Jon Kleppe

Joint optimization of oil well placement and controls

Well placement and control optimization in oil field development are commonly performed in a sequential manner. In this work, we propose a joint approach that embeds well control optimization within the search for optimum well placement configurations. We solve for well placement using derivative-free methods based on pattern search. Control optimization is solved by sequential quadratic programming using gradients efficiently computed through adjoints. Joint optimization yields a significant increase, of up to 20% in net present value, when compared to reasonable sequential approaches. The joint approach does, however, require about an order of magnitude increase in the number of objective function evaluations compared to sequential procedures. This increase is somewhat mitigated by the parallel implementation of some of the pattern-search algorithms used in this work. Two pattern-search algorithms using eight and 20 computing cores yield speedup factors of 4.1 and 6.4, respectively. A third pattern-search procedure based on a serial evaluation of the objective function is less efficient in terms of clock time, but the optimized cost function value obtained with this scheme is marginally better.

Nonlinear inversion for estimating reservoir parameters from time-lapse seismic data

Saturation and pore pressure changes within a reservoir can be estimated by a history matching process based on production data. If time-lapse seismic data are available, the same parameters might be estimated directly from the seismic data as well. There are several ways to combine these data sources for estimating these reservoir parameters. In this work, we formulate a nonlinear inversion scheme to estimate pressure and saturation changes from time-lapse seismic data. We believe that such a formulation will enable us to include seismic data in the reservoir simulator in an efficient way, by including a second term in the leastsquares objective function. A nonlinear Gauss–Newton inversion method is tested on a 2D synthetic dataset inspired by a field offshore from Norway. A conventional reservoir simulator has been used to produce saturation and pore pressure changes as a function of production time. A rock physics model converts these data into synthetic time-lapse seismic data. Finally, the synthetic time-lapse data are used to test the derived inversion algorithm. We find that the inversion results are strongly dependent on the input model, and this is expected since we are dealing with an ill-posed inversion problem. Since we estimate pressure and saturation change for each grid cell in the reservoir model, the number of model parameters is high, and therefore the problem is undetermined. From testing, using this particular dataset, we assume neither pressure nor saturation changes for the initial model. Although uncertainties associated with the proposed method are high, we think this might be a useful tool, since there are ways to reduce the number of model parameters and constrain the objective function by including production data and reservoir simulation data into this algorithm.

A derivative-free approach for the estimation of porosity and permeability using time-lapse seismic and production data

In this study, we apply a derivative-free optimization algorithm to estimate porosity and permeability from time-lapse seismic data and production data from a real reservoir (Norne field). In some circumstances, obtaining gradient information (exact and/or approximate) can be problematic e.g. derivatives are not available from a commercial simulator, or results are needed within a very short time frame. Derivative-free optimization approaches can be very time consuming because they often require many simulations. Typically, one iteration roughly needs as many simulations as the number of optimization variables. In this work, we propose two ways to significantly increase the efficiency of an optimization methodology in model inversion problems. First, by principal component analysis we decrease the number of optimization variables while keeping geostatistical consistency, and second, noticing that some optimization methods are very amenable to being parallelized, we apply them within a distributed computing framework. If we combine all this, the model inversion approach can be robust, fairly efficient and very simple to implement. In this paper, we apply the methodology to two cases: a semi-synthetic model with noisy data, and a case based entirely on field data. The results show that the derivative-free approach presented is robust against noise in the data.

Porosity and permeability estimation by integration of production and time-lapse near and far offset seismic data

This study presents a method based on the Gauss–Newton optimization technique for continuous reservoir model updating with respect to production history and time-lapse seismic data in the form of zero offset amplitudes and amplitude versus offset (AVO) gradients. The main objective of the study is to test the feasibility of using these integrated data as input to reservoir parameter estimation problems. Using only production data or zero offset time-lapse seismic amplitudes as observation data in the parameter estimation process cannot properly limit the solution space. The emphasis of this work is to use the integrated data combined with empirical knowledge about rock types from laboratory measurements, to further constrain the inversion process. The algorithm written for this study consists of three parts: the reservoir simulator, the rock physics petro-elastic model and the optimization algorithm. The Gauss–Newton inversion is tested at a 2D semi-synthetic model inspired by real field data from offshore Norway. The algorithm reduces the misfit between the observed and simulated data which make it possible to estimate porosity and permeability distributions. The Gauss–Newton optimization technique is an efficient parameter estimation technique. However, the numerical estimation of the gradient is time consuming, and it can be prohibitive for practical applications. This method is suitable for distributed computing which considerably reduces the total optimization time. The amount of reduction depends mainly on the number of available processors.

