Abstract
To determine the development mode of layered sandstone reservoir, a system economic model was established, which thought the layer in production and its upper (downer) layer as a system, and the overall benefits of the two modes were contrasted using the existing well (UEWM) or the method of drilling a new well (DNWM); then, the upper (downer) oil layer development mode could be determined quickly by the model. The method can avoid the chemical agent effect of the upper target layer, which also makes the calculation more accurate. In the model, the cumulative oil production limits of the producing layer are described at different oil prices of DNWM and UEWM methods. Then, an economic ultimate water cut (EUWC) model is established. According to this model, when the water cut attains to EUWC, the oilfield should be abandoned. Meantime, the arctangent prediction model for water cut is combined with the water drive curve method, to forecast the accumulative oil from the planning time of the upper target layer production to the abandonment time of the first production layer of oilfield. And then, the development mode could be decided through contrast with the cumulative oil production limit. When the oil price is 40$/bbl, the EUWC of the block is 97.55%, and time is May 2020, earlier than the planned upper layer production time January 2023, so its rest cumulative production would be , which is less than the cumulative production limit of . Hence, the UEWM should be chosen. When the oil price is $70/bbl, EUWC is 98.93%, and the corresponding time is August 2027. From the planned return time of January 2023 to August 2027, the block has cumulative oil production of , greater than the cumulative oil limitation of . The old exiting well still has larger economic productivity; hence, the DNWM method should be chosen. This work provides theoretical support for up (down) formation development mode of production layer. It is of great significance to guide the development of layered sandstone reservoirs. The system economic model established can decide development mode with drilling wells or using exiting well, and it was first created in the field of oil reservoirs. This method fills up the theoretical blank of development mode for upper or downer layer of the producing layer in layered sandstone reservoir.
1. Introduction
Most of oil reservoirs in China belong to continental deposits, which have multilayers, strong heterogeneity, low water displacement efficiency, and low natural energy [1]. One of the typical reservoirs in Daqing Oilfield is the terrestrial multilayered sandstone reservoir [2, 3]. Three reservoir groups Saertu, Putaohua, and Gaotaizi were exploited vertically, including more than ten oil layers. These oil reservoirs were divided into 3 types in the production period. The 1st typical reservoir was PI (reservoir Putaohua I) formation, whose sedimentary unit was fluvial facies. Its effective permeability was more than μm2, and its effective thickness was more than 4 m. The 2nd type of reservoir was SII (reservoir Saertu II) formation, whose sedimentary unit of the fluvial sand area was more than 30%. Its effective permeability was more than μm2. Its sand deposition channel width was 200 to 1000 m [4–6]. The 3rd type GI-III (reservoir Gaotaizi I-III) layer was thin and poor oil situation. In the 1990s, the oil layer PI was determined to be developed first, which ensured that steady oil production of t in the Daqing Oilfield for 27 years. Till now, all PI oil layers have been put into tertiary recovery development. Polymer flood of the first stage of 2nd type reservoirs was developed in 2002, and these layers gradually entered the follow-up water flooding stage. Now, polymer development of the neighbor layer (up or down layer of the first stage layer) has been planned, which raises some inevitable questions in many respects such as the development of the up (down) layers, the arrangement of the sequence, the upward or downward of the production, and the choice of the development method of drilling well or using the original well. Many researchers worked in different ways to answer these questions. A mathematical model was proposed to describe the relationship between the total oil well production and the interval of reservoir series in a homogeneous multilayer reservoir [7]. Bailón et al. studied the development focused on the lower U sequence of the Iro field and confirmed that it was wrong, but the study was only confined to controlling the water shut off [5]. To better understand key drivers for successful stimulation of multiple fractured horizontal wells, Mohammed et al. researched the Montney Formation by comparing and contrasting the Upper and the Lower Montney completions and fracture stimulation statistical results with a reservoir and fracture simulation study [8]. Dashash et al. researched high-resolution sequence-stratigraphic correlation and facies characterization of the Upper Thamama (Lower Cretaceous) reservoir [9], Barragan et al. researched innovative applications for extending the oil production of the gas lift for lower zone and natural flow for upper zone [10], and Dejam and Hassanzadeh derived a reduced-order model for tracer dispersion in stratified porous media and found that the field scale mixing may not necessarily originate from the Taylor dispersion and could be due to the modified advection terms and the cross-diffusive flux between the two layers [11] and so on [12, 13]. However, the problems have not been solved that a quick method to determine whether use an old well or drill a new one still cannot be given.
