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A practical approach for optimization of infill well placement in tight gas reservoirs
Journal of Natural Gas Science and Engineering 1 (2009) 165–176
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Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
A practical approach for optimization of infill well placement in tight gas reservoirs Yueming Cheng a, *, Duane A. McVay b, W. John Lee b a b
Department of Petroleum & Natural Gas Engineering, West Virginia University, Morgantown, WV 26506-6070, USA Department of Petroleum Engineering, Texas A&M University, College Station, TX 77843-3116, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 August 2009 Accepted 14 October 2009 Available online 28 November 2009
Despite their low production rates, tight gas wells contribute significantly to the Nation’s energy supply. Because permeabilities in tight reservoirs can be as low as fractions of a millidarcy, or even in the microdarcy range, drainage areas are small and many more wells are needed to drain tight gas fields than conventional gas fields. Infill drilling has been the most common and effective means to revitalize tight gas fields, by adding new reserves and accelerating recovery. Given the marginal nature of tight gas fields, optimization of infill well placement is extremely important to ensure economic viability of infill drilling programs. However, optimal placement of infill wells in tight gas fields is challenging. First, the reservoirs are usually quite complex and reservoir characteristics are often not well understood, even though most of these fields are mature. Second, data are usually scarce. It is not uncommon for only production data to be available in a marginal, tight gas field. Third, these fields often contain a large number of existing wells, which can require the evaluation of hundreds of potential infill drilling candidates. Finally, interference between wells affects placement of infill drilling wells and must be considered in the evaluation. Given the marginal nature of these gas fields, a conventional evaluation approach, such as detailed reservoir characterization and simulation, is usually prohibitively time-consuming and costly. Thus, a rapid and cost-effective approach to optimal infill drilling design that adequately addresses these issues would be quite valuable to operators. In this paper, we present a systematic methodology for efficient design of an infill drilling scheme for marginal gas reservoirs. The approach consists of two major components. The first is a sequential inversion algorithm for rapid history matching. The algorithm is conditional to the correlation between permeability and porosity, if any. The inversion provides not only the spatial distribution of both permeability and pore volume, but also the spatial distribution of remaining gas in place. The second component of the approach is a successive selection strategy for infill candidate locations. The method fully addresses well interference between existing and infill wells, as well as interference between infill wells. It is rapid and cost effective. Synthetic and field examples are provided to demonstrate the applicability and power of the method. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Tight gas reservoir Optimal infill well placement Reservoir characterization Inverse modeling Automatic history matching Production forecast
1. Introduction Redevelopment of marginal gas fields has been in rapid expansion with the increase in demand and gas price. Onshore natural gas production from marginal gas wells increased appreciably in the past few years, accounting for about 11% of the U.S. onshore natural gas production in 2003 (Duda et al., 2005). Infill drilling is one of the most common and effective means to accelerate field development, alleviate decline of gas production, and add reserves in such fields. It
* Corresponding author. Tel.: þ1 304 293 3973. E-mail address: [email protected] (Y. Cheng). 1875-5100/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jngse.2009.10.004
has been one of the most important activities for development of tight gas reservoirs in recent years. For example, in East Texas, active downspacing to tap tight-gas zones has dominated production growth in this basin since 2000 (Clouser and Wagman, 2006). Tightgas sands produced about 1.2 billion cubic feet (Bcf) a day in 2005, representing an average annual 12.5% increase over the past five years. As Clouser and Wagman (2006) summarized in their report, ‘‘high natural gas prices and advanced technologies, particularly fracturing techniques, have spurred drilling activity and turned a once-marginal economic venture into a lucrative pursuit.’’ The decisions of where to place infill wells and how many to place are critical to the economics of an infill drilling program. Before implementing any program to increase well density, the
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potential of infill drilling must be reliably assessed to justify such infill activities both technically and economically, especially for marginal oil and gas fields. Without reliable evaluation of infill potential, some unprofitable infill campaigns may be initiated while other promising infill campaigns may be terminated prematurely due to disappointing early results (Cheng et al., 2008). It is well realized that design of an infill drilling program is a challenging task and can be very time consuming. Because of the complexity and variability of marginal gas reservoirs, an integrated reservoir study, including detailed geological, geophysical, petrophysical, reservoir engineering and reservoir simulation studies, is the most accurate method for evaluating infill drilling potential. Unfortunately, such integrated studies cannot always be justified due to scarcity of data and marginal economics. An important requirement in the reservoir simulation part of an integrated study is matching historical production performance. It can be very challenging and time consuming to achieve a satisfactory history match in a field with hundreds or thousands of wells in a traditional simulation study, since the initial geological model is often quite different than a reservoir model capable of matching the historical production performance of wells and fields. On the other hand, determining infill well locations can also be a tedious task. To determine optimal well locations, the influences of reservoir heterogeneity (spatial variations of reservoir properties), well interference (between infill wells and existing wells, and between infill wells), and available reservoir energy (pressure) must be comprehensively considered. With a manual trial and error process, as is commonly used in traditional simulation studies, the determined well placements may not be optimal. In recent years, the issue of optimal well placement has been followed with much interest. Cottini-Loureiro and Araujo (2005) proposed using a quality map to identify infill areas with maximum field production. In their study, ‘‘quality’’ is a measure of the expected hydrocarbon production at a well location when no other wells exist in the reservoir. This map is generated by running a reservoir simulation model multiple times with vertical wells placed in selected grid cells, based on a hydrocarbon saturation map, and then using an interpolation method such as kriging to cover all cells. Their method was applied to new well selection for
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the Maureen field. The authors could not consider potential interference between infill wells in the process of selecting the wells, but they checked for interference after these wells were placed. Santellani et al. (1998) used an external optimization code coupled with a simulator to implement an automatic selection of optimal well locations. They first screened grid blocks based on given constraints for petrophysical properties (such as fluid saturation) and potential production performance to determine maximum well count with all possible grid cells (one well per cell). Then they simulated the reservoir with the maximum well count. At the end of the forecast, the wells were ranked according to a fitness function in terms of ultimate well recoveries or the well production rates. The worst performing wells were eliminated and the number of wells was recounted for a new run. This process was repeated until the desired number of wells was reached. The authors did not address whether the final number of wells reached was optimum. Cipolla and Mayerhofer (1996) studied the effectiveness of uniform infill drilling with different well spacings (from 160 acres to 80 acres to 40 acres) for reserve growth in a layered tight gas reservoir. Narayanasamy et al. (2006) discussed current well placement methods in some detail. Although current methods in the literature for determining optimal well locations differ, they all presume the existence of a detailed and accurate reservoir description. However, in marginal gas fields, this is not always the case. A detailed reservoir description is often unavailable because a complete reservoir study is not economically justifiable. Even when detailed geological modeling is possible, the model may contain large uncertainties (McCain et al., 1993; Lee and Hopkins, 1989). As Lee and Hopkins (1989) stated, for tight gas reservoirs, many standard formation evaluation techniques do not provide adequate results. For example, standard log-based correlations for permeability or other productivity indicators often fail. A rapid, approximate reservoir description for assessment of infill drilling potential in marginal gas reservoirs would clearly be a useful reservoir management tool. Cheng et al. (2008) developed a new inverse modeling algorithm to generate an approximate reservoir description from production data. This new algorithm provides a rapid, cost-effective and reliable assessment of infill potential. It employs a sequential inversion of both permeability and pore volume distributions through integration of production data. With this algorithm, they can obtain not only an estimation of the large-scale permeability distribution but also an estimation of the pore volume distribution, starting with estimated average reservoir properties (average net thickness, porosity, gas saturation
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A sound reservoir description is the foundation of reasonable and reliable reservoir engineering analyses. In this section, a sequential inversion algorithm conditional to the correlation between permeability and porosity is presented to investigate the improvement in reservoir description. Determination of optimal infill well locations to maximize production of gas is an essential task in marginal gas field development. In this section, we present an approach for determining optimal infill drill locations and also address several practical issues associated with infill drilling.
