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Improving Reservoir History Matching and Uncertainty Quantification Using Sea Water Production Data

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Improving Reservoir History Matching and Uncertainty Quantification Using Sea Water Production Data (SPE Submission)
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  SPE Improving History Matching and Uncertainty Quantification Using Sea Water Production Data Nwafor Obinna  August 2013 Keyword: History Matching, Uncertainty Quantification, Particle Swarm Optimisation, Neighbourhood Approximation Bayes, Multi-Objective Optimisation  Abstract   History matching is used in reservoir calibration. Conventional history matching could be improved by addition of more constraints to be matched. The injected sea water, produced as part of associated water could have the potential of serving as an additional constraint. Such data can be obtained cheaply by using ion in sea water as natural tracers. This study aimed to determine the extent of improvement to history matching and reduction of uncertainty in forecasts brought about by the addition of injected sea water production data to the history matching process. The study was carried out using the PUNQS3 reservoir model. It is a synthetic reservoir model that has been used for similar studies and severally to test out methods in history matching and uncertainty quantification. The uncertain parameters in the PUNQS3 model are the porosity and permeability. Two cases of automatic history matching were carried out. One involved the use of injected sea water tracer production data as additional constraint. The other involved using only the conventional production data. The automatic history matching was based on multi-objective particle swarm optimization (PSO). Which is a nature inspired stochastic optimization technique. The uncertainty quantification was done using Neighbourhood Approximation method (NA-Bayes) based on a Bayesian framework. The result for the two cases was compared on the basis of advance of their pareto front towards lower misfit values. The quality of history matching and size of uncertainty were also considered. They all show that addition of injected sea water production data improves the history matching process, reduced uncertainty in forecast, as well as create more robust uncertainty quantification. However the improvements were not large, but could be more significant for more complex reservoir history matching problems. Introduction   It is common to use numerical simulators to predict the performance of a reservoir. The reliability of a reservoir simulation result is dependent on the inputs to the reservoir model description. This input can be classified as relating to static (geological) properties description, or dynamic (fluid flow) properties. Such information is gathered in the course of exploration and appraisal. Static data will include time independent information derived from cores, wire line logs, seismic surveys, etc. Dynamic data are time dependent data derived from flow relations, they relate to reservoir properties such as relative permeability, fluid saturations, viscosity, flow rate, fractional flows, etc. (Cheng et al., 2004, p.1). It is impossible to eliminate all uncertainties in a reservoir. History Matching is a major technique for calibrating the reservoir model in order to maximize reliability of simulation results. It is the fine tuning of estimated reservoir description parameters to match known past performance of the reservoir such as fluid rates, well bottom-hole pressures, field average pressures, etc. History matching is an inverse problem, we attempt to  2 use the observed data about a reservoir to predict its properties. As is typical of inverse mathematical problem, the solutions are never unique (Cunha, Prais, & Rodrigues, 2002, p.1). Conventional history matching involves manual variation of field description parameters. Simulation runs are made for each variation of model parameters, and the simulation results are compared with the historical values. This is expensive in terms of human labour and computing time. It is also highly subjective as the iteration direction depends on experience and insight.  Automatic History Matching and Mathematical Optimization Several History matching techniques have been studied and applied in the quest to automate the process of finding solutions to history matching problems. They take the approach of treating the inverse problem as a mathematical optimisation problem, in which a defined objective function is either maximized or minimized. This objective function takes the form of a function of the difference between observed history data and simulated result data (Cunha et al., 2002). Cunha et al. (2002, p.2) also indicates that automatic history matching can be broadly classified into two groups, gradient based techniques and stochastic techniques. (Sarma, Durlofsky, Aziz, & Chen, 2007, p.1) identified the streamline based history matching technique as a class of its own. Each method has its own limitations and strengths. The deterministic or gradient based techniques uses gradients of the mathematical model, related to the parameterised properties of the model, to minimize the objective function which is based on misfits between historical data and simulated results (Cunha et al., 2002, p.2). They are known to converge very fast. However, they are poorly adapted to the multi-modal and non-unique nature of solutions to history matching problems. Sarma et al.(2007) and Cunha et al.(2002) agree that gradient based minimization is easily trapped into local minima point. Stochastic history matching techniques have the exact opposite properties to gradient techniques. They require a large number of simulation, hence, convergence and computing time is quite significant. However, they are not easily trapped in local minima point, rather they effect a more efficient search of the solution space. Sarma et al. (2007, p.1) noted that stochastic techniques more easily honour complex geological models as they treat the simulator as a black box. The Streamlined based history matching techniques are limited by their inability to model complex physics .  Natural Water Tracers in the Reservoir    Valestrand et al.