Probabilistic analysis of the value of a smart well for sequential production of a stacked reservoir

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stacked reservoir price of US$12/bbl and a discount rate of 7%), and perfect valves, the mean of the incremental NPV distribution was positive with 99% confidence limits of US$10.57 million and US$11.00 million. When, in addition, an infant mortality probability of 5% was taken into account for the individual ICVs, assuming them permanently closed at failure, the mean of the difference in cumulative oil production remained positive with a 99% confidence interval between 35.3� 103 and 67.7� 103 m3 (222� 103 and 426� 103 bbl). Also water and gas production were still lower than in the conventional scenario. As a result, while taking into account the risk of valve failure, the mean of the incremental NPV remained positive with 99% confidence limits of US$7.70 million and US$9.15 million. D 2004 Elsevier B.V. All rights reserved. Keywords: Smart wells; Unconventional wells; Intelligent wells; Statistical analysis; Probabilistic analysis; Uncertainty; Reliability; Value assessment R. van der Poela, J.D. Jansena,b,* aDepartment of Applied Earth Sciences, Delft University of Technology, P.O. Box 5028, 2600 GA Delft, The Netherlands bShell International Exploration and Production, P.O. Box 60, 2280 AB Rijswijk, The Netherlands Abstract Smart wells enable a quick reaction to unexpected events during the life of a reservoir, and have the potential to positively influence the net present value (NPV) of a project development. To quantify this potential, we examined the influence of a smart completion on the probability density functions (PDFs) of cumulative oil, gas and water production and incremental NPV. We considered a one-well development of a stacked reservoir consisting of four blocks with comparable pressure regimes, but with large uncertainties in the gas–oil and oil–water contacts. A Monte Carlo analysis of 2� 500 paired simulations was performed in a reservoir simulator for a sequential production scenario with a conventional and a smart well completion. The smart well was equipped with on–off inflow control valves (ICVs) in each zone, which were opened and closed alternatingly to maximize the oil rate while staying below pre-set limits for gas and water production. In addition, we took into account the uncertainty in the reliability of the ICVs. For the scenario and the economic parameters considered, we concluded that smart well technology results in an increase of the incremental NPV. The mean cumulative oil production of the conventional scenario was between 831�103 and 866� 103 m3 (5.23� 106 and 5.45� 106 bbl) with 99% confidence. Assuming fully reliable ICVs, the mean of the differences in cumulative oil production for the smart and the conventional scenarios was positive with a value between 102� 103 and 109� 103 m3 (640� 103 and 683� 103 bbl) with 99% confidence. Furthermore, water and gas production both decreased significantly. For the given economic parameters (which include an oil Probabilistic analysis of the val production of a ue of a smart well for sequential www.elsevier.com/locate/petrol Journal of Petroleum Science and Engineering 44 (2004) 155–172 0920-4105/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2004.02.012 * Corresponding author. Department of Applied Earth Sciences Section Petroleum Engineering, Delft University of Technology, P.O. Box 5028 2600 GA Delft, The Netherlands. E-mail addresses: [email protected], [email protected] (J.D. Jansen). 1. Introduction 1.1. Influence of smart wells on uncertainty For the purpose of this paper, a well is considered ‘‘smart’’ when it is equipped with sensors and inflow control valves (ICVs) to measure and control the flow from the reservoir to well segments separated from each other by packers (see Fig. 1). Various publica- tions have described the potential benefits of such wells and many smart completions have been installed during the past years. The value of smart wells can result from reduced intervention costs, reduced or delayed production of undesired fluids, and acceler- PDF. Given that smart well technology influences the NPVof a project, it should also influence the shape of the PDF. Fig. 3 summarizes the effect that smart well s, showing zonal isolation (packers) and inflow control valves. Not shown oil water R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172156 ated or increased production of desired fluids; see e.g. Jalali et al. (1998), Algeroy et al. (1999), Erlandsen (2000), Akram et al. (2001), and Glandt (2003). An important advantage of a smart well is the possibility to change its configuration in reaction to unexpected events. For example, a completed zone which suffers early water breakthrough can be shut off or choked down (see Fig. 2). In a conventional well, shutting off the watered-out zone would require a workover, resulting in increased expenditure and lost production. Furthermore, it is usually not feasible to re-open a zone once it has been shut off. As a result of the increased flexibility offered by ICVs, smart well technology has the ability to positively influence the net present value (NPV) of a development. A smart well drilled through separate reservoir blocks can be used to produce the blocks commingled in a con- trolled fashion; see e.g. Jalali et al. (1998). Alterna- tively, the well can be used to produce the blocks Fig. 1. Schematic smart well completion for four separate inflow zone are cement, measurement devices