Porosity and Permeability Estimation by Gradient-Based History Matching using Time- Lapse Seismic Data

A method based on the Gauss-Newton optimization technique for continuous model updating with respect to 4D seismic data is presented. The study uses a commercial finite difference black oil reservoir simulator and a standard rock physics model to predict seismic amplitudes as a function of porosity and permeabilities. The main objective of the study is to test the feasibility of using 4D seismic data as input to reservoir parameter estimation problems. The algorithm written for this study, which was initially developed for the estimation of saturation and pressure changes from time-lapse seismic data, consists of three parts: the reservoir simulator, the rock physics petro-elastic model, and the optimization algorithm. The time-lapse seismic data are used for observation purposes. In our example, a simulation model generated the seismic data, then the model was modified after this the algorithm was used to fit the data generated in the previous step.

Multiphase Flow in Fractured Reservoirs

Naturally fractured reservoirs represent a complex class of reservoirs. Multiphase flow in such reservoirs adds to the complexity and has been studied extensively over the last few years.

Results of the First Norne Field Case on History Matching and Recovery Optimization Using Production and 4D Seismic Data

In preparation for the SPE Applied Technology Workshop, ``Use of 4D seismic and production data for history matching and optimization – application to Norne (Norway)’’ held in Trondheim 14-16 June 2011, a unique test case (Norne E-segment) study based on real field data of a brown field offshore Norway was organized to evaluate and compare mathematical methods for history matching as well as methods on optimal production strategy and/or enhanced oil recovery. The integrated data set provided an opportunity to discuss emerging and classical history matching and optimization methods after being tested using real field data. The participants of this comparative case study were expected to come up with a history matched model preferably using an integration of production and time-lapse seismic data and with an optimal production strategy for the remaining recoverable resources for the future period. Participants were allowed to suggest techniques to enhance recovery. Taking into account that the Norne benchmark case is a case study based on real data and no one exactly knows the true answer, participants and delegates were encouraged to discuss the methods, results and challenges during the course of the workshop, and thus in this case there are no winners or losers. Everyone who participated gained experience during the course of the exercise. Participants were asked to history match the model until the end of 2004 and optimally predict the production (oil, water and gas rates) performance until the end of 2008. Participants were from different universities in collaboration with other research organizations namely Stanford University in collaboration with IBM and Chevron, TU Delft in collaboration with TNO, Texas A&M University, and NTNU in collaboration with Sintef. This paper summarizes the presented results from these groups and the outcome of the discussion of the workshop delegates. Introduction The Center of Integrated Operation in petroleum industry at NTNU (IO Center) in conjunction with the Society of Petroleum Engineers (SPE) organized an applied technology workshop about the use of real data from the Norne Field. The workshop attracted 80 delegates and international speakers from more than ten countries all over the world, namely the United States of America, Saudi Arabia, the Netherlands, Brazil, Denmark, Angola, Nigeria, the United Kingdom, Russia, India, and Norway. The uniqueness of this workshop was that it addressed for the first time a comparative case study that uses real field data that includes time lapse seismic data. The purpose of reservoir management is to control operations to maximize both shortand long-term production. This consists of life-cycle optimization based on reservoir model uncertainties together with model updating by production measurements, timelapse seismic data and other available data. Time-lapse seismic data helps to determine reservoir changes that occur with time and can be used as a new dimension in history matching since they contain information about fluid movement and pressure changes between and beyond the wells. The well production schedule and history are provided for the period from Dec. 1997 to Dec. 2004 and comprise the observation data for the history match. A previous full field calibration was performed by the operator to match the history up until 2003. The reservoir attributes previously calibrated include fault transmissibility multipliers, regional relative