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and permeability) or with a prior geological model, if such a model is available. The notable features of this algorithm are (1) rapid and cost-effective automatic history matching able to handle large numbers of wells (hundreds to thousands of wells); (2) reliable reservoir characterization of large-scale heterogeneity for both permeability and pore volume; and (3) minimal data requirements, with only dynamic data and average reservoir properties required. In this paper, we further improve reservoir characterization by conditioning the sequential inversion algorithm to the correlation between permeability and porosity, if any. We then develop a practical well placement approach to automatically determine optimal infill candidate locations. The approach fully addresses well interference effects, including the interference between existing and infill wells, and the interference between new infill wells. It can deliver solutions to critical questions, such as how many wells can we or should we drill; where should we drill these wells; what production performance can we expect; what will the incremental gas recovery be; and what will the acceleration effect be? In this paper we first discuss the improvement in reservoir characterization by conditioning inversion to the correlation of permeability and porosity. We then present a successive well selection strategy for optimization of infill drilling locations. We validate these new developments with a synthetic example and, finally, demonstrate the applications in a field example.
2.1. Sequential inversion algorithm conditioned to the correlation between permeability and porosity The sequential inversion algorithm presented by Cheng et al. (2008) depends primarily on observed production data. For marginal gas fields, we find that reservoir pressure data are often limited and that wells often operate at capacity production with line pressures that do not vary significantly with time. Thus, in our inversion, we do not constrain wells at constant rate production and match on pressures, as is usually done. Instead, we constrain wells at constant flowing bottom hole pressure and match on flow rate (Cheng et al., 2008; Gao and McVay, 2004). Therefore, we match the observed well production rate to estimate reservoir property fields (permeability and pore volume). In addition to well production data, core analysis data are often available, which may help establish a correlation between permeability and porosity. Although the correlation is not high in many cases, it can still provide valuable information about the reservoir. We expect that, with more information available for inversion, the reservoir description will be improved further. In our inversion algorithm, we adjust permeability and a pore volume multiplier through integration of dynamic data during the inversion process. In this study, we add a constraint to the inversion to reflect an approximate relation between permeability and porosity. The procedure is similar to that in previous work (Cheng et al., 2008). The slight difference is that we calculate porosity from the permeability-porosity correlation after the permeability field is calibrated, and then use the updated porosity field in the inversion of pore volume. This modification simply adds a permeabilityporosity correlation in the inverse modeling process, which does not increase computation cost significantly. Our new method is still
Fig. 4. Permeability distributions for synthetic case.
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Fig. 5. Conditioned vs. reference 4*h distributions for synthetic case.
cost-effective and rapid in determining permeability and pore volume distributions. For clarity, we summarize the procedure. Run the forward model and calculate sensitivity coefficients of production rate response with respect to permeability using the generalized pulse-spectrum technique (GPST) (Tang and Chen, 1989). Estimate the change in permeability required to honor the production data using inverse modeling, and update the permeability field. Calculate porosity based on the permeability-porosity correlation using the calibrated permeability field. Replace the porosity values in each grid block of the reservoir model with the new ones. Run the forward model with the calibrated permeability and updated porosity fields and calculate sensitivity coefficients of production response with respect to pore volume multiplier using the GPST. Estimate the change in pore volume required to honor the production data using inverse modeling, and update the pore volume field correspondingly.
Iterate between inversion on permeability and pore volume until convergence is achieved. This approach can better capture heterogeneity in pore volume, while resulting in both permeability and pore volume fields that better reproduce actual well and field production performance. 2.2. Successive selection strategy for optimal infill well placement New well planning is based on available reservoir information or a reservoir model built from available information. We recognize that the information about the reservoir is always limited and the data used to construct a reservoir model always contain uncertainties; thus, no reservoir model can be a complete and deterministic representation of the true subsurface reservoir. Clearly, the planned well locations are only as accurate as the reservoir model used to determine them. One should not expect that the determined optimal well placements exactly represent the true optimal well locations. However, we can reasonably assume that the estimated optimal well placements determined from available reservoir information are the best approximation to the true optimal well locations. In this work, our objective is to define a set of
Fig. 6. Unconditioned vs. reference 4*h distributions for synthetic case.
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optimal locations for vertical infill wells based on the best reservoir model that can be constructed or derived from available data. In particular, we address the interference issue for infill wells by developing a successive selection strategy. Cheng et al. (2008) presented a procedure for assessment of infill drilling potential by estimating the incremental field production for each of the potential infill well locations in the field. For convenience in later presentation, we describe the procedure here again:
In this study, we propose a successive selection strategy to determine a set of optimal well locations, fully taking well interference effects into account. As in previous work, incremental field production is the primary basis for this optimization, although we consider economics as well. We first use the procedure summarized above to determine the distribution of incremental field production due to the drilling of one infill well at all possible locations. We then apply an economic limit incremental field production to determine those locations that are economic. Assuming there is at least one economic location, we then determine the infill well location with the maximum incremental field production, Infill #1. Then, around this location, a region is defined that represents the potential influence area of this first selected well. This region is typically defined to be several times the well spacing to be sure to address all well interference effects. We then rerun the procedure only for grid cells within the influence region, considering Infill #1 to be an existing well. In the influence region, we consider only those cells that do not have existing wells and that result in an incremental field production greater than the economic limit, thus minimizing the number of runs to make. After running the procedure, we update the values of incremental field production for each cell in the influence region. As Infill #1 is in the group of existing wells, well interference can be fully considered for a new infill well inside the influence region. Because the region is selected so that Infill #1 has no influence outside the influence region, values of incremental production for infill well locations outside the influence region do not change. A new fieldwide distribution of incremental field production is obtained by updating the incremental field production values
1. Invert reservoir properties to establish a reservoir model conditioned to the production response. 2. Forecast base case production with existing wells. 3. Place a new well in the first grid block of the reservoir model and forecast the incremental field production (difference in cumulative production from base case) to be gained by a new well in this grid block. 4. Repeat Step 3 for each grid block in the system except those containing existing wells. A distribution is thus generated of the incremental field production attributable to one new well at all the possible grid locations in the reservoir. The authors pointed out that, since the reservoir description determined was approximate, this map can be used as an indicator for selection of potential infill drilling areas, but not necessarily to provide individual infill well locations. Although the interference of a single infill well with existing wells was addressed, identification of multiple infill well locations is not straightforward since possible interference of multiple infill wells with existing wells and between multiple new infill wells is not fully considered.
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within the influence region. The grid cell with the highest value in this new fieldwide distribution is the location for the second optimal infill well, Infill #2. Note that Infill #1 has been removed from the list of infill candidates and does not participate in selection henceforth. Similarly, a new region is evaluated, around Infill #2 this time. Another new fieldwide distribution of incremental field production is generated for selection of Infill #3. The procedure is repeated until the last economic infill well is found, thus establishing the optimal number of infill wells, or until a maximum budgeted number of infill wells is reached. Note that, instead of rerunning the entire field each cycle, only a small region is rerun for every optimal infill well determination. Thus, computation time is greatly reduced while an equivalent exhaustive search process is achieved. It should be noted that a successive procedure for selecting infill locations results in truly optimal well locations only in fields that are already densely drilled, where it is unlikely that more than one additional well will be required in any undrilled contiguous area. In sparsely drilled areas, it would be necessary to determine n locations simultaneously for the locations to be considered truly optimal. Considering that a simultaneous determination of many optimal locations is prohibitively expensive and that infill drilling
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Fig. 11. Optimal infill well placements for synthetic case.
will usually be done sequentially, a successive selection procedure is a reasonable approximation. It should be also noted that optimal infill well placement may have different meanings under different design considerations (Hazlett and Babu, 1989). In many cases, wells are planned to maximize well cumulative production or net present value (NPV). Sometimes, optimization of infill well productivity index is the main concern (Hazlett and Babu, 1989). In this study, we use net increase in field cumulative production due to addition of an infill well to select and rank infill well candidates. A minimum net increase in field cumulative production is determined based on the economic factors of infill drilling, such as drilling and completion cost, operating cost, natural gas price, tax rate, capital cost and environmental cost. Note that this minimum net production increase serves as a proxy of economic criteria since it dictates how many infill wells can be drilled, and the specific net field production increment per individual infill well is used to rank the selected infill wells.