and hydraulic and electric control lines sequentially, with the flexibility to open and close zones many times. An example of such a sequential production scenario with smart wells in the Tern field has been described by Akram et al. (2001). In this paper, we only consider sequential production. Any field development comes with a large degree of uncertainty in the eventual outcome. Uncertainty exists in technical and economic parameters such as reservoir properties or oil price. These uncertainties can be expressed by means of probability density functions (PDFs) of parameters. Using stochastic simulation techniques (Monte Carlo analysis) it is then possible to also express the project’s NPV by a Fig. 2. A watered-out zone can easily be shut off when an ICV is installed for that particular zone, as there is no need for a workover. . DF o proba R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172 157 technology could have on the PDF of the NPV. The mean (l) of the smart development PDF is shifted to the right compared to the conventional development PDF. The ability to adapt to (unexpected) events could possibly also lead to less uncertainty in the outcome. This is shown by a smaller value for the standard deviation (r) of the smart development PDF. The combination of the mean shifting to the right and the narrowing of the PDF increases the chance on a positive NPV, which is represented by the area under the curve to the right of the NPV= 0 line. In practice, the decision to install a smart completion is not always based on the expected NPV alone. In particular, the possibility of encountering costly problems because of valve failure may lead a ‘‘risk averse’’ decision maker Fig. 3. Potential beneficial influence of smart well technology on the P a reduced uncertainty in the outcome and as a result, (3) a reduced not to choose for a smart completion, even when the average effect of the completion on the NPV is positive; see Yeten et al. (2004). Recently, examples have been presented of capturing the additional value of smart completions in a more approximate fashion through the application of option valuation techniques as used in the financial world; see Sharma et al. (2002) and Han (2003). In the present paper, we restrict our analysis to a ‘‘risk neutral’’ classic NPV approach in a probabilistic framework. 1.2. Objective and approach If we want to compare the difference in value between a conventional and a smart completion, we do not need to consider the full project NPV but can restrict the analysis to the incremental NPVof the two options. The incremental NPV only depends on the additional expenditure for the smart completion, in- cluding installation and operating costs, and the differ- ences in revenues and processing costs of produced fluids. The objective of our study was therefore to test the validity of the following proposition: Smart well technology results in an increase of the incremental NPV. In particular, the study focussed on the use of a smart well to drain four adjacent reservoir blocks with uncertain fluid contacts. We used a strongly simplified version of a reservoir model of a real asset. The results of many realisations with varying reservoir parameters f the NPVof a project development. (1) An increase in the mean, (2) bility of a negative NPV. (fluid contact levels) for a smart well were compared to the results for a conventional well. From the incremental NPV distribution resulting from the smart well technology the validity of the proposition was tested. In addition, uncertainty in ICV reliability was taken into account by assuming an infant mortality probability for each ICV. A list of symbols and abbreviations can be found in Appendix A. 2. Numerical model 2.1. Introduction Three proprietary software packages were used to generate data, and manage the workflow: a reservoir simulator, a wellbore flow simulator and a workflow manager capable of generating random data, control- ling simulations and post-processing simulation results. 2.2. Reservoir model 2.2.1. Geometry and grid We used a box-type, one-well model with a cross- section as displayed in Fig. 4. The main characteristic of the reservoir is its segmentation in four individual layers. Layer A actually consists of two zones with different permeabilities and porosities. The width ( y- direction) of our model was chosen such that the model approximately represented the drainage area of one well in the original model. The horizontal well was located exactly in the middle of the ‘box’, which makes the model symmetrical around the x–z-plane. This allowed for a reduction in simulation time through halving the model. However, all results in this paper are given in terms of the whole model. 2.2.2. Reservoir and fluid properties Porosity and absolute permeability were modelled as homogeneous in each sand with a kv–kh ratio equal to 0.10 (see Table 1). Relative permeability and capillary pressure data were taken equal for all layers (see Table 3). The corresponding capillary pressure zones were small and did not play a major role. Net- to-gross was set to unity for all layers. Gas, oil and water properties were taken directly from the original Table 1 Layer properties Layer Units A1 A2 B C D Thickness m 62.5 62.5 100.0 60.0 120.0 Simulation layers – 5 5 10 6 10 Porosity (/) – 0.201 0.216 0.195 0.170 0.177 Absolute permeability (k) mD 1069 1680 735 369 485 R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172158 Table 1 gives further details on the model geometry and Table 2 lists the grid properties. All gridblocks with an initial oil saturation higher than the residual value were refined. Near the wellbore, the width ( y- direction) of the primary gridblock size was reduced to 5 m (blocks containing the wellbore) and 20 m (adjacent gridblocks). Fig. 4. x–z cross-section of the synthetic reservoir model, showing satura model (see Table 4). To each layer an aquifer was connected with a length of 250 m. All other aquifer properties were taken from the adjacent gridblocks. 