(2008, p.2) defined tracers as inert chemical or radioactive compounds used to label fluids or track fluid movements. Artificial water tracers are used for inter-well tracer tests. The interest of this study lies on natural water tracers. Even though ions in sea water are affected by chemical activities, Huseby et al., (2009, p.2) indicated that in most cases ions in sea water only react moderately with the formation water. Such ions can be used as natural tracers of sea water. Ions which may be used for such application include SO 42- , Mg 2+ , K + , Ba 2+ , Sr  2+ , Ca 2+ , Cl -  (Huseby et al., 2009, p.2). The second option for natural tracers of water are isotopes. Hydrogen isotopes are the best being abundant in water. Another isotope is Strontium 87 Sr, a radiogenic isotope found in high concentration in potassium rich rocks (Huseby et al., 2009, p.2). The high concentration is transferred to formation waters with which such rocks have equilibrated. The ratio of 87 Sr to the more abundant 86 Sr isotope can be used as tracers for formation water. The choice of natural water tracers might be an economic decision rather than a choice based on quality. Ion content data of produced water are routinely analysed as part of the flow assurance, hence, has little extra acquisition cost compared to isotopes. For this study, the  3 assumptions is that there are scale risks in our synthetic reservoir which exclude the use of SO 42- as a tracer. The alternative choice is the use of Cl -  ions as tracers. These ions do not move in between reservoir phases and are not subject to portioning effects (Valestrand et al., 2008, p.2). Description of Study The investigated of this study is the extent of improvements to reservoir history match and uncertainty quantification induced by the use of natural chemical water tracer data to specify historic production of injected sea water fractions. It has been proposed by several studies that since injected sea water carried complementary information on flow paths within the reservoir, its addition as a constraint to reservoir calibration should improve the quality of history match and also reduce the amount of uncertainty in forecast.  (Arnold, Vazquez, Demyanov, & Christie, 2012; Huseby et al., 2009; Valestrand et al., 2008; Vazquez, McCartney, & Mackay, 2013; Vazquez, MacMillan, et al., 2013). Specifically this study aims to answer the following questions. Question 1:  Does adding natural tracer data reduce the mean square error misfit achieved by sampled models with reference to oil rate and bottom-hole pressure historical data? Question 2:  Does adding natural tracer data generally reduce the range of uncertainties specified by Bayesian credibility intervals over the history match and forecast period? Question 3:  Does adding natural tracer data reduce the range of uncertainties specified by Bayesian credibility at the terminal point of the forecast period? While none of the earlier studies has sought to compare the effect of adding natural sea water tracer data to history matching by measuring the range of uncertainties, Arnold et al.(2012) had observed that it made improvements to forecast generally. The comparison by misfit of sampled models has been a bit more complicated due to earlier studies use us single optimization techniques, which requires addition or removal of tracer data points before misfit values could be compared (Arnold et al., 2012, p.6). This study will be carried out using multi-objective particle swarm optimisation to allow a free comparison of misfit values and also maximise the space searched by the optimisation algorithm. Reservoir Model: PUNQS3 The PUNQS3 is a synthetic reservoir model based on an actual reservoir developed by Elf petroleum. The synthetic case was initially developed for the PUNQ (production forecasting with uncertainty quantification) project sponsored by the European Community. It has however become a benchmark for testing methods in history matching and uncertainty quantification (Arnold et al., 2012, p.2). The reservoir model consist of 19x28x5 grid blocks, of which 1761 blocks are active. It is bounded to the east and south by a fault, the north and west are linked to a strong aquifer. It also includes a gas cap, while six well are located around the gas oil contact. There were no injector wells since the reservoir had a strong aquifer support. The production scheduling is based on the real reservoir. Wells are under production constraint based on flow. The scheduled flow periods are for a first year of extended well testing, followed by a three year shut-in period, before field production commences. During field production, two weeks shut-in period for each year is included for each well to collect shut-in pressure data. Total production period is for 16.5years or 6025 days. The geological description of the reservoir is provided by imperial college (―Geological Description for PUNQS3 Reservoir Model,‖ n.d.) . Layers 1, 3, and 5 consist of fluvial channel  4 fills encased in floodplain mudstone. These linear streaks of high-porous sands (ϕ > 20 %)  lie along an azimuth between 110 and 170 degrees SE Layer 2 represents marine or lagoonal clay with some distal mouthbar deposits; and Layer 4 contains mouthbars or lagoonal deltas within lagoonal clays, so a lobate shaped flow unit is expected which consists of an intermediate porosity region (ϕ ~ 15  in a low-porosity matrix (ϕ < 5%) . Further details are given in the table below. Table 1 Expected facies with estimates for width and spacing of major flow units Layer Facies Width Spacing 1 Channel Fill 800 m 2-5 km 2 Lagoonal Shale —   —   3 Channel Fill 1000 m 2-5 km 4 Mouthbar 500-5000 m 10 km 5 Channel Fill 2000 m 4-10 km This study worked on the problem of determination of the porosity and permeability distributions for the 5 layers on the PUNQS3 model. However, the focus was to assess the impact of adding injected sea water production data as an additional constraint to the history matching method. The PUNQS3 was initially designed without any injection wells due to the strong aquifer support modelled. It is imperative that sea water is injected into the reservoir for this study, hence four Injections wells have been added to the reservoir as shown in figure 1. These modifications necessitate the generation of a new history data using the truth case data provided at the PUNQS3 website of Imperial College (―Geological Description for PUNQS3 Reservoir Model,‖ n.d.) . Parameterisation The reservoir description for the PUNQS3 indicates the existence three layers (1, 3 and 5) which have fluvial sand channels embedded in a flood plain. For these sand channels we assume that the channels direction is mid-way between the specified range at 145 degrees azimuth. This is to reduce the number of required parameters, variations of 35 degrees in azimuth is not expected to have a major impact on the reservoir performance. The parameterisation was based on regions to capture the heterogeneity across layers of the reservoir. Since the position of the sand channels is unknown, as region scheme has been adopted which allows flexibility in the location and width of the sand channels, while also minimizing the resulting of geometrically unrealistic models.  As illustrated in the Figures 2 A-E below, the parameter regions have been defined diagonally in the approximate direction of 145 degrees azimuth. The Larger regions whose width(448m) is about half the minimum sand channel width(800m) described is alternated with two smaller regions of width (256m) in order to build in reasonable flexibility on the location of the sand channels. This is at the expense of having some poor models with sand width less than 800m. The same parameter regions is used in layers 3 and 5, being mindful that the sand channels in in layer 5 have widths of about 2km. This arrangement was adopted with the expectation that the best models will identify several adjacent regions to be of similar high permeability to form  Figure 1 Injectors and Producer Wells on the  PUNQS3 Reservoir Model   
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