Fig. 10. Maps of 10-year incremental field gas production for synthetic case.
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In this section, we present a synthetic gas field example with heterogeneous permeability and porosity distributions. This example is used to validate both our sequential inversion technique conditioned to the permeability-porosity correlation for improving reservoir characterization, and the successive selection strategy for optimal infill drilling design. For a synthetic example, the true reservoir property distributions are known. Therefore, we can compare the estimated reservoir property distributions with the true distributions and we can also compare the estimated optimal well locations with the optimal well locations determined from the true reservoir model.
3.1. Reservoir description improvement This synthetic example has 25 wells initially with a production history of 23 years. The simulation grid system is 31 31 1, shown in Fig. 1. The synthetic reservoir, called the reference model, has
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heterogeneous permeability and porosity fields. Porosity is distributed normally with a mean of 8.0%. The logarithm of permeability was correlated to porosity (as shown in Fig. 2), and the permeability field has a mean of 0.112 md. Other reservoir properties, such as net thickness and gas saturation, were assumed uniform. Thus, heterogeneity in pore volume reflects the heterogeneity of the porosity field. We initiated automatic history matching with uniform average values of reservoir properties, 0.112 md and 8.0%, respectively, for permeability and porosity. We used the true values of all other reservoir properties. Fig. 3 shows history matching and 10-year prediction results for field-wide cumulative production and daily rate by applying sequential inversion conditioned to the permeability-porosity correlation. The true production performance resulting from the reference model is also included in Fig. 3. The curves obtained from the inverse model virtually overlay those from the reference model for both history matching and prediction. This indicates that the inverse model is a good representation of the reference model. Fig. 4 compares the inverted permeability distribution to the permeability distribution in the reference model, while Fig. 5 makes the same comparison for the 4*h (product of porosity and net thickness) distribution determined by conditioning to the permeability-porosity correlation. As demonstrated in these figures, the inverted distributions of permeability and pore volume successfully capture the main features of the true property distributions on
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Fig. 16. Simulation grid system for field case.
a large scale. We do not expect to reproduce the distributions on a small scale because production is an integrated response. To examine the effectiveness of conditional sequential inversion, we also present the 4*h field without conditioning to the permeability-porosity correlation (Fig. 6). To isolate the effect of conditioning on the 4*h field, we intentionally used the same permeability inversion for both cases. We performed nine iterations for permeability inversion first, then used the correlation to update the porosity field from the calibrated permeability distribution for the conditional case, and did not use the correlation for the unconditioned case. Nine iterations for pore volume multiplier then followed. Thus, the inverted permeability field is identical for both cases while the inverted 4*h fields differ. Both inverted 4*h fields capture large-scale features, but the inverted 4*h field from the conditional inversion better captures the low pore-volume areas. Fig. 7 displays histograms of permeability distributions, showing that the inverted permeability field has a distribution similar to that of the reference field. Fig. 8 shows histograms of 4*h distributions. The histogram of 4*h from the unconditional inversion has a sharp peak at the value of 1.3, slightly larger than the mean of 1.2, indicating a relative uniform 4*h field. The distribution of 4*h from conditional inversion is closer to the reference
distribution, indicating that more heterogeneous features are being captured. Note that we obtain similar good history matches and predictions with unconditioned sequential inversion (a 0.85% relative error in cumulative production) and conditioned sequential inversion (a 0.54% relative error in cumulative production), as shown in Fig. 9, due to the lesser sensitivity of the production response to the low-pore volume regions. From the discussion above, we can see that reservoir characterization using the sequential inversion algorithm conditioned to the permeability-porosity correlation is effective and results in a more representative reservoir model.
3.2. Optimal infill drilling design Prediction of future production performance and evaluation of infill well potential can be performed based on the inverted permeability and pore volume distributions and the reservoir pressure distribution at the end of history. Since the inversion resolves large-scale reservoir property trends well, but not always fine-scale details, we would expect the method to accurately identify areas of the field with potential for infill drilling, but not necessarily to identify exact optimal locations of individual infill
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wells. Fig. 10 shows the infill drilling incremental field production maps for the conditioned sequential inverse model and the reference model. Infill potential was assessed for a ten-year period following the end of the history match. The number on the scale bar represents field incremental gas production per infill well over the ten-year period. The trends in field incremental gas production using the conditioned inverse model are quite consistent with those using the reference model. Given certain economic criteria, our method provides optimal infill drilling design. In this example, we assumed an economic limit of 20 MMSCF incremental field production per infill well, and selection of optimal infill well locations was performed based on this economic limit. Fig. 11 shows the optimal infill well locations identified by the conditional inverse model (pink squares) and the reference model (blue dots). In both cases, there were 34 wells that resulted in incremental field gas above the specified economic limit and were thus selected as optimal wells. Although the well locations from the two cases do not overlay, most pairs of wells from the two cases are in close proximity. Fig. 12 illustrates the effectiveness of these selected infill wells in field production increase for various cases. Case 1 is a base case with no infill wells, as shown by the grey line. Case 2 is a prediction with the true reservoir model with optimal infill well locations determined from the true model, as shown by the pink dashed line. Case 2 represents an ideal case. Case 3 is a prediction with the inverted reservoir model with optimal infill well locations determined from the inverted model, as shown by the blue line. The predictions from Case 3 are quite consistent with the ideal case, with a relative error of 1.89% for cumulative production in the forecast period. The difference is small because, even though the inverted reservoir description is not exact, optimal infill well locations have been determined relative to the inexact reservoir description. Case 4 is a prediction with the true reservoir model and with optimal infill well locations determined from the inverted model, as shown in green squares. Case 4
Fig. 20. Inverted permeability distribution for field case.
represents the production response that would be realized in the field by drilling infill wells that are suboptimal relative to the true reservoir description. The error in Case 4 is 8.89% relative to the ideal case (Case 2), which is quite acceptable. The horizontal dashed line in Fig. 12 indicates that, with the designed infill wells, the cumulative production from existing wells only can be obtained within a much shorter time period, indicating significant production acceleration as well as an increase in reserves. We compared Case 4, the expected production response from the optimal infill drilling design with 34 wells, and a uniformly spaced infill drilling scheme with 36 wells (Fig. 13). Differences in incremental field daily rate and cumulative production (relative to the base case without infill drilling) for the forecast period are shown in Fig. 14. The cumulative production increase, 24.7%, from the optimal infill drilling design is significantly higher than that from the uniform infill scheme, even though the uniform infill drilling scheme has two more infill wells for production. The average production increase per infill well is 32.05% higher for optimal infill drilling than for the uniform pattern. We also compared effectiveness of optimal infill drilling designs determined from conditioned (to the permeability-porosity correlation) and unconditioned inverse models. As in Case 4 above, the designs were run in the true reservoir model to generate the response to be realized in the field. Fig. 15 shows incremental daily rate and cumulative production due to infill drilling for these two cases. With the unconditioned inverse model, 37 optimal wells were selected under the given economic limit. As a result, the unconditioned inverse model yields 6.45% higher cumulative production overall but 1.80% lower average cumulative production per infill well than the conditioned inverse model at the end of forecast. Factoring in the cost of the 3 additional wells, it is clear that the conditioned inverse model yields a superior infill drilling design. 4. Application In this section, we apply our new methodology to the Garden Plains field, Alberta, Canada (Cheng et al., 2008). It has produced for
Fig. 22. Inverted 4*h distribution for field case.