2.2.3. Well model The inflow section of the well, located at a depth of 2425.5 m, was modelled with a Peaceman inflow tions, (refined) simulation grid, well perforations and layer names. model. A skin value of 5 was used, reflecting the not sure about the fluid contacts. No well has been drilled through the blocks yet, but the prospect is located in a well-developed region and the Table 2 Geometrical and grid properties for the full model Property Units Value Model dimension m 675� 850� 435 Dip in x-direction deg. 45 z-origin m � 2050 Grid dimension – 27� 19� 39 Primary gridblock size m 25� 50� 10 Number of active gridblocks – 30,769 Table 4 PVT data Phase Property Symbol Units Value Gas stock tank density qg,sc kg/m 3 0.815 CGR rp m 3/m3 1.23e� 4 FVF (dry) Bg m 3/m3 4.60e� 4 viscosity (dry)a lg mPa s 0.022 Oil stock tank density qo,sc kg/m 3 830.2 GOR Rp m 3/m3 168.5 FVF Bo m 3/m3 1.578 viscositya lo mPa s 0.247 viscosibilitya – bar� 1 1.81e� 3 compressibilitya co bar � 1 2.49 Water stock tank density qw,sc kg/m 3 1000 viscositya lw mPa s 0.4 viscosibilitya – bar� 1 0.0 compressibilitya cw bar � 1 4.0e� 5 a Values at reference pressure of 231.9 bar. R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172 159 situation in the original real asset. To model the pressure drop in the vertical section, lift tables were generated, using the wellbore simulator, for a tubing size of 4-1/2 in. Pressure drop along the horizontal part of the well was not taken into account to simplify the analysis. Perforating or plugging a layer, and opening or closing an on–off ICV was simply mod- elled as activating or deactivating a perforated well segment in the reservoir simulator. No detailed mod- elling of the completion was performed. We assumed the presence of measurement equipment to allocate gas, oil and water rates to each of the zones at predefined time intervals. Measurement errors were not taken into account. 2.3. Uncertainty model In our study, fluid contact levels were considered to be the uncertain parameters. The four gas–oil contacts and the four oil–water contacts in the model were therefore chosen as random variables, corresponding to the following scenario: An oil company suspects that four neighbouring reservoir blocks contain oil, gas and water, but is Table 3 Water–oil and gas–oil residual saturations, end-point permeabil- ities and Corey exponents to calculate relative permeability curves Water–oil Gas–oil Parameter Units Value Parameter Units Value Swc – 0.23 Sgc – 0.00 Sorw – 0.26 Sorg – 0.35 krwV – 0.30 krgV – 0.14 krowV – 0.74 krogV – 0.74 nw – 4.0 ng – 2.0 no – 2.0 no – 4.0 Fig line PD reservoir properties are assumed to equal those of neighbouring reservoirs. The company has a production platform nearby which has a single slot and sufficient ullage available. The company wants to drill one horizontal well through all four . 5. PDF of the GOCs and OWCs with their means (dashed s), and the fixed depth of the horizontal section of the well. Both Fs have a standard deviation of 10 m. blocks, to maximize the chance of an economic development. For each run, the workflow management software assigned a value to the eight different contact levels, randomly picked from a normal distribution with a mean of � 2395 m for the gas–oil contact (GOC) and � 2456 m for the oil–water contact (OWC), and each with a standard deviation of 10 m (see Fig. 5). In the case that the OWC ended up above the GOC, the OWC was interpreted as a gas–water contact. The workflow manager also controlled grid refinement in the oil-containing gridblocks, such that the entire oil rim, including the fluid contacts was always com- pletely refined. 2.4. Production scenarios 2.4.1. Conventional completion A further role of the workflow management soft- ware was to control the sequence of events during simulation of each of the two production scenarios (conventional and smart). A conventional scenario consisted of sequentially perforating and plugging R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172160 Fig. 6. Flow chart for conv entional production. each of the four zones working from the toe of the well towards the heel (see the flowchart in Fig. 6). Production from a layer continued until a critical value for the gas oil ratio (GOR) or water cut was exceeded or until lift die-out occurred. GOR and water cut were checked at predefined time intervals, which generally did not coincide with the variable simulation time step intervals. 