There are three difficulties in production mode selection and timing of upper (downer) layer development in multilayer reservoirs. First, the time of the upper (downer) layer begin to development needs to be determined; in this paper, the economic limit water-cut model is established by using the breakeven principle, and the time of the first stage abandonment is determined; that is, the time of up-down layer development is determined. The second is how to predict the subsequent production of the first stage accurately; if not accurately, it will cause reserves of the first stage sealed up. So, the method of arctangent function and the water drive curve are used for the first time to predict the follow-up production and water cut of the first stage, which enrich the prediction method of the oilfield development index, the predict result is more accurate, and the relative error of the predict water cut is only less than 0.2%. Thirdly, there is no quick way to compare the economic benefits of the two methods of using the existing well method (UEWM) or the drilling a new well method (DNWM). By establishing the system economic model of the two methods, the development mode of drilling wells or using exiting well could be decided, which is firstly created in the field of oil reservoirs. The research method fills up the theoretical blank in the selection of development mode of up or down return of layered sandstone reservoir.
The method advantage can quickly decide the target layer development method and can avoid the chemical agent effect of the upper target layer, which also makes the calculation more accurate. The model provides definite suggestions on whether to drill a new well for specific oilfield development. However, the method has limitations still, and only one oilfield can be considered one time; for the meantime, some specific economic parameter needs to be provided.
The steps of the work are as follows: first, use system economic model to decide the production layer cumulative production limit, then use arctangent method to forecastand make sure EUWC with the economical ultimate water cut model, and then,of planned upper layer production time to EUWC time is calculated by the D-type water drive rule curve method, and at last, decide target layer development method judge byand production limit.
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2. Method
2.1. The System Economic Evaluation Model Establishment
UEWM is defined as the way to use a well to plug the first production layer and fill the hole in the upper layer for development. DNWM is defined as the way to retain product by the first layer wells and drill new wells to develop the upper layer.
To determine a better method of oil field development from UEWM and DNWM, the first layer stage and the upper layer are treated as one system, and the overall benefits of the two modes are contrasted; then, the return layer development model would be determined (Figure 1).
According to the model, the benefit of UEWM for development is expressed as where is the benefit of the upper return section that will produce oil, M$; is the retention benefits of cumulative oil produced by the first reservoir, M$; is the first reservoir section block charge, M$; and is the cost of old well perforate upper layer, M$.
The benefit of DNWM is expressed as follows: where is the drilling new well costs, M$; is the new well construction cost, M$; is the perforation cost, M$; is the cumulative oil production benefit of return to upper reservoir interval, M$; and is the benefit of retaining yield of the first stage, M$.
The development mode is determined by comparing the benefits of UEWM and DNWM. If , that is, the benefit of UEWM is less than DNWM. Then, the DNWM is adopted.
Therefore,
Assume that the new well is drilled at the exiting well location, so conditions to develop the upper strata of new wells would be the same with that of the existing wells. Substitute in formula (3), and then, it is simplified
The benefit comparison of the two methods is then transformed into the investment comparison. The DNWM would be adopted if its investment is less than UEWM.
In practice, the new well would be drilled in the best well location, rather than the existing location. Therefore, the enhanced oil recovery factor “” is calculated to indicate how the DNWM could improve oil recovery compared with UEWM.
Then, formula (4) is changed to
Here, is the benefit of DNWM through well infill and adjustment to enhance oil recovery. It could be seen from formula (5) that the expenses for plugging (), supplementary perforation cost () of UEWM, the expenses for drilling (), construction cost on ground (), and perforation cost () of DNWM are determined in the oilfield development designing. All the five constants could be known from the reservoir development planning. The profit of recoverable reserves in the first reservoir stage () is the only variable, so the key factor in formula (5) is the remaining oil which could be the product of the first layer stage.
If , both UEWM and DNWM could be used, and then, it should be chosen according to the completeness of the injection-production system on the ground surface. While , old well pattern utilization methods should be used, and the formula derivation is the same as the above steps.
