative only , and not unduly limit the scope of the appended claims . the disclosure provides novel methods , systems and devices for modeling hydrocarbon production . specifically , growth modeling methods are combined with data driven models to efficiently model production and forecast with a quick turn around time . when producing oil from the subsurface , engineers often build a detailed 3d geological model of the oil reservoir . this numerical representation of the underlying rocks and fluids is then used to predict the flow behavior , under a given set of controls . the controls usually represent the amount of pressure or flow that is imposed at the producing and injecting wells . due to the noisy and sparse nature of seismic data , core samples , and well logs , uncertainty is an inherent characteristic of any geological model . the unique true distribution of reservoir properties is usually unknown . to quantify the uncertainty in a geological model , geo - statistical methods can be used through the construction of multiple equally probable realizations of reservoir properties . simulation of oil production from sagd is a very difficult task , because it involves reproducing complex physical phenomena and strong nonlinearities ( e . g . large variation of fluid properties with temperature ). however , because sagd is economically more costly than conventional oil production , it is an ideal candidate for optimization via modeling . computer analysis of production for an oil reservoir is usually divided into two phases , history matching and prediction . when an oil field is first discovered , a reservoir model is constructed utilizing geological data . once the petroleum field enters into the production stage , many changes take place in the reservoir . for example , the extraction of oil / gas / water from the field causes the fluid pressure of the field to change . injection of steam and fractures can cause mobility to change . various procedures can affect porosity . in order to obtain the most current state of a reservoir , these changes need to be reflected in the model . history matching is the process of updating the reservoir descriptor parameters in a given computer model to reflect such changes , based on production data collected from the field . production data essentially give the fluid dynamics of the field ; examples include water , oil and pressure information , well locations and performances . thus , reservoir models use empirically acquired data to describe a field . in the history matching phase , geological data and production data of the reservoir and its wells are used to build a mathematical model which can predict production rates from wells in that reservoir . the model is generally a “ black box ” with unknown parameters . given the water / oil rates and other production information collected from the field , the model is modified to identify these unknown parameter values such that the reservoir gives flow outputs matching the production data . this takes time because more than one combination of reservoir parameter values give the same flow outputs , a large number of well - matched or “ good ” reservoir models needs to be obtained in order to achieve a high degree of confidence in the history - matching results . furthermore , analysis of the production of a petroleum reservoir is an ongoing process . these models are constantly being rerun and further tuned to improve their ability to match newly gathered production data . as expected , the above - described process of history matching for prediction is a very time consuming process and can be very inefficient if the effect of multiple unknown parameters have to be investigated . the presently described method overcomes the time consuming approach by developing surrogate models of a reservoir using growth function models and the data - driven models . fig4 displays a flow chart of steps generally taken to determine optimal reservoir controls . a full model simulation , such as that described above , is used to develop a surrogate with reduced reservoir conditions . data assimilation tools , such as kalman filters and smoothers , track uncertainties and update both the simulation and surrogate models according to timely incoming data . the reservoir controls are optimized based on these models . new data from real field operations using the new parameters is then collected to continually evolve the models . however , there is no tool for capturing trends and physics involved with each reservoir such that meaningful predictions can be made . having this information would be especially imperative because it would allow for proactive use of the models in the field and lead to more reliable decisions . in the presently disclosed method , growth modeling and data driven modeling are used to build two surrogates that can be combined for predictive modeling and forecasting . the analytical models capture trends in production process by incorporating underlying physics theories . the data - driven models capture the discrepancy between the analytical models and the actual physics of the well , i . e . between real field data and the computed data from the analytical model . the two surrogates can be combined because deterministic models , such as growth function models , require an accurate estimate of modeled properties ( e . g . multiphase flow , transport through porous media , etc ), especially those that affect the estimation and location of recoverable reserves , in addition to revealing true subsurface flow characteristics under various injection scenarios . as such , there is a need to improve accuracy while reducing the uncertainty associated with reservoir characterization . this is where the data - driven models are used . the data driven surrogate can be used as a corrections tool for the growth model based surrogate . this will allow for modification of the growth model for more accurate predictions . analytical models , such as growth functions , are mathematical models that have a closed form solution , i . e . the solution to the equations used to describe changes in a system can be expressed as a mathematical analytic function . simple analytical models provide an important tool for deconstructing the mechanisms underlying complex physical