2.4.2. Smart completion For the smart case, we assumed the availability of an on–off ICV for each oil-containing layer as well as three-phase flow measurement equipment. The ‘smart’ production strategy for non-commingled flow was to ‘cycle’ through the oil-containing layers (see Fig. 7 for a schematic overview). Starting from the oil-containing layer closest to the toe, the ICV in that layer was closed when the GOR (R) or the water cut ( fw) exceeded a critical value (Rcrit or fw,crit), or when lift die-out occurred. These critical parameters initially had a low value so that production switched to the next oil- containing layer as soon as gas or water broke through. After completion of a cycle, i.e. after oil had been produced from every oil-containing layer, the critical values were increased by a predefined amount, and the cycling process continued until the critical values led pr R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172 161 Fig. 7. Schematic overview of the control script for non-comming increased gradually every cycle until their maximum value has been reach oduction and smart completion. Critical values Rcrit and fw,crit are ed. 2.5. Simulation parameters Fig. 8. Production acceleration through frequent switching of on–off ICVs. R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172162 reached a maximum. The advantage of producing in a cyclic manner is twofold: production is accelerated, and the ultimate recovery is increased. The recovery increase occurs because layers are not permanently abandoned when a cut-off GOR or water cut has been reached, and because the water or gas cones are given the opportunity to retreat while the other layers are being produced. The acceleration occurs because peri- ods of decreasing production in between plateau pro- duction from the individual layers are being replaced by a single gradual, although somewhat wiggly, de- crease at the end of the field life (see Fig. 8). Switching producing intervals in the conventional case requires a workover, i.e. a plug needs to be installed and the well needs to be re-perforated. The measurement time interval was chosen much shorter for the smart case than for the conventional case to allow for the lead time required for the workovers. Table 5 Simulation parameters Property Units Conventional Smart Depth GOC (all layers) m 2395 2395 Depth OWC (all layers) m 2456 2456 Maximum liquid rate m3/day 2000 2000 Minimum THP bar 15 15 STOIIP 106 m3 2.572 2.572 GIIP 109 m3 0.706 0.706 Critical GOR (step 1) m3/m3 – 1000 Critical water cut (step 1) m3/m3 – 0.2 GOR increment m3/m3 – 1000 Water cut increment m3/m3 – 0.2 Maximum GOR m3/m3 4000 4000 Maximum water cut m3/m3 0.9 0.9 Measurement time interval month 3.0 0.33 Table 5 lists the most important parameter values and constraints used in the reservoir simulator, and the resulting stock tank oil initially in place (STOIIP) and gas initially in place (GIIP). All parameters, except for the contact levels, were kept constant for all runs. Two operating constraints were used: a maximum (target) liquid rate and a minimum allowed tubing head pressure (THP). The liquid rate was maintained by gradually reducing the THP until it reached its min- imum allowed value. The increments for Rcrit and fw,crit were chosen such that during smart production four cycles through all the layers occurred. To com- pute the incremental NPV of the conventional and smart completions we used the economic parameters listed in Table 6. Table 6 Economic parameters used to calculate the incremental NPV Parameter Units Amount Oil price $/m3 75.5 Oil processing costs $/m3 1 Water processing costs $/m3 0.15 Gas processing costs $/m3 0.035 Workover costs for a conventional completion $ 700,000 Costs of one on–off ICV $ 150,000 Costs of one ICV control unit $ 100,000 Additional completion time to install ICVs days 7 Rig rate $/day 100,000 Discount rate % 7 3. Numerical simulation results 3.1. Base case A base case was defined as the scenario in which all eight fluid contacts are at the mean of their assigned PDFs. Fig. 9 shows the simulation results for the base case for both scenarios. As was to be expected, the plot for the oil production resembles Fig. 8. Production for the conventional scenario lasted about 6.5 months longer than for the smart scenario. This is a result of the different size in measurement time interval: the smart well is shut-in quickly after exceeding the critical value, whereas for the conven- tional well this usually takes much longer. The GOR and water cut plots reveal that switching was triggered by reaching the critical value for the water cut, not the GOR. Table 7 displays the cumulative production ) for t R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172 163 Fig. 9. Base case results. Oil rate ( qo,sc), GOR (R) and water cut ( fw and OWC values. he conventional and the smart production scenarios with fixed GOC results for both runs. The smart production scenario looks very promising. There is a considerable increase in cumulative oil production and a decrease in cumu- lative water production. We used the parameters from Table 6 to compute the incremental NPV of the two base case options, resulting in a positive value of US$6.08 million. Clearly, the smart production sce- nario is the better option for the base case. lx¯ ¼ l and rx¯ ¼ r= ffiffiffi n p ; ð2Þ where the term r= ffiffiffi n p is known as the standard error of the sample mean. We use the random variable x to describe the population of sample means, which can be normalized according to z ¼ x� lx¯ rx¯ ¼ x� l r= ffiffiffi n p ; ð3Þ Under the assumption that the sample means are R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172164 3.2. Monte Carlo simulation 3.2.1. Statistical analysis Tables 8 and 9 and Figs. 10–12 summarize the results of 500 Monte Carlo simulations for the con- ventional and the smart scenarios in terms of the cumulative oil, water and gas production Np, Wp and Gp. The simulations were performed with a standard deviation of 10 m for the depth of each of the eight fluid contacts. We are primarily interested in the difference between the means of the distributions of the cumulative