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Fig. 23. Reservoir pressure following history matching, field case.
Fig. 25. Incremental field production for field case.
27 years since its first gas well was put on production in April 1979. Based on available field data, there are 772 wells producing mainly from the Second White Specks (SSPK) formation at the end of 2004. This is a full field study, covering about 492,000 acres, which was discretized using a 166*85*1 simulation grid with dimensions of 1232 ft*1232 ft for each grid block. Fig. 16 shows the 772 existing wells superimposed on the simulation grid system. We matched history using the sequential inversion algorithm, starting with estimated average values of permeability (0.1 md), porosity (11%), net thickness (12 ft), and gas saturation (35%). A permeability-porosity correlation was generated from available core data (Fig. 17) and used in conditioning the inversion. The initial pressure in this reservoir was estimated to be approximately 957 psi. The bottom hole flowing pressure was specified in the simulation to be 250 psi, based on experience with other nearby fields. History matching results are shown in Figs. 18 and 19 in terms of fieldwide cumulative production and daily rate, respectively. These figures demonstrate that history matching is quite good, with consistent trends between calculated production and actual production performance. The gas permeability distribution determined by sequential inversion is shown in Fig. 20. Since we used a constant-thickness model, the kh distribution has the same trends as the permeability distribution. Early performance of well production, in particular the best year of production, can be an indicator of permeability-thickness, kh (Voneiff and Cipolla, 1996; Guan et al., 2002). Fig. 21 shows a map of the best year of production for this field. Similar large-scale trends are observed in both Figs. 20 and 21, which provides some comfort in the reliability of the inverted permeability distribution. The inverted porositythickness product (obtained by multiplying the inverted pore volume multiplier times the product of porosity and thickness) is shown in Fig. 22. Similar trends are observed between kh (Fig. 20) and fh (Fig. 22), as expected. Fig. 23 shows the reservoir pressure distribution at the end of the history match period. As can be seen, central and northeastern areas show signs of pressure depletion,
whereas other areas remain near original reservoir pressure. Combining the pore volume distribution with the pressure distribution yields the distribution of remaining gas in place (Fig. 24). Using the inverted permeability and pore volume distributions and the reservoir pressure distribution at the end of history, we then forecast future production performance, evaluate infill well potential and identify an optimal set of infill well locations. Fig. 25 shows the infill drilling incremental field production map for a three-year period following the history match. The numbers on the scale bar represent field incremental gas production in MMSCF per infill well over the three-year period. The areas with highest infill potential are located in central and southwestern parts of the field, with relatively high permeability and pore volumes and moderate pressure. Note that other higher permeability and pore volume areas to the northeast do not have as much infill potential because of pressure depletion. We assumed an economic limit of 80 MMSCF for the three-year period. This means that the addition of a new infill well has to generate a net increase in field cumulative production of at least 80 MMSCF for this new well to be selected into the set of infill well locations. The economic limit value selected is arbitrary and does not necessarily represent the actual economic limit for this field. Fig. 26 presents the optimal well locations for infill drilling, which consists of 106 infill wells. The selected well placements are concentrated in the central and southwestern parts of the field, corresponding to the areas of high incremental production shown in Fig. 25. Note that each square block on Fig. 26 represents 2*2 simulation grid cells. In Fig. 27, we show three cumulative gas production curves: (1) total from existing wells plus the 106 infill wells, (2) from existing wells without infill drilling, and (3) from existing wells only while the 106 infill wells are producing from the reservoir. The 106 infill wells yield an incremental field gas production of 10,617 MMSCF over the three-year period, the difference between (1) and (2). The decrease in production from existing wells due to infill drilling, the difference between (2) and (3), is 290 MMSCF. This is only 2.7% of the incremental field production, indicating minimal interference of these new infill wells with the existing wells. Note that we used a three-year forecast period and a field incremental production economic limit of 80 MMSCF over the threeyear period to design the optimal infill drilling program. The design may change if different forecast and economic parameters are used. The infill assessment approach described in this paper is rapid and computationally efficient. For this field example, which involves more than 800 existing plus infill wells, the history matching took about 8 CPU hours and the automatic selection of optimal well locations took about 28 CPU hours using a PC with 1 Gbyte of memory and a speed of 3.2 GHz. Compared to conventional simulation with a trial-and-error process, which can take several man-months for a fieldwide reservoir study like this, our approach presents significant time and cost savings.
Fig. 24. Remaining gas in place for field case.
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Fig. 26. Optimal infill well placement from successive selection strategy for field case.
determined. Analysis of incremental gas recovery and production acceleration is also provided. 4. The approach was validated by a synthetic example in which large-scale reservoir property trends were accurately reproduced and infill well design was close to the true optimal design. Applicability of our approach was demonstrated in an actual producing field containing more than 800 existing and infill wells.
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5. Conclusions In this paper, we developed a systematic methodology for rapid and cost-effective design of an infill drilling program for tight gas reservoirs. The approach can be an approximate alternative to a full integrated reservoir study, and may be particularly useful in marginal gas reservoirs where reservoir data are very limited and/or a detailed reservoir study cannot be economically justified. From this study, the following conclusions can be drawn: 1. Heterogeneous distributions of permeability and pore volume can be obtained from dynamic data using the sequential inversion method presented. The distributions are conditioned to a permeability-porosity correlation, if such a correlation is available. 2. The well placement algorithm presented can automatically determine optimal infill well locations, while fully addressing well interference between existing and infill wells, as well as interference between infill wells. 3. Given predefined economic criteria, the number of viable infill wells is identified and the optimal locations of these wells are
Acknowledgment This paper was originally presented as SPE 104574 at the 2006 SPE Eastern Regional Meeting, held Oct. 11-13 in Canton, Ohio. References Cheng, Y., McVay, D.A., Wang, J., Ayers, W.B., June 2008. Simulation-Based Technology for Rapid Assessment of Redevelopment Potential in Marginal Gas Fields - Technology Advances and Validation in Garden Plains Field, Western Canada Sedimentary Basin. SPEREE 521. Cipolla, C.L., Mayerhofer, M., 1996. Infill Drilling & Reserve Growth Determination in Lenticular Tight Gas Sands, Paper SPE 36735 Presented at the 1996 SPE Annual Technical Conference and Exhibition, Denver, Colorado, 7–9 October. Clouser, G., Wagman, D., Mar 2006. East Texas Thrives. A Supplement to Oil and Gas Investor - Tight Gas 8. Cottini-Loureiro, A., Araujo, M., 2005. Optimized Well Location by Combination of Multiple Realization Approach and Quality Map Methods, Paper SPE 95413 Presented at the 2005 SPE Annual Technical Conference and Exhibition, Dallas, Texas, 9–12 October. Duda, J.R., et al., 2005. Projections of Marginal Wells and Their Contributions to Oil and Natural Gas Supplies, Paper SPE 98014 Presented at the 2005 SPE Eastern Regional Meeting, Morgantown, W.V., 14–16 September. Gao, H., McVay, D.A., 2004. Gas Infill Well Selection Using Rapid Inversion Methods. Paper SPE 90545 Presented at the 2004 Annual Technical Conference and Exhibition, Houston, TX, 26–29 September. Guan, L., et al., 2002. Evaluation of a Statistical Infill Candidate Selection Technique. Paper SPE 75718 Presented at the SPE Gas Technology Symposium, Calgary, Alberta, Canada, 30 April–2 May, 2002. Hazlett, R.D., Babu, D.K., Sept 1989. Optimal well placement in heterogeneous reservoirs through semianalytic modeling. SPE Journal 286. Lee, W.J., Hopkins, C.W., Nov 1989. Characterization of tight reservoirs. Journal of Petroleum Technology 956. McCain, W.D., et al., 1993. A Tight Gas Field Study: Carthage (Cotton Valley) Field. Paper SPE 26141 Presented at the 1993 SPE Gas Technology Symposium, Calgary, Alberta, Canada, 28–30 June. Narayanasamy, R., Davies, D.R., Somerville, J.M., 2006. Well Location Selection from a Static model and Multiple Realizations of a Geomodel Using Productivity-
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Potential Map Technique. Paper SPE 99877 Presented at the 2006 SPE Europec/ EAGE Annual Conference and Exhibition, Vienna, Austria, 12–15 June. Santellani, G., Hansen, A.B., Terring, T., 1998. Survival of the Fittest’ and Optimized Well Location Algorithm for Reservoir Simulation, Paper SPE 39754 Presented at the 1998 SPE Asia Pacific Conference, Kuala Lumpur, Malaysia, 23–24 March.