permeability parameters, and large-scale (absolute) permeability and porosity heterogeneity using regional and constant multipliers, in total defining a global history match for a single (structural) reservoir description. The exercise was to improve the match and then perform a recovery optimization. In total five groups participated in this exercise and four presented their results during the workshop (see Table 1). The limited number of participants was due to the inaccesability of the Norne database (license limitation) to commercial companies. Table 1: Participants to the case study. University/Company Main Contributors Stanford University, Chevron & IBM Amit Suman, Drosos Kourounis, Tapan Mukerji and Khalid Aziz Delft / TNO Slawomir Szklarz, Lies Peters and Remus Hanea Texas A&M Eric Bhark, Rey Alvaro, Mohan Sharma, Akhil DattaGupta NTNU Ola T. Miljeteig, Richard Rwechungura, Anass Ammar and Jon Kleppe University of Texas Austin Reza Tavakoli and Mary Wheeler** **Did not present the results in the workshop Description of the Norne Field The Norne Field is located in the blocks 6608/10 and 6508/10 on a horst block in the southern part of the Nordland II area in the Norwegian Sea. The rocks within the Norne reservoir are of Late Triassic to Middle Jurassic age. The present geological model consists of five reservoir zones. They are the Garn, Not, Ile, Tofte and Tilje. Oil is mainly found in the Ile and Tofte Formations, and gas in the Garn formation. The sandstones are buried at a depth of 2500-2700 m. The porosity is in the range of 25-30% while permeability varies from 20 to 2500 mD (Steffensen and Karstad, 1995; Osdal et al., 2006). The data consist of near, mid and far stack 3D seismic data acquired in 2001, 2003 and 2004. More information about the Norne field, provided data and first case release are given in Chapter 5 (Rwechungura et al., 2010). The first package includes the E-segment of the Norne field; other benchmarks will include larger parts of the field. Further, the seismic data were also separated to suit the requirement of coverage of the Esegment only. Accordingly, the E-segment was chosen because it has the highest quality seismic data of the entire field. The E-segment of the Norne Field consists of 8733 active grids and 5 wells as of the end of 2004, i.e., 2 injectors and 3 producers. Participants were given a password to access the Norne database through the website www.ipt.ntnu.no/~norne. Description of the Exercise The exercise was defined six months prior to the workshop on History Matching and EOR optimization using both production and time lapse seismic data. This benchmark case considers the time frame from 1997 to 2004 for history matching and 2005 to 2008 for recovery optimization. The actual 2004 simulation model containing all information and properties was given. In addition, production and injection data from 1997 to the end of 2004, and 4D-seismic data for the same period (2003-2001 and 2004-2001) were provided. These data are the basis for the history match performed by participants. The following was the defined workflow:  Download the Eclipse Norne model and import it into their reservoir simulator. The production history for 1997-2004, reports and all required data are given in the website http://www.ipt.ntnu.no/~norne.  Participants were required to history match the model until the end of 2004 and predict the production (oil, water and gas rates) performance until end of 2008.  Using the history matched results from above, create an optimal production strategy for the remaining recoverable resources for the future period. Participants might also suggest techniques to enhance recovery, since significant amount of the recoverable reserves were already produced by the end of October 2008.  The format for the production strategy should contain time, pressure (BHP) or flow rates for the wells.  The following constraints should apply to the strategy: 1. For each injector well the maximum FBHP = 450 bar 2. For each producer well the minimum FBHP = 150 bar 3. For each injector well the maximum water rate = 12000 Sm/day 4. For each producer well the maximum liquid rate = 6000 Sm/day 5. Maximum water-cut = 95% 6. A maximum of two wells can be sidetracked to increase recovery  The following economic parameters were given : Oil price 75 US

Numerical simulations for designing Oil/CO2 gravity-drainage laboratory experiments of a naturally fractured reservoir

per bbl Discount rate 10% reference time is January 2005 Cost of water handling/injection 6 US

Sample Mechanistic Modeling of Alkaline Surfactant Polymer Flooding for Snorre Field from Core-scale to Larger Scale of One-Spot Pilot

per bbl Cost of gas injection 1.2 US

Applicability and Rate Sensitivity of Several Up Scaling Techniques in Fractured Reservoir Simulation

per Mscf (M = 1000) Cost of a new side-tracked well 65 million US