This method could quickly determine whether the DNWM or UEWM should be adopted in the oil block. It could also provide a reference for the effective development of layer sandstone reservoir. According to the system model, there is only one variable , that is, the benefit at the first stage of reserve yield, which could be predicted based on the follow-up oil production () from the planning time of the upper-layer beginning production to the time of the economic ultimate water cut (EUWC) or of block abandoned of the first layer section. Then, the upper layer development method is determined by comparing the cumulative oil production with the chart calculated by the system economic model.
Therefore, the EUWC of the block should be calculated first, and then, the accumulated oil production to EUWC () ought to be calculated.
2.2. The Accumulated Oil Production () to EUWC
The development characteristics of the water drive stage after being flooded by the polymer strictly conform to the water drive characteristic [14–19]. Due to the influence of the swept volume and water cut rising in the ultrahigh water cut stage [20], the higher predicted recoverable reserves and oil recovery value were obtained using the characteristic curve method of water drive [21, 22]. The arctangent curve method is used to predict the water cut, while the recovery degree could be predicted based on the water-drive curve method, which could eliminate the influence of high-prediction values from the water drive curve method.
2.2.1.
According to the contrast results, the D-type water drive rule curve method’s straight line segment has the highest fitting degree. Hence, the D-type curve method is chosen as the main method for accumulated oil production prediction [13, 23]. where
The reserve production of the first layer in follow-up water drive results from the cumulative oil production to EUWC minus the initial oil production of the upper layer. where and .
2.2.2. Water Cut
The water cut curve of follow-up water flood after polymer flooded is shown in Figure 2. The water cut increases rapidly in the next 2~3 years after the polymer flooding stop and then rises slowly. This feature could be predicted by the arctangent method exactly. So, the arctangent method is used for water cut prediction 6. The results show that the arctangent method is feasible indeed.
It is found that the graph is a straight line ~. Here, “” is the slope of the straight line, and “” is the intercept.
Then, the oil block water cut could be predicted according to
2.2.3. Economical Ultimate Water Cut (EUWC)
When the sales revenue equals to the cost, the water cut is EUWC of the block [24]. EUWC could be calculated directly from current inputs and outputs based on the production data of the oil block.
The basic formula of breakeven analysis is where
Equation (12) could be rewritten as
After reorganizing, the EUWC of the block is obtained:
3. Results and Discussion
3.1. Basic Overview of Block S
The L structure is the northernmost structure of Daqing Oilfield, which is a typical layered sandstone reservoir controlled by a short-axis anticline structure. It is a hydrodynamic system with a unified oil and water interface. Block S is in L’s southernmost, whose average burial depth is 958~1192 m and the tectonic high point is 758 m. The type II reservoir in the block includes 16 sandstone groups such as SII, SIII, PI4-7, PII, and GI1-4+5. In 2012, the block was determined to carry out the EOR development for the type II reservoir. After preparing the reservoir engineering development plans, five-layer combinations of SII1-6, SII7-16, SIII1-7, SIII8-PI4-7, and PII1-GI4+5 are identified for development. The first oil layer combination of SIII1-7 is developed. Its production time is August 2012, while the polymer injection time is March 2013. Till now, the block water cut is 97.07% (Table 1).
3.2. The System Economic Evaluation Model Calculation
Based on the static/dynamic data and economical parameters of block S (Tables 1–3), the upper layer return development mode of the block is determined. The costs of supplementary perforation and plugging in old well patterns are shown in Table 2, while Table 3 shows the costs of new wells’ drilling and construction. The development mode of the block could be determined by the economic loss, which is caused by the oil production blocked at the first reservoir stage. Considering that the conversion rate between barrels/tons is 7.425, the commodity rate of crude oil is obtained as 98.37%.
According to the relationship between the actual strata and the well pattern, a new well will be drilled in the optimal well position, so well adjustment could make contribute to higher oil recovery than the old well pattern. Formula (5) could be changed to . According to the following production of the first formation and EOR () of DNWM and UEWM methods, a theory chart under different oil prices could be set up, and the development method could be chosen from it.