Tang, T.N., Chen, Y.M., 1989. Generalized pulse-spectrum technique for 2-D and 2phase history matching. Applied Numerical Mathematics 5, 529. Voneiff, G.W., Cipolla, C.L., 1996. A New Approach to Large-Scale Infill Evaluations Applied to the OZONA (Canyon) Gas Sands. Paper SPE 35203 Presented at the 1996 Permian Basin Oil & Gas Recovery Conference, Midland, TX, 27–29 March.
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
A practical approach for optimization of infill well placement in tight gas reservoirs Yueming Cheng a, *, Duane A. McVay b, W. John Lee b a b
Department of Petroleum & Natural Gas Engineering, West Virginia University, Morgantown, WV 26506-6070, USA Department of Petroleum Engineering, Texas A&M University, College Station, TX 77843-3116, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 August 2009 Accepted 14 October 2009 Available online 28 November 2009
Despite their low production rates, tight gas wells contribute significantly to the Nation’s energy supply. Because permeabilities in tight reservoirs can be as low as fractions of a millidarcy, or even in the microdarcy range, drainage areas are small and many more wells are needed to drain tight gas fields than conventional gas fields. Infill drilling has been the most common and effective means to revitalize tight gas fields, by adding new reserves and accelerating recovery. Given the marginal nature of tight gas fields, optimization of infill well placement is extremely important to ensure economic viability of infill drilling programs. However, optimal placement of infill wells in tight gas fields is challenging. First, the reservoirs are usually quite complex and reservoir characteristics are often not well understood, even though most of these fields are mature. Second, data are usually scarce. It is not uncommon for only production data to be available in a marginal, tight gas field. Third, these fields often contain a large number of existing wells, which can require the evaluation of hundreds of potential infill drilling candidates. Finally, interference between wells affects placement of infill drilling wells and must be considered in the evaluation. Given the marginal nature of these gas fields, a conventional evaluation approach, such as detailed reservoir characterization and simulation, is usually prohibitively time-consuming and costly. Thus, a rapid and cost-effective approach to optimal infill drilling design that adequately addresses these issues would be quite valuable to operators. In this paper, we present a systematic methodology for efficient design of an infill drilling scheme for marginal gas reservoirs. The approach consists of two major components. The first is a sequential inversion algorithm for rapid history matching. The algorithm is conditional to the correlation between permeability and porosity, if any. The inversion provides not only the spatial distribution of both permeability and pore volume, but also the spatial distribution of remaining gas in place. The second component of the approach is a successive selection strategy for infill candidate locations. The method fully addresses well interference between existing and infill wells, as well as interference between infill wells. It is rapid and cost effective. Synthetic and field examples are provided to demonstrate the applicability and power of the method. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Tight gas reservoir Optimal infill well placement Reservoir characterization Inverse modeling Automatic history matching Production forecast
1. Introduction Redevelopment of marginal gas fields has been in rapid expansion with the increase in demand and gas price. Onshore natural gas production from marginal gas wells increased appreciably in the past few years, accounting for about 11% of the U.S. onshore natural gas production in 2003 (Duda et al., 2005). Infill drilling is one of the most common and effective means to accelerate field development, alleviate decline of gas production, and add reserves in such fields. It
* Corresponding author. Tel.: þ1 304 293 3973. E-mail address: [email protected] (Y. Cheng). 1875-5100/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jngse.2009.10.004
has been one of the most important activities for development of tight gas reservoirs in recent years. For example, in East Texas, active downspacing to tap tight-gas zones has dominated production growth in this basin since 2000 (Clouser and Wagman, 2006). Tightgas sands produced about 1.2 billion cubic feet (Bcf) a day in 2005, representing an average annual 12.5% increase over the past five years. As Clouser and Wagman (2006) summarized in their report, ‘‘high natural gas prices and advanced technologies, particularly fracturing techniques, have spurred drilling activity and turned a once-marginal economic venture into a lucrative pursuit.’’ The decisions of where to place infill wells and how many to place are critical to the economics of an infill drilling program. Before implementing any program to increase well density, the
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potential of infill drilling must be reliably assessed to justify such infill activities both technically and economically, especially for marginal oil and gas fields. Without reliable evaluation of infill potential, some unprofitable infill campaigns may be initiated while other promising infill campaigns may be terminated prematurely due to disappointing early results (Cheng et al., 2008). It is well realized that design of an infill drilling program is a challenging task and can be very time consuming. Because of the complexity and variability of marginal gas reservoirs, an integrated reservoir study, including detailed geological, geophysical, petrophysical, reservoir engineering and reservoir simulation studies, is the most accurate method for evaluating infill drilling potential. Unfortunately, such integrated studies cannot always be justified due to scarcity of data and marginal economics. An important requirement in the reservoir simulation part of an integrated study is matching historical production performance. It can be very challenging and time consuming to achieve a satisfactory history match in a field with hundreds or thousands of wells in a traditional simulation study, since the initial geological model is often quite different than a reservoir model capable of matching the historical production performance of wells and fields. On the other hand, determining infill well locations can also be a tedious task. To determine optimal well locations, the influences of reservoir heterogeneity (spatial variations of reservoir properties), well interference (between infill wells and existing wells, and between infill wells), and available reservoir energy (pressure) must be comprehensively considered. With a manual trial and error process, as is commonly used in traditional simulation studies, the determined well placements may not be optimal. In recent years, the issue of optimal well placement has been followed with much interest. Cottini-Loureiro and Araujo (2005) proposed using a quality map to identify infill areas with maximum field production. In their study, ‘‘quality’’ is a measure of the expected hydrocarbon production at a well location when no other wells exist in the reservoir. This map is generated by running a reservoir simulation model multiple times with vertical wells placed in selected grid cells, based on a hydrocarbon saturation map, and then using an interpolation method such as kriging to cover all cells. Their method was applied to new well selection for
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the Maureen field. The authors could not consider potential interference between infill wells in the process of selecting the wells, but they checked for interference after these wells were placed. Santellani et al. (1998) used an external optimization code coupled with a simulator to implement an automatic selection of optimal well locations. They first screened grid blocks based on given constraints for petrophysical properties (such as fluid saturation) and potential production performance to determine maximum well count with all possible grid cells (one well per cell). Then they simulated the reservoir with the maximum well count. At the end of the forecast, the wells were ranked according to a fitness function in terms of ultimate well recoveries or the well production rates. The worst performing wells were eliminated and the number of wells was recounted for a new run. This process was repeated until the desired number of wells was reached. The authors did not address whether the final number of wells reached was optimum. Cipolla and Mayerhofer (1996) studied the effectiveness of uniform infill drilling with different well spacings (from 160 acres to 80 acres to 40 acres) for reserve growth in a layered tight gas reservoir. Narayanasamy et al. (2006) discussed current well placement methods in some detail. Although current methods in the literature for determining optimal well locations differ, they all presume the existence of a detailed and accurate reservoir description. However, in marginal gas fields, this is not always the case. A detailed reservoir description is often unavailable because a complete reservoir study is not economically justifiable. Even when detailed geological modeling is possible, the model may contain large uncertainties (McCain et al., 1993; Lee and Hopkins, 1989). As Lee and Hopkins (1989) stated, for tight gas reservoirs, many standard formation evaluation techniques do not provide adequate results. For example, standard log-based correlations for permeability or other productivity indicators often fail. A rapid, approximate reservoir description for assessment of infill drilling potential in marginal gas reservoirs would clearly be a useful reservoir management tool. Cheng et al. (2008) developed a new inverse modeling algorithm to generate an approximate reservoir description from production data. This new algorithm provides a rapid, cost-effective and reliable assessment of infill potential. It employs a sequential inversion of both permeability and pore volume distributions through integration of production data. With this algorithm, they can obtain not only an estimation of the large-scale permeability distribution but also an estimation of the pore volume distribution, starting with estimated average reservoir properties (average net thickness, porosity, gas saturation
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A sound reservoir description is the foundation of reasonable and reliable reservoir engineering analyses. In this section, a sequential inversion algorithm conditional to the correlation between permeability and porosity is presented to investigate the improvement in reservoir description. Determination of optimal infill well locations to maximize production of gas is an essential task in marginal gas field development. In this section, we present an approach for determining optimal infill drill locations and also address several practical issues associated with infill drilling.