production variables for the two sce- narios. Our null hypothesis for each production var- iable is that there is no difference between the means for the two scenarios, but obviously we hope to find enough statistical evidence to reject these hypotheses. In our statistical analysis we can make use of the fact that our data are paired: each reservoir realisation was used to simulate both the conventional and the smart production scenario. In comparing the differences between paired variables, the effect of ‘‘between- subject’’ variability is to a large extent removed and we are left with the ‘‘within-subject’’ variation which is just what we are interested in (Altman, 1991). We are therefore considering the populations of differ- ences between the conventional and the smart results for each of the cumulative production variables. In particular, we hope to find statistical evidence that mean of these populations is higher than zero (for Np) Table 7 Simulation results for base case scenario Property Units Conventional Smart Relative difference (%) Np 10 3 m3 836 974 14.0 Wp 10 3 m3 1398 1258 � 10.0 Gp 10 6 m3 875 875 0.0 6 V 10 $ 10.92 or lower than zero (for Wp and Gp). Testing a hypothesis about the mean of a population based on a randomly chosen sample is usually done with the aid of the ‘‘Student’’ t-test. For large sample sizes, as used in our study, testing can also be performed with the aid of the standard normal distribution. The mean and the standard deviation of our sample of n = 500 simulations are given by x¯ ¼ Xn i¼1 xi n ; s ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn i¼1 ðxi � x¯Þ2 n� 1 vuuut ; ð1Þ where xi=(xsmart)i� (xconv)i is the difference in any of the cumulative production variables (Np,Wp or Gp) for simulation i. We can now test the null-hypothesis that the population mean l equals zero through consider- ing the (theoretical) distribution of the sample means which could (in theory) be obtained by taking many samples of n simulations. It can be shown that the mean ls and the standard deviation rx¯ of the distribution of sample means are related to the population mean l and population standard deviation r according to Table 8 Statistics for the means of the differences in cumulative oil, water and gas production, and for the mean of the incremental NPV, excluding the effect of ICV reliability Property Units x¯ z* a s=ffiffiffi n p Lower limit Upper limit Np 10 3 m3 105 79.4 0.000 1.33 102 109 Wp 10 3 m3 � 193 43.4 0.000 4.44 � 204 � 181 Gp 10 6 m3 � 25.2 14.7 0.000 1.72 � 29.7 � 20.8 V 106 $ 10.79 128.5 0.000 0.084 10.57 11.00 A two-tailed test has been used. Variables z* and a are dimensionless. normally distributed, we can, for a given sample with or 50 R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172 165 parameters x¯ and s, determine the probability a that jz| exceeds a value z* defined as z* ¼ x¯� l r= ffiffiffi n p c x¯ s= ffiffiffi n p ; ð4Þ where we have set l = 0 in line with the null hypoth- esis, and where we have used the sample standard deviation s as an estimate for the unknown population standard deviation r. The probability a (also known as the level of significance) reflects the chance that we Fig. 10. Histogram showing the results for cumulative oil production f reject the null hypothesis based on a sample with a certain mean and standard deviation, whereas in reality the null-hypothesis is correct. We can find a from the standard normal distribution which is avail- able in, e.g. MS Excel. (Excel, 2003). As a result of the central limit theorem, the distribution of sample means always approaches a normal distribution for increasing sample sizes, even when the population (and therefore most of the samples) are not normally distributed. Our sample size of n = 500 can be con- sidered large in statistical terms, and therefore we may use the hypothesis test for means even if our sample would display a considerably non-normal distribution. Table 8 lists the values for z* and a for each of the cumulative production variables. The lower the value of a, the larger the probability that an observed beneficial effect of smart well technology in our sample is representative for the entire population. Typically a statistical result corresponding to a value of a below 0.05 is referred to as significant, and a result corresponding to a value below 0.01 as highly significant. Table 8 also displays the corresponding confidence limits which are given by x¯Fz1�a=2s= ffiffiffi n p ; ð5Þ where for a = 0.01, z1� a/2 = 2.58, and which have the following meaning: there is a probability of a, i.e. of 0.01, that the population mean of the differences is above the upper confidence limit or below the lower 0 simulations of the conventional and the smart production scenarios. limit. In other words, there is a 100� (1� a) = 99% chance that the population mean is within the con- fidence interval bounded by the limits. Because we hope to find values of the mean that are either much larger (for Np), or much smaller (for Wp and Gp) than zero, we hope to find that the entire confidence interval is either considerably above or considerably below zero. 3.2.2. Cumulative production Fig. 10 clearly shows that the PDF for the cumulative oil distribution has shifted to the right: the mean of the differences between the conventional and the smart runs is positive with a magnitude of 105� 103 m3 (661�103 bbl), which represents an increase of 12.4% with respect to the mean of the conventional case. From the calculated values a for a two-tailed test we can be highly confident that the mean of the cumulative oil production indeed shifts to the right and this is confirmed by the narrow 99% confidence interval with limits of 102� 103 and 109� 103 m3 (640� 103 and 683� 103 bbl) (see Table 8). The mean cumulative oil production of the conventional scenario was between 831�103 and 866� 103 m3 (5.23� 106 and 5.45� 106 bbl) with a 99% confidence interval (see Table 9). Fig. 11 depicts the change in cumulative water production: furthermore gas production is directly related to oil production, which increased. 