processes , for interpreting numerical simulations and , for making connections to observational or laboratory data . thus , when applied to new data or records , an analytical model can predict outcomes based on historical patterns . growth curve models are a type of analytical model commonly used in biology and health sciences , such as population dynamics ( of e . g ., cells or humans ). most models are based on the logistic growth curve or verhulst model , wherein the e . g . population dynamics has an exponential growth : wherein r is the intrinsic growth rate ( or proportionality constant ) and represents growth rate per capita in this particular example , t is time , and n is the growing variable of interest , in this case population . the resulting growth model is sigmoidal and shows an initial stage of growth having an exponential nature , which slows as saturation begins and finally stops at maturity . growth function models based on the initial verhulst equation are still very prominent today . tsoularis ( 2001 ) and fekedulegn ( 1999 ) both detail the variety of growth curves that have been developed for population dynamics , general biological growth , and forestry . wo2013041670 details the use of a logistic growth model to model the growth kinetics for p . putida while it produces rhamonolipids . us20090119020 describes a method for processing data representing growth curves to determine whether valid or signification growth has occurred . however , these types of models are mainly used for science and some economic evaluations , and have not yet been applied to oil and gas simulations . data - driven techniques such as neural networks or polynomial regressions and variations thereof have found use in modeling sagd . however , a disadvantage of these models is that they do not include the physical structure of the reservoir in the model . instead , these models are based on the analysis of the data characterizing the system under study . in the present method , a data driven technique is used to build models of the error probability distribution for the physical - based analytical model . thus , it is being used as a uncertainty prediction model . the proposed method seeks to bridge the analytical models with data driven techniques by capturing the main trend of the process into an analytical and monotonic increasing function , such as cumulative production , and performing data driven corrections to the discrepancies that field data and computed data may show . in the present method , the rate and shape of the growth function model can be correlated to geological , geometrical and operational factors determining sagd steam chamber growth and shape . in turn , this steam chamber features can be associated with e . g . cumulative production and rates . the difference in these two modeling methods used in the present disclosure is illustrated below in tables 1 and 2 : the advantage of using growth curve based methods lies in their ability to use the underlying physics of the hydrocarbon reservoirs to predict sagd performance . all of this can be done with a much faster turnaround time . furthermore , the growth models do not required specialized software and can be implemented on most any platform , including open source platforms . another advantage is the ability to combine the growth model with a data - driven model . fig6 shows the idealized result of a surrogate according to the combined models . in theory , the growth model and the corrections from the data driven model will accurately predict the field data . fig5 a and 5b show the method of using the correction for an open loop and closed loop system , respectively . in the open loop system , the parameters of interest are modeled using a growth model to create a deterministic parametric surrogate and the field data is modeled to create the stochastic non - parametric model . these can be combined into a single surrogate model to predict performance response of the reservoir of interest . in a closed loop system , the surrogate model prediction can be compared with actual data ( y 1 ) and any discrepancies can lead to an adjustment of the growth model . the method was applied to data collected from multiple sagd operations owned by conocophillips . a modified gompertz growth function model , shown in fig7 , was found to have the best fit and prediction for the studied parameters in the examples described below . the particular model fits the data to the following equation : y ( t )= c · e − ae − bt − c · e − a equation 1 wherein for example , y is the cumulative oil production , t is time , e is the natural exponential function , and a , b and c can be associated with physical parameters , e . g ., taken from the reservoir . this particular growth model is based on three analytical coefficients , namely , a , b and c , that can be associated with physical parameters . in the experiments described below , coefficient a controls the growth rate , coefficient b controls the variation of the growth rate with respect to time , and coefficient c controls the y - scale of the cumulative oil production . fig7 shows cumoil ( y ) versus time ( x ) and illustrates the behavior of the model given by equation 1 for a fixed value of c = 1 , and different values of coefficients a and b , wherein a is the growth rate and b is the variation in growth rate over time ( see labeled axes ). the data driven model component can be optionally realized as a time - dependent model based on nonlinear system identification method designed to correct for residuals given by the mismatch between the original data and the fitting model . the flexibility of fitting cumulative oil from cumulative steam performance profile using model equation 1 is illustrated in fig8 on field data obtained from different assets with each having a different production history . the number of fits corresponds to 57 different well pairs , wherein open circle data points represent historical data , and closed circles represent the predicted data using equation 1 . the model in fig8 did not rely on the data - driven component given the good quality of fit and the restricted number of sampled cases . while the growth function appears to be capturing the main production trends contained in the data , an optional data - driven component step can also be used to improve the quality of the fit and to capture the lower - order effects . fig9 indicates that the quality of the fit for cumulative steam and oil ratio ( csor ) ranges from 0 . 