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and permeability) or with a prior geological model, if such a model is available. The notable features of this algorithm are (1) rapid and cost-effective automatic history matching able to handle large numbers of wells (hundreds to thousands of wells); (2) reliable reservoir characterization of large-scale heterogeneity for both permeability and pore volume; and (3) minimal data requirements, with only dynamic data and average reservoir properties required. In this paper, we further improve reservoir characterization by conditioning the sequential inversion algorithm to the correlation between permeability and porosity, if any. We then develop a practical well placement approach to automatically determine optimal infill candidate locations. The approach fully addresses well interference effects, including the interference between existing and infill wells, and the interference between new infill wells. It can deliver solutions to critical questions, such as how many wells can we or should we drill; where should we drill these wells; what production performance can we expect; what will the incremental gas recovery be; and what will the acceleration effect be? In this paper we first discuss the improvement in reservoir characterization by conditioning inversion to the correlation of permeability and porosity. We then present a successive well selection strategy for optimization of infill drilling locations. We validate these new developments with a synthetic example and, finally, demonstrate the applications in a field example.
2.1. Sequential inversion algorithm conditioned to the correlation between permeability and porosity The sequential inversion algorithm presented by Cheng et al. (2008) depends primarily on observed production data. For marginal gas fields, we find that reservoir pressure data are often limited and that wells often operate at capacity production with line pressures that do not vary significantly with time. Thus, in our inversion, we do not constrain wells at constant rate production and match on pressures, as is usually done. Instead, we constrain wells at constant flowing bottom hole pressure and match on flow rate (Cheng et al., 2008; Gao and McVay, 2004). Therefore, we match the observed well production rate to estimate reservoir property fields (permeability and pore volume). In addition to well production data, core analysis data are often available, which may help establish a correlation between permeability and porosity. Although the correlation is not high in many cases, it can still provide valuable information about the reservoir. We expect that, with more information available for inversion, the reservoir description will be improved further. In our inversion algorithm, we adjust permeability and a pore volume multiplier through integration of dynamic data during the inversion process. In this study, we add a constraint to the inversion to reflect an approximate relation between permeability and porosity. The procedure is similar to that in previous work (Cheng et al., 2008). The slight difference is that we calculate porosity from the permeability-porosity correlation after the permeability field is calibrated, and then use the updated porosity field in the inversion of pore volume. This modification simply adds a permeabilityporosity correlation in the inverse modeling process, which does not increase computation cost significantly. Our new method is still
Fig. 4. Permeability distributions for synthetic case.
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Fig. 5. Conditioned vs. reference 4*h distributions for synthetic case.
cost-effective and rapid in determining permeability and pore volume distributions. For clarity, we summarize the procedure. Run the forward model and calculate sensitivity coefficients of production rate response with respect to permeability using the generalized pulse-spectrum technique (GPST) (Tang and Chen, 1989). Estimate the change in permeability required to honor the production data using inverse modeling, and update the permeability field. Calculate porosity based on the permeability-porosity correlation using the calibrated permeability field. Replace the porosity values in each grid block of the reservoir model with the new ones. Run the forward model with the calibrated permeability and updated porosity fields and calculate sensitivity coefficients of production response with respect to pore volume multiplier using the GPST. Estimate the change in pore volume required to honor the production data using inverse modeling, and update the pore volume field correspondingly.
Iterate between inversion on permeability and pore volume until convergence is achieved. This approach can better capture heterogeneity in pore volume, while resulting in both permeability and pore volume fields that better reproduce actual well and field production performance. 2.2. Successive selection strategy for optimal infill well placement New well planning is based on available reservoir information or a reservoir model built from available information. We recognize that the information about the reservoir is always limited and the data used to construct a reservoir model always contain uncertainties; thus, no reservoir model can be a complete and deterministic representation of the true subsurface reservoir. Clearly, the planned well locations are only as accurate as the reservoir model used to determine them. One should not expect that the determined optimal well placements exactly represent the true optimal well locations. However, we can reasonably assume that the estimated optimal well placements determined from available reservoir information are the best approximation to the true optimal well locations. In this work, our objective is to define a set of
Fig. 6. Unconditioned vs. reference 4*h distributions for synthetic case.
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optimal locations for vertical infill wells based on the best reservoir model that can be constructed or derived from available data. In particular, we address the interference issue for infill wells by developing a successive selection strategy. Cheng et al. (2008) presented a procedure for assessment of infill drilling potential by estimating the incremental field production for each of the potential infill well locations in the field. For convenience in later presentation, we describe the procedure here again:
In this study, we propose a successive selection strategy to determine a set of optimal well locations, fully taking well interference effects into account. As in previous work, incremental field production is the primary basis for this optimization, although we consider economics as well. We first use the procedure summarized above to determine the distribution of incremental field production due to the drilling of one infill well at all possible locations. We then apply an economic limit incremental field production to determine those locations that are economic. Assuming there is at least one economic location, we then determine the infill well location with the maximum incremental field production, Infill #1. Then, around this location, a region is defined that represents the potential influence area of this first selected well. This region is typically defined to be several times the well spacing to be sure to address all well interference effects. We then rerun the procedure only for grid cells within the influence region, considering Infill #1 to be an existing well. In the influence region, we consider only those cells that do not have existing wells and that result in an incremental field production greater than the economic limit, thus minimizing the number of runs to make. After running the procedure, we update the values of incremental field production for each cell in the influence region. As Infill #1 is in the group of existing wells, well interference can be fully considered for a new infill well inside the influence region. Because the region is selected so that Infill #1 has no influence outside the influence region, values of incremental production for infill well locations outside the influence region do not change. A new fieldwide distribution of incremental field production is obtained by updating the incremental field production values
1. Invert reservoir properties to establish a reservoir model conditioned to the production response. 2. Forecast base case production with existing wells. 3. Place a new well in the first grid block of the reservoir model and forecast the incremental field production (difference in cumulative production from base case) to be gained by a new well in this grid block. 4. Repeat Step 3 for each grid block in the system except those containing existing wells. A distribution is thus generated of the incremental field production attributable to one new well at all the possible grid locations in the reservoir. The authors pointed out that, since the reservoir description determined was approximate, this map can be used as an indicator for selection of potential infill drilling areas, but not necessarily to provide individual infill well locations. Although the interference of a single infill well with existing wells was addressed, identification of multiple infill well locations is not straightforward since possible interference of multiple infill wells with existing wells and between multiple new infill wells is not fully considered.