3.2.3. Individual comparison The shifts in mean reported above are in some sense representative for the entire sample of 500 simulations. However, they do not yield any infor- mation on whether or not the relative changes in production are dependent on the location of the contact levels. Because the actual values assigned to the contact levels are the same for the conventional and smart scenario, it is possible to compare the outcome of the runs on an individual basis. In Figs. 13–15 the dots represent the individually paired results, and the dotted lines are linear regression lines forced to pass through the origin. Note that if there would be no difference between a conventional and a smart production result, the corresponding dot would Table 9 Statistics for the mean cumulative oil, water and gas production of the conventional scenario Property Units x¯conv sconv=ffiffiffi n p Lower limit Upper limit Np 10 3 m3 849 6.78 831 866 Wp 10 3 m3 1357 9.11 1334 1381 Gp 10 6 m3 847 3.13 839 855 A two-tailed test has been used. R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172166 the mean for the smart runs is 14.2% lower than the mean of the conventional runs. The statistical signif- icance of this effect is confirmed by the corresponding narrow confidence intervals and low value of a. The shift in mean of the cumulative gas production figures shows a small change of minus 3.0% (see Fig. 12). The effect of the smart scenario on minimising gas production is not as large as on water production. This is because in most simula- tions the water production, and not the gas produc- tion triggered the switching of layers, while Fig. 11. Histogram showing the results for cumulative water production scenarios. be on the solid diagonal. The results in Fig. 13 show a strong correlation. The earlier reported increase in cumulative oil production for the individual runs of 12.4% is reflected in the slope of the regression line. The relative increase in production resulting from the smart completion is apparently not strongly dependent on the location of the contact levels. Fig. 14 confirms the results for water production reported above. Al- though the correlation is weaker than for oil, a clear trend can still be observed. In no single case is the water production of the smart scenario higher than that for 500 simulations of the conventional and the smart production of the conventional scenario. Also for gas, the ob- served trend is in line with the results reported earlier Table 6. The resulting PDF and cumulative distribution function have been displayed in Fig. 16. Based on the Fig. 12. Histogram showing the results for cumulative gas production for 500 simulations of the conventional and the smart production scenarios. R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172 167 (see Fig. 15). 3.2.4. Economics We performed an incremental NPV analysis for all paired results using the economic parameters from Fig. 13. Individual comparison of conventional and s sample results we found that increased cumulative oil production was by far the most influential factor contributing to the incremental NPV, on average 88%. The remaining increase in value resulted from decreased gas production (6%) and reduced interven- mart performance for cumulative oil production. Fig. 14. Individual comparison of conventional and smart performance for cumulative water production, non-commingled production. R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172168 tion costs (6%). Due to the relatively low water processing costs the contribution of reduced water production to the incremental NPV was negligible. Some extreme incremental NPV values from the data set were left out of Fig. 16 for plotting purposes. The Fig. 15. Individual comparison of conventional and sm sample mean of the incremental NPV is US$10.79 million, and the lower and upper 99% confidence limits for the population mean are US$10.57 million and US$11.00 million, respectively. This can be regarded as very strong evidence that our proposition art performance for cumulative gas production. in Section 1.2 (‘‘Smart well technology results in an increase of the incremental NPV’’) is correct, at least tal N R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172 169 as long as we do not take ICV failure into account. Also from the data for z and a in Table 8 we conclude that, for perfect ICVs, the beneficial effect of smart wells on the incremental NPV is statistically highly significant. Fig. 16. Incremen 4. Equipment reliability 4.1. Introduction Much of the reluctance against installing smart well technology results from concerns about equip- ment reliability. To assess the effect of valve reliability on our results we repeated the Monte Carlo analysis with an infant mortality probability for the ICVs of 5%. In other words, we assumed that at the start of a simulation each ICV had a 5% chance of not opening, resulting in lost production from the entire layer. It is noted that this is a very pessimistic scenario, because in real life most likely a workover would be per- formed to re-open the ICV, or at least to perforate the corresponding section. Another failure mechanism is one where an ICV fails to close. If commingled production is not acceptable this would lead to a situation where the well is only produced from the zone with the failed valve until lift die-out occurs. In practice, either the well would have to be worked- over, or commingled production would have to be accepted. We did not address the failure-to-close mechanism in our study. 