5 to 4 . 0 percent , which is very good given both the noise and the incidence of second order physical effects ( e . g ., pressure operation changes , sub - cooling control , downtime and coalescence ) that may not be entirely captured by the proposed growth model . the fitting was carried out with the aid of a nonlinear least squares method with bounded constraints and globalized via the levenberg - marquardt algorithm . note that end point of production may not be necessarily fitted with high accuracy as the main emphasis in probabilistic forecasting is to capture the overall cumulative oil production trend under parameter and observation uncertainty and ultimately , to minimize possible overfitting . to evaluate probabilistic forecasting , three well pair cases from three different assets are considered from the set displayed in fig8 . these cases vary in geology , operational and reservoir geometrical conditions as well in production history . in the following , these cases are presented in increasing availability of history time ( expressed in months of production ). to validate the methodology , an early portion of the history is used as a base to perform the stochastic forecasts . the end of each of these sections of historical data is indicated with a solid yellow vertical line . the input uncertainty is described by uniformly sampling one million combinations of values for growth parameters a , b , c and d . by means of a monte carlo procedure , fits yielding a relative error of 1 % were collected to reconstruct the distribution of cumulative oil values at each month of predicted production . once the distribution of these values are constructed , it is possible to estimate the probability associated to predict a cumulative oil value for a given amount of cumulative steam injected at any time . forecast probabilistic bounds are indicated via px percentiles , that is , the number of forecast that will fall below an x % of the cases . hence , p0 and p100 provides the minimum and maximum bounds of cumulative oil that can be obtained , respectively ; p10 and p90 provide practical bounds for low and high estimates of oil recovered and , p50 , is the probability that the oil recovered will equal or exceeded the mean estimate . in the following figures , p0 and p100 are indicated in green lines , p10 and p90 are indicated in dashed blue lines and p50 with a solid blue line . the best fit is indicated with a solid red line . ideally , extrapolation of the best fit should represent the p50 trend of the forecast data and should stay as close as possible to future cumulative oil measured at the field . the data before and after history is indicated in black to illustrate the quality of the fitting and percentiles used to bound the forecast data . fig1 shows the fitting and forecast using 20 months ( over 1 . 5 years ) of historical data . stochastic forecast were set to 17 additional months of production assuming a cumulative steam injection of 350 , 000 mm 3 at the end of the period . the csor ( cumulative steam / cumulative oil ratio ) shows a nearly linear trend that is accurately captured by the modified gompertz model . the extrapolation of the best fit during the history period , the mean of possible forecasts , namely p50 , and the data are close to each other . the p10 and p90 estimates enclose almost in a symmetrical way these 3 trends , thus denoting a non - skewed gaussian distribution for all possible forecasts . similar conclusions can be drawn from cumulative oil as a function of time as depicted in fig1 . despite the sudden change in cumulative oil production at 15 months , the trend is accurately predicted during the whole period of 37 months . this example shows that relative long - term predictions can be made from short historical data . fig1 - 13 show another cumulative oil prediction case as a function of cumulative steam injected and time , respectively . this case not only relies on a longer history than the previous case , but it also displays an unexpected change of trend right after the history of 50 months of production . the modified gompertz growth model is capable of foreseeing an immediate decline of production after 60 months ( 5 years ) and the uncertainty bounds p10 and p90 are still good enough to provide a reliable forecast for more than 50 additional months ( over 4 years ). the plateau in cumulative oil production is not exactly captured , but it is still close to the p50 and extrapolated best fitting curve . it is fair to say that as more history is incorporated before forecast , the decline in production will be increasingly captured by the growth model . a third case is shown in fig1 - 15 . this case has even longer history ( 100 months ) and longer forecast horizon ( 83 months ) than the previous two cases . it also shows a new feature that challenges the prediction and it has to do with a sudden change of slope in cumulative oil production before the end of history . this change of slope may be due to sudden changes in reservoir pressure as a result of coalescence effects ( communication of steam chambers by neighboring well pairs ), bottom - hole pressure changes induced during operations or high contrast of permeability zones . in such situation the forecast tends to be conservative as the actual production exceeds the p90 estimate . note that the best - fit line ( red ) follows the same trend as p90 , which may indicate that many pessimistic models ( i . e ., with high relative error ) were considered for the stochastic forecasting . nevertheless , since the deterministic forecasting does a good job predicting the amount of cumulative oil , it is advisable to refine the probabilistic assessment of forecasts by lowering relative error tolerances . also , the growth model is able to capture both increasing and decreasing changes of production as illustrated by this case and the previous one . the following references are incorporated by reference in their entirety for all purposes . akin , s . 2005 . mathematical modelling of steam - 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