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within the influence region. The grid cell with the highest value in this new fieldwide distribution is the location for the second optimal infill well, Infill #2. Note that Infill #1 has been removed from the list of infill candidates and does not participate in selection henceforth. Similarly, a new region is evaluated, around Infill #2 this time. Another new fieldwide distribution of incremental field production is generated for selection of Infill #3. The procedure is repeated until the last economic infill well is found, thus establishing the optimal number of infill wells, or until a maximum budgeted number of infill wells is reached. Note that, instead of rerunning the entire field each cycle, only a small region is rerun for every optimal infill well determination. Thus, computation time is greatly reduced while an equivalent exhaustive search process is achieved. It should be noted that a successive procedure for selecting infill locations results in truly optimal well locations only in fields that are already densely drilled, where it is unlikely that more than one additional well will be required in any undrilled contiguous area. In sparsely drilled areas, it would be necessary to determine n locations simultaneously for the locations to be considered truly optimal. Considering that a simultaneous determination of many optimal locations is prohibitively expensive and that infill drilling
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Fig. 11. Optimal infill well placements for synthetic case.
will usually be done sequentially, a successive selection procedure is a reasonable approximation. It should be also noted that optimal infill well placement may have different meanings under different design considerations (Hazlett and Babu, 1989). In many cases, wells are planned to maximize well cumulative production or net present value (NPV). Sometimes, optimization of infill well productivity index is the main concern (Hazlett and Babu, 1989). In this study, we use net increase in field cumulative production due to addition of an infill well to select and rank infill well candidates. A minimum net increase in field cumulative production is determined based on the economic factors of infill drilling, such as drilling and completion cost, operating cost, natural gas price, tax rate, capital cost and environmental cost. Note that this minimum net production increase serves as a proxy of economic criteria since it dictates how many infill wells can be drilled, and the specific net field production increment per individual infill well is used to rank the selected infill wells.
Fig. 10. Maps of 10-year incremental field gas production for synthetic case.
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In this section, we present a synthetic gas field example with heterogeneous permeability and porosity distributions. This example is used to validate both our sequential inversion technique conditioned to the permeability-porosity correlation for improving reservoir characterization, and the successive selection strategy for optimal infill drilling design. For a synthetic example, the true reservoir property distributions are known. Therefore, we can compare the estimated reservoir property distributions with the true distributions and we can also compare the estimated optimal well locations with the optimal well locations determined from the true reservoir model.
3.1. Reservoir description improvement This synthetic example has 25 wells initially with a production history of 23 years. The simulation grid system is 31 31 1, shown in Fig. 1. The synthetic reservoir, called the reference model, has
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heterogeneous permeability and porosity fields. Porosity is distributed normally with a mean of 8.0%. The logarithm of permeability was correlated to porosity (as shown in Fig. 2), and the permeability field has a mean of 0.112 md. Other reservoir properties, such as net thickness and gas saturation, were assumed uniform. Thus, heterogeneity in pore volume reflects the heterogeneity of the porosity field. We initiated automatic history matching with uniform average values of reservoir properties, 0.112 md and 8.0%, respectively, for permeability and porosity. We used the true values of all other reservoir properties. Fig. 3 shows history matching and 10-year prediction results for field-wide cumulative production and daily rate by applying sequential inversion conditioned to the permeability-porosity correlation. The true production performance resulting from the reference model is also included in Fig. 3. The curves obtained from the inverse model virtually overlay those from the reference model for both history matching and prediction. This indicates that the inverse model is a good representation of the reference model. Fig. 4 compares the inverted permeability distribution to the permeability distribution in the reference model, while Fig. 5 makes the same comparison for the 4*h (product of porosity and net thickness) distribution determined by conditioning to the permeability-porosity correlation. As demonstrated in these figures, the inverted distributions of permeability and pore volume successfully capture the main features of the true property distributions on
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Fig. 16. Simulation grid system for field case.
a large scale. We do not expect to reproduce the distributions on a small scale because production is an integrated response. To examine the effectiveness of conditional sequential inversion, we also present the 4*h field without conditioning to the permeability-porosity correlation (Fig. 6). To isolate the effect of conditioning on the 4*h field, we intentionally used the same permeability inversion for both cases. We performed nine iterations for permeability inversion first, then used the correlation to update the porosity field from the calibrated permeability distribution for the conditional case, and did not use the correlation for the unconditioned case. Nine iterations for pore volume multiplier then followed. Thus, the inverted permeability field is identical for both cases while the inverted 4*h fields differ. Both inverted 4*h fields capture large-scale features, but the inverted 4*h field from the conditional inversion better captures the low pore-volume areas. Fig. 7 displays histograms of permeability distributions, showing that the inverted permeability field has a distribution similar to that of the reference field. Fig. 8 shows histograms of 4*h distributions. The histogram of 4*h from the unconditional inversion has a sharp peak at the value of 1.3, slightly larger than the mean of 1.2, indicating a relative uniform 4*h field. The distribution of 4*h from conditional inversion is closer to the reference
distribution, indicating that more heterogeneous features are being captured. Note that we obtain similar good history matches and predictions with unconditioned sequential inversion (a 0.85% relative error in cumulative production) and conditioned sequential inversion (a 0.54% relative error in cumulative production), as shown in Fig. 9, due to the lesser sensitivity of the production response to the low-pore volume regions. From the discussion above, we can see that reservoir characterization using the sequential inversion algorithm conditioned to the permeability-porosity correlation is effective and results in a more representative reservoir model.
3.2. Optimal infill drilling design Prediction of future production performance and evaluation of infill well potential can be performed based on the inverted permeability and pore volume distributions and the reservoir pressure distribution at the end of history. Since the inversion resolves large-scale reservoir property trends well, but not always fine-scale details, we would expect the method to accurately identify areas of the field with potential for infill drilling, but not necessarily to identify exact optimal locations of individual infill
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wells. Fig. 10 shows the infill drilling incremental field production maps for the conditioned sequential inverse model and the reference model. Infill potential was assessed for a ten-year period following the end of the history match. The number on the scale bar represents field incremental gas production per infill well over the ten-year period. The trends in field incremental gas production using the conditioned inverse model are quite consistent with those using the reference model. Given certain economic criteria, our method provides optimal infill drilling design. In this example, we assumed an economic limit of 20 MMSCF incremental field production per infill well, and selection of optimal infill well locations was performed based on this economic limit. Fig. 11 shows the optimal infill well locations identified by the conditional inverse model (pink squares) and the reference model (blue dots). In both cases, there were 34 wells that resulted in incremental field gas above the specified economic limit and were thus selected as optimal wells. Although the well locations from the two cases do not overlay, most pairs of wells from the two cases are in close proximity. Fig. 12 illustrates the effectiveness of these selected infill wells in field production increase for various cases. Case 1 is a base case with no infill wells, as shown by the grey line. Case 2 is a prediction with the true reservoir model with optimal infill well locations determined from the true model, as shown by the pink dashed line. Case 2 represents an ideal case. Case 3 is a prediction with the inverted reservoir model with optimal infill well locations determined from the inverted model, as shown by the blue line. The predictions from Case 3 are quite consistent with the ideal case, with a relative error of 1.89% for cumulative production in the forecast period. The difference is small because, even though the inverted reservoir description is not exact, optimal infill well locations have been determined relative to the inexact reservoir description. Case 4 is a prediction with the true reservoir model and with optimal infill well locations determined from the inverted model, as shown in green squares. Case 4
Fig. 20. Inverted permeability distribution for field case.