4.2. Set up of simulations Table 10 shows all possible failure scenarios, i.e. all possible combinations of ICV failure, and their PV distribution. respective probability of occurrence. The probability of a scenario is the product of the individual proba- bilities. Multiplying each scenario probability with the original number of simulations (500), we obtain the number of simulations in which we may expect each scenario to occur. This prediction of scenario occur- rences makes it possible to repeat a Monte Carlo analysis including ICV failure with only a limited number of runs, because the data set for a zero failure probability is already available. In the majority of the runs (407), no failure is expected to occur and these runs therefore do not need to be repeated. In approx- imately 86 runs (21.43, four times, indicated in bold in Table 10) a scenario is expected in which one ICV fails. Therefore, runs 1 to 86 of the original data set were repeated. In runs 1 to 21 failure scenario (0,0,0,1) was enforced, in runs 22 to 42 failure scenario (0,0,1,0), in runs 43 to 64 scenario (0,1,0,0) and in runs 65 to 86 scenario (1,0,0,0) (note that any other combination of 86 runs could have been cho- Table 10 Infant mortality failure scenarios and probabilities Scenario Individual probabilities Combined Expected A B C D A B C D probability no. of runs 0 0 0 0 0.95 0.95 0.95 0.95 0.8145 407.3 0 0 0 1 0.95 0.95 0.95 0.05 0.0429 21.43 0 0 1 0 0.95 0.95 0.05 0.95 0.0429 21.43 0 0 1 1 0.95 0.95 0.05 0.05 0.0023 1.128 0 1 0 0 0.95 0.05 0.95 0.95 0.0429 21.43 0 1 0 1 0.95 0.05 0.95 0.05 0.0023 1.128 ns ind io. R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172170 sen). The same strategy was used to simulate the expected seven runs with two valves failing (six times 1.128, indicated in italics in Table 10), by repeating runs 87 to 93 with the various two-valve failure scenarios. The failure scenarios in which three or 0 1 1 0 0.95 0.05 0 1 1 1 0.95 0.05 1 0 0 0 0.05 0.95 1 0 0 1 0.05 0.95 1 0 1 0 0.05 0.95 1 0 1 1 0.05 0.95 1 1 0 0 0.05 0.05 1 1 0 1 0.05 0.05 1 1 1 0 0.05 0.05 1 1 1 1 0.05 0.05 Failure is indicated by 1, no failure by 0. The expected number of ru the runs indicated in italics correspond to a two-valve failure scenar more ICVs fail have a very low probability and are expected to occur only in about 0.24 runs (four times, 0.059 plus one time 0.003). Therefore they were not simulated. The results of the 93 repeated runs were then combined with the original data set for smart production, leaving out the first 93 original results. 4.3. Simulation results Table 11 displays the results for the 500 Monte Carlo simulations including the effects of ICV fail- Table 11 Statistics for the means of the differences in cumulative oil, water and gas effect of ICV reliability Property Units x¯ z* Np 10 3 m3 51.5 8.2 Wp 10 3 m3 � 247 31.2 Gp 10 6 m3 � 66.1 12.2 V 106 $ 8.43 29.8 A two-tailed test has been used. Variables z* and a are dimensionless. ure. The results for the conventional runs are iden- tical to those in Table 8. Most importantly, the sample mean of the differences in cumulative oil production between the two production scenarios is still 6.1% higher compared to the mean for the 0.05 0.95 0.0023 1.128 0.05 0.05 0.0001 0.059 0.95 0.95 0.0429 21.43 0.95 0.05 0.0023 1.128 0.05 0.95 0.0023 1.128 0.05 0.05 0.0001 0.059 0.95 0.95 0.0023 1.128 0.95 0.05 0.0001 0.059 0.05 0.95 0.0001 0.059 0.05 0.05 0.0000 0.003 icated in boldface correspond to a one-valve failure scenario, while conventional production scenario. The 99% confi- dence interval for the mean of the differences be- tween the conventional and the smart scenarios is now much wider, but still entirely in the positive range, with limits given by 35.3 � 103 and 67.7� 103 m3 (222� 103 and 426� 103 bbl). As indicated in Table 11, also the means of the differ- ences in water and gas production still have the desired tendency, and even show reductions larger than those from the simulations without valve failure in Table 8. The reason for this increased reduction is production, and for the mean of the incremental NPV, including the a s= ffiffiffi n p Lower limit Upper limit 0.000 6.28 35.3 67.7 0.000 7.94 � 267 � 227 0.000 5.41 � 80.0 � 52.1 0.000 0.283 7.70 9.15 stribu R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172 171 probably that losing a layer through ICV failure automatically results in a lower cumulative gas and water production for the well. The incremental NPV has been displayed in Fig. 17. Although the distri- bution is strongly skewed to the left, the sample mean is positive with a value of US$8.43 million, and with 99% confidence limits for the population mean of US$7.70 million and US$9.15 million. Increased cumulative oil production was still the most influential factor contributing to the incremental NPV, on average 70%, followed by decreased gas Fig. 17. Incremental NPV di production (22%) and reduced intervention costs (8%). Although the increase in oil production was reduced to about half of the value for perfect valves, the NPV was reduced much less, mainly because of a larger effect of the decrease in gas production. Apparently, even for the pessimistic valve failure scenario the smart well technology still provides considerable value. 