According to the statistics of the parameters in block S, the geological reserves of the target return strata are t. DNWM could increase the recovery rate by about 2% compared to UEWM. The increased oil production is . Then, and could be obtained. The crude oil commodity rate is 98.37%. The reference chart of the actual development is calculated under different oil prices of 40, 50, 60, 70, 80, and 90$/bbl (Figure 3), which could be used to judge the upper (downer) layer development way of oil block.
When the oil price is $40/bbl, the first layer production contribution is less than minimum limit , and as for the oil price $70/bbl, if is less than t, the UEWM method should be adopted. Otherwise, the DNWM method should be chosen.
Method validation is as follows: assume new well is drilled at the exiting well location of the first layer formation; that is, the new drilling well’s perforations and situation of upper (downer) target layer are completely consistent with the old exiting well, and when the subsequent production of the first layer is , the system inputs of DNWM or UEWM with different oil prices tend to the total costs in Tables 2 and 3 (Figure 4), which show that the established model is correct.
3.3. Calculation of Cumulative Oil Production in the First Section of the Block
3.3.1. Water Cut Prediction
The injection time of block S is March 2013. The production had been sustained for 63 months by May 2018. According to Equation (10), we put the tangent of the actual water cut and production time into the Cartesian coordinate system, and is in a straight line with time (Figure 5); here, , and ; then, Equation (10) is changed to ; the water cut per time could be calculated using the formula. The results are shown in Table 4; the relative error of the water cut is less than 0.2% (Table 5), which could be used to optimize the block development model.
3.3.2. Cumulative Oil Production
According to the block’s production data from May 2018 to July 2019, / versus is drawn in Figure 5, which is a straight line. Here, , , and the correlation is 0.9999. Formula (7) could be rewritten as (Figure 6). Then, the cumulative oil production per time is calculated. The prediction error of oil production is about 1.0% (Table 5).
3.3.3. EUWC Calculation of Block
According to the economic parameters of oil block S in 2019 (Table 4), the EUWC (Figure 7) is calculated. When the oil price increases, the water cut also increases at the same liquid condition. As liquid increases, the water cut increases slowly. Besides, the EUWC tends to be the same when liquid is higher. When the liquid volume is 140 t/d and the oil price is $40/bbl, the EUWC becomes 97.55%, and the daily oil production reaches 3.43 t/d.
3.4. Determination of Block Development Mode
The upper layer production time of block S is expected to be January 2023 based on design planning. According to the calculation method in Chapter 3.3.1, the predicted water cut will be 98.34% that time. When the oil price is $40/bbl, the EUWC of the block is 97.55%. The time of EUWC is May 2020, when the block reached to abandoned level. It is earlier than the planned return production time, so its rest cumulative production would be , which is less than the cumulative production minimum limit . Hence, the UEWM should be chosen. But when oil price is $70/bbl, EUWC is 98.93%, and the corresponding time is August 2027; from the planned return time of January 2023 to August 2027, the block has cumulative oil production , greater than the cumulative oil limitation , means the exiting well still has economic productivity need to keep work, hence, the DNWM method should be chosen.
4. Summary, Conclusions, and Policy Implications
The system economic model is established based on the EUWC model of the block. Combining the solution prediction model of arctangent water cut curve and water drive curve method, the type II reservoir secondary upper (downer) layer development model of block S is built. When the oil price is 40$/bbl, the time to EUWC is May 2020, early than the planning time January 2023 of the upper layer begin to production, and the production layer should be abandoned, so the UEWM mode should be chosen. However, when the oil price is 70$/bbl, the accumulated oil production reaches from the planned return production time to EUWC 98.93% corresponding time August 2027, which is higher than the limited cumulative production (). In this case, the DNWM method should be chosen for block S.
The model provides definite suggestions on whether to drill a new well for specific oilfield development. Significant guidance is given to developing layered sandstone reservoirs. However, the method has limitations still. Only one oilfield can be considered at the same time, and a specific economic parameter needs to be provided.