represents the production response that would be realized in the field by drilling infill wells that are suboptimal relative to the true reservoir description. The error in Case 4 is 8.89% relative to the ideal case (Case 2), which is quite acceptable. The horizontal dashed line in Fig. 12 indicates that, with the designed infill wells, the cumulative production from existing wells only can be obtained within a much shorter time period, indicating significant production acceleration as well as an increase in reserves. We compared Case 4, the expected production response from the optimal infill drilling design with 34 wells, and a uniformly spaced infill drilling scheme with 36 wells (Fig. 13). Differences in incremental field daily rate and cumulative production (relative to the base case without infill drilling) for the forecast period are shown in Fig. 14. The cumulative production increase, 24.7%, from the optimal infill drilling design is significantly higher than that from the uniform infill scheme, even though the uniform infill drilling scheme has two more infill wells for production. The average production increase per infill well is 32.05% higher for optimal infill drilling than for the uniform pattern. We also compared effectiveness of optimal infill drilling designs determined from conditioned (to the permeability-porosity correlation) and unconditioned inverse models. As in Case 4 above, the designs were run in the true reservoir model to generate the response to be realized in the field. Fig. 15 shows incremental daily rate and cumulative production due to infill drilling for these two cases. With the unconditioned inverse model, 37 optimal wells were selected under the given economic limit. As a result, the unconditioned inverse model yields 6.45% higher cumulative production overall but 1.80% lower average cumulative production per infill well than the conditioned inverse model at the end of forecast. Factoring in the cost of the 3 additional wells, it is clear that the conditioned inverse model yields a superior infill drilling design. 4. Application In this section, we apply our new methodology to the Garden Plains field, Alberta, Canada (Cheng et al., 2008). It has produced for
Fig. 22. Inverted 4*h distribution for field case.
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Fig. 23. Reservoir pressure following history matching, field case.
Fig. 25. Incremental field production for field case.
27 years since its first gas well was put on production in April 1979. Based on available field data, there are 772 wells producing mainly from the Second White Specks (SSPK) formation at the end of 2004. This is a full field study, covering about 492,000 acres, which was discretized using a 166*85*1 simulation grid with dimensions of 1232 ft*1232 ft for each grid block. Fig. 16 shows the 772 existing wells superimposed on the simulation grid system. We matched history using the sequential inversion algorithm, starting with estimated average values of permeability (0.1 md), porosity (11%), net thickness (12 ft), and gas saturation (35%). A permeability-porosity correlation was generated from available core data (Fig. 17) and used in conditioning the inversion. The initial pressure in this reservoir was estimated to be approximately 957 psi. The bottom hole flowing pressure was specified in the simulation to be 250 psi, based on experience with other nearby fields. History matching results are shown in Figs. 18 and 19 in terms of fieldwide cumulative production and daily rate, respectively. These figures demonstrate that history matching is quite good, with consistent trends between calculated production and actual production performance. The gas permeability distribution determined by sequential inversion is shown in Fig. 20. Since we used a constant-thickness model, the kh distribution has the same trends as the permeability distribution. Early performance of well production, in particular the best year of production, can be an indicator of permeability-thickness, kh (Voneiff and Cipolla, 1996; Guan et al., 2002). Fig. 21 shows a map of the best year of production for this field. Similar large-scale trends are observed in both Figs. 20 and 21, which provides some comfort in the reliability of the inverted permeability distribution. The inverted porositythickness product (obtained by multiplying the inverted pore volume multiplier times the product of porosity and thickness) is shown in Fig. 22. Similar trends are observed between kh (Fig. 20) and fh (Fig. 22), as expected. Fig. 23 shows the reservoir pressure distribution at the end of the history match period. As can be seen, central and northeastern areas show signs of pressure depletion,
whereas other areas remain near original reservoir pressure. Combining the pore volume distribution with the pressure distribution yields the distribution of remaining gas in place (Fig. 24). Using the inverted permeability and pore volume distributions and the reservoir pressure distribution at the end of history, we then forecast future production performance, evaluate infill well potential and identify an optimal set of infill well locations. Fig. 25 shows the infill drilling incremental field production map for a three-year period following the history match. The numbers on the scale bar represent field incremental gas production in MMSCF per infill well over the three-year period. The areas with highest infill potential are located in central and southwestern parts of the field, with relatively high permeability and pore volumes and moderate pressure. Note that other higher permeability and pore volume areas to the northeast do not have as much infill potential because of pressure depletion. We assumed an economic limit of 80 MMSCF for the three-year period. This means that the addition of a new infill well has to generate a net increase in field cumulative production of at least 80 MMSCF for this new well to be selected into the set of infill well locations. The economic limit value selected is arbitrary and does not necessarily represent the actual economic limit for this field. Fig. 26 presents the optimal well locations for infill drilling, which consists of 106 infill wells. The selected well placements are concentrated in the central and southwestern parts of the field, corresponding to the areas of high incremental production shown in Fig. 25. Note that each square block on Fig. 26 represents 2*2 simulation grid cells. In Fig. 27, we show three cumulative gas production curves: (1) total from existing wells plus the 106 infill wells, (2) from existing wells without infill drilling, and (3) from existing wells only while the 106 infill wells are producing from the reservoir. The 106 infill wells yield an incremental field gas production of 10,617 MMSCF over the three-year period, the difference between (1) and (2). The decrease in production from existing wells due to infill drilling, the difference between (2) and (3), is 290 MMSCF. This is only 2.7% of the incremental field production, indicating minimal interference of these new infill wells with the existing wells. Note that we used a three-year forecast period and a field incremental production economic limit of 80 MMSCF over the threeyear period to design the optimal infill drilling program. The design may change if different forecast and economic parameters are used. The infill assessment approach described in this paper is rapid and computationally efficient. For this field example, which involves more than 800 existing plus infill wells, the history matching took about 8 CPU hours and the automatic selection of optimal well locations took about 28 CPU hours using a PC with 1 Gbyte of memory and a speed of 3.2 GHz. Compared to conventional simulation with a trial-and-error process, which can take several man-months for a fieldwide reservoir study like this, our approach presents significant time and cost savings.
Fig. 24. Remaining gas in place for field case.
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Fig. 26. Optimal infill well placement from successive selection strategy for field case.
determined. Analysis of incremental gas recovery and production acceleration is also provided. 4. The approach was validated by a synthetic example in which large-scale reservoir property trends were accurately reproduced and infill well design was close to the true optimal design. Applicability of our approach was demonstrated in an actual producing field containing more than 800 existing and infill wells.
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5. Conclusions In this paper, we developed a systematic methodology for rapid and cost-effective design of an infill drilling program for tight gas reservoirs. The approach can be an approximate alternative to a full integrated reservoir study, and may be particularly useful in marginal gas reservoirs where reservoir data are very limited and/or a detailed reservoir study cannot be economically justified. From this study, the following conclusions can be drawn: 1. Heterogeneous distributions of permeability and pore volume can be obtained from dynamic data using the sequential inversion method presented. The distributions are conditioned to a permeability-porosity correlation, if such a correlation is available. 2. The well placement algorithm presented can automatically determine optimal infill well locations, while fully addressing well interference between existing and infill wells, as well as interference between infill wells. 3. Given predefined economic criteria, the number of viable infill wells is identified and the optimal locations of these wells are
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