5. Conclusions � For the cases considered in this study, the increase in NPV resulting from the application of a smart well was statistically highly significant. For these cases the proposition in the Introduction (‘‘Smart well technology results in an increase of the incremental NPV’’) is therefore almost certainly correct. � Increased cumulative oil production was by far the most influential factor contributing to the incre- mental NPV. The remaining increase in value resulted from decreased gas production and reduced intervention costs. Due to the relatively low water processing costs, the contribution of reduced water production to the incremental NPV was negligible. � Probabilistic analysis of reservoir drainage with stochastically varying reservoir properties is a powerful, although time-consuming, means to assess the value of smart wells. tion including valve failure. � Probabilistic value assessment should preferably be based on paired simulations, such that each simulation is performed for both the conventional and the smart case, to reduce the effects of between-subject variability in the populations. Acknowledgements The authors would like to thank Gerard Joosten, formerly with Shell International Exploration and Production (SIEP), for his inspiration and for the initial probabilistic results which formed the start- ing point of this study. They also would like to thank Roelof Daling of SIEP for his help in developing the reservoir model and the scenario manager, and Maartje Hooning of the Netherlands Cancer Institute for her assistance with the statistical analysis. Appendix A. Nomenclature Glossary CGR condensate–gas ratio FVF formation volume factor 81107 presented at the Latin American and Caribbean Petroleum intelligent well application. Paper SPE 82018 presented at the Hydrocarbon Economics and Evaluation Symposium, Dallas, R. van der Poel, J.D. Jansen / Journal of Petroleum Science and Engineering 44 (2004) 155–172172 Physical variables fw water cut k permeability kV end point permeability n Corey exponent t time Gp cumulative gas production R GOR (production figure) Rp producing GOR (fluid property) Np cumulative oil production V incremental NPV Wp cumulative water production S saturation x, y, z coordinates / porosity Statistical variables i counter n sample size s sample standard deviation x random variable x¯ sample mean z normalized random variable z* threshold value a probability that | z|>z*, also known as level of significance l population mean r population standard deviation Subscripts c connate calc calculated conv conventional production scenario crit critical g gas h horizontal max maximum min minimum o oil p produced r residual smart smart production scenario v vertical w water 5–8 April. Jalali, Y., Bussear, T., Sharma, S., 1998. Intelligent completion sys- tems—the reservoir rationale. Paper SPE 50587 presented at the European Petroleum Conference, The Hague, 20–22 October. Sharma, A.K., Chorn, L.G., Han, J., Rajagopolan, S., 2002. Quan- tifying value creation from intelligent completion technology implementation. Paper SPE 78277 presented at the European Petroleum Conference, Aberdeen, 29–31 October. Yeten, B., Brouwer, D.R., Durlofsky, L.J., Aziz, K., 2003. Decision analysis under uncertainty for smart well deployment. Journal of Petroleum Science and Engineering, 44, 175–191. Engineering Conference, Port-of-Spain Trinidad, 27–30 April. Han, J.T., 2003. There is value in operational flexibility: an GIIP gas initially in place GOC gas–oil contact GOR gas–oil ratio ICV inflow control valve NPV net present value (cumulative discounted cash flow) OWC oil–water contact PDF probability density function STOIIP stock tank oil initially in place THP tubing head pressure References Akram, N., Hicking, S., Blythe, P., Kavanagh, P., Reijnen, P., Mathieson, D., 2001. Intelligent well technology in mature assets. Paper SPE 71822 presented at the Offshore Europe Con- ference, Aberdeen, 4–7 September. Algeroy, J., Morris, A.J., Stracke, M., Auzerais, F., Bryant, I., Raghuraman, B., Rathnasingham, R., Davies, J., Gai, H., Johan- nessen, O., Malde, O., Toekje, J., Newberry, P., 1999. Controlling reservoirs from a far. Oilfield Review, Autumn, 18–29. Altman, D.G., 1991. Practical Statistics for Medical Research. Chapman & Hall/CRC, Boca Raton. Erlandsen, S.M., 2000. Production experience from smart wells in the Oseberg field. Paper SPE 62953 presented at the Annual Technical Conference and Exhibition, Dallas, 1–4 October. Excel, 2003. http://www.microsoft.com/office/excel. Glandt, C.A., 2003. Reservoir aspects of smart wells. Paper SPE Probabilistic analysis of the value of a smart well for sequential production of a stacked reservoir Introduction Influence of smart wells on uncertainty Objective and approach Numerical model Introduction Reservoir model Geometry and grid Reservoir and fluid properties Well model Uncertainty model Production scenarios Conventional completion Smart completion Simulation parameters Numerical simulation results Base case Monte Carlo simulation Statistical analysis Cumulative production Individual comparison Economics Equipment reliability Introduction Set up of simulations Simulation results Conclusions Acknowledgements Nomenclature References


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