Nomenclature
| : | Benefit of UEWM development, M$ |
| : | Benefit of DNWM development, M$ |
| : | The benefit of the upper layer return section will produce oil, M$ |
| : | Retention benefits of cumulative oil that produced by first reservoir, M$ |
| : | Perforation block charge of the first reservoir layer section, M$ |
| : | The cost of the old well perforate upper layer, M$ |
| : | Drilling new well costs, M$ |
| : | New well construction cost, M$ |
| : | Perforation cost, M$ |
| : | Cumulative oil production benefit of return to upper reservoir interval, M$ |
| : | Benefit of retaining yield of the first stage, M$ |
| : | The benefit of recovery improved that the new well drilling method increased than old well used through well infill and adjustment, M$ |
| : | Remaining recoverable reserves of the target returning layer when existing well pattern was used to develop, 104 t |
| : | Ton and barrel unit conversion rate, 7.425 |
| : | Exchange rate of RMB to US dollar, 6.19 |
| : | Commodity rate of crude oil, 98.37% |
| : | The first development formation has remaining recoverable reserves, 104 t |
| : | The number of oil wells that need to be plugged for using to the upper layer |
| : | Unit price of oil well plugging first layer, M$ |
| : | The number of water wells that need to be plugged for using to the upper layer |
| : | The unit price of water well plugging, M$ |
| : | Number of oil wells to be supplementary perforation used for upper layer development |
| : | Unit price of oil well supplementary perforation, M$ per well |
| : | Number of water wells to be supplementary perforation used for lower layer development |
| : | Unit price of water injection well supplementary perforation, M$ |
| : | Number of oil wells drilled in the new drilling method |
| : | Number of water injection wells drilled in the new drilling method |
| : | Drilling depth, m |
| : | Unit drilling footage price, $/m |
| : | Oil well number for construction |
| : | Water injection well number for construction |
| : | Construction investment per well, M$ |
| : | Number of oil well perforated in DNWM |
| : | Number of water well perforated DNWM |
| : | Perforation cost per well, M$ |
| : | Remaining recoverable reserves of upper layer after development use new drilled well, 104 t |
| : | The upper layer geologic reserve, 104 t |
| : | EOR of new drilling well pattern encryption and adjustment than old well used to develop, % |
| : | Variable costs, composed with fluid production, oil production, and water injection costs, $ |
| : | Average annual production time for a single well, days |
| : | Daily oil production, t/d |
| : | Commodity rate of crude oil, % |
| : | Daily liquid production, t/d |
| : | Tax of a ton oil, it consists of value added tax, urban construction fee, resources tax, and surtax for education expense, $/t |
| : | The sum of material cost per ton oil, fuel charge, and power cost, yuan |
| : | Treatment cost of a ton of liquid, yuan |
| : | Price of crude oil, $/t |
| : | Water injection cost, $/m3 |
| : | Economic ultimate water cut, decimal |
| : | The average fixed total cost of a single well, which is composed of salary, up-hole operation cost, oilfield maintenance charge, mine field cost, enterprise management fee, overhaul fund, scientific research fee, and depreciation fee, $ |
| : | Water cut of block, decimal |
| : | Time, month |
| , : | Parameters need to calculate |
| : | Fluid cumulative production of block, 104 t |
| : | Cumulative oil production of block, 104 t |
| : | Cumulative water produced of block, 104 t |
| : | Block oil production cumulative when block is economic abandoned, 104 t |
| : | Cumulative oil production at the time of upper layer need to production, 104 t |
| : | Economic limited water cut, decimal |
| : | Water cut when the time of upper layer need production, decimal |
| , : | Parameters need to calculate. |
Data Availability
The economic parameters and well production parameters in this paper are all obtained in Daqing Field. They are being used now and are reliable.
Disclosure
The manuscript has been presented as preprint in “Select the Optimal Development Strategy for Layered Sandstone Reservoir by Creating System Economic Model and the Accumulated Oil Production Prediction Method” according to the following link: https://assets.researchsquare.com/files/rs-961586/v1_covered.pdf?c=1634655547 [25].
Conflicts of Interest
The authors declare that they have no competing interests.
Authors’ Contributions
WFL and ZYF worked on the data collection and wrote the manuscript. FYJ directed the project and provided ideas and goals as well as logistical support. All the authors proofread the manuscript and provided their comments and insights. All the authors read and approved the final manuscript.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (No. 51074035) and Daqing Oilfield Science and Technology Project: the oilfield test use water flooding well pattern to develop the reserves after chemical flooded of type II reservoir (dqp-2021-yqcgc-xcsy-002).