This paper presents an integrated modeling approach for history matching and economic optimization of wells producing from liquids-rich shale reservoirs (LRSRs). History matching uses daily pressures and gas-/oil-/water-production data to estimate average parameters in a 2D/3D finite-difference (FD) horizontal-multifractured-well model. Economics-based well design uses the same FD model to maximize net present value (NPV) by finding optimal well-completion parameters.
Introduction
Long-term historical liquid production from LRSR wells has not yet provided the industry with sufficient understanding of fundamental performance mechanisms needed to develop reliable empirical forecasting methods such as decline-curve analysis. History matching LRSR wells with a detailed FD-model description provides more-reliable liquids-production forecasting and oil-recovery predictions as well as the ability to study sensitivity of performance to model-parameter uncertainty.
Combining a detailed FD model with a valid economics model provides a quantitative mechanism to optimize value by controlling well-design parameters such as horizontal-well length and fracture size and spacing. If the FD model has been history matched to an existing well, then the historical performance and economic model are “known” for the existing well, and well-design optimization can therefore study how alternative completions would have increased profitability. For new wells, optimization can be used to guide the selection of critical well-design parameters and estimate economic uncertainties.
The modeling strategy presented here has been used to history match and optimize well design for LRSR wells producing from the Eagle Ford, Bakken, Avalon, and Montney formations in the US and Canada. Unfortunately, publication of field data was not permitted.
For a detailed description of the model, and its use in determining bottomhole pressures (BHPs) and water-injection conditions, please see the complete paper.
History Matching
When history matching the FD model to observed pressure and rate data, it is preferred to control the model on BHPs measured or calculated from surface data. The most important reason to control the model on BHPs is the strong correlation between producing oil/gas ratio (OGR) and flowing BHP. Model rate performance is matched to observed data by minimizing the sum of squares (SSQ). The SSQ for the individual data types are summed together to form the total SSQ minimized through history matching. The relative size of the individual SSQ may be very different. An additional set of weighting factors, W, is used to normalize the individual SSQ.
Manual, visual inspection of the model performance compared with observed data is normally required to find reasonable weighting factors. The absolute values of the unweighted SSQ are in most cases not a good indication of how well the model fits observed data. Short transients in production rates after well shut-ins are usually not captured properly by the FD model, causing large contributions to the SSQ. The weighting factors for these periods should in most cases be set to zero. Proper weighting of the SSQ is a trial-and-error process requiring careful study of data mismatch and engineering judgement.
The effect of the most significant reservoir parameters on model performance was studied. Matrix permeability is a key history-matching variable that significantly affects model performance. Because the permeability is assumed to be homogeneous throughout the matrix in the proposed model, the history-matched permeability will in effect be a composite permeability of any heterogeneities and natural fractures present. Fig. 1 shows the effect of changing all relative permeability exponents equally. Producing OGR is not greatly affected in any of the cases. Fig. 2 shows the effect of changing only the oil relative permeability exponent nog. As the oil relative permeabilities become more pessimistic, more oil is left behind immobile in the formation. Initializing the model with a higher gas/oil ratio (GOR) oil has much the same effect. If the in-situ fluid composition is uncertain, as usually is the case, it might be difficult to differentiate between oil relative permeability effects and in-situ fluid composition.
Fracture half-length and matrix permeability are also two important history-matching variables. There is a strong correlation between the two parameters. Any model with a given productivity term xf√¯¯kwill have similar performance. This relationship is not exact for liquids-rich systems. As the fluid system gets richer, the performance for models with a given productivity term deviates increasingly.
A model with fracture half-length of 200 ft was attempted to be history matched to the base model with 150-ft fracture half-length. Matrix permeability was the only history-matching variable. The combined oil and gas rate SSQ was minimized, with all weighting factors equal to unity. The best-fit producing OGR performance is presented in Fig. 3. The history-matched permeability is 60 nd, giving a productivity term of 1.55 ft-md½ (compared to 1.50 ft‑md½ for the base model). Producing OGR is consistently underpredicted for the xf=200-ft model, while gas-production rates are much better matched. If the gas-rate SSQ had been given a lower weighting factor, the OGR match would become better at the expense of the gas-rate match. With real field data, mismatch of the magnitude seen in Fig. 3 may be hard to detect. Significant scatter in measured oil rates is common, giving rise to uncertainty in the well producing OGR performance.
Optimizing Drawdown
The flowing BHP of wells producing from LRSRs determines the amount of liquid dropout in the formation. The producing OGR for gas/condensate (GC) wells is close to the solution OGR at the flowing BHP. Most of the liquids falling out of solution in the matrix stay immobile for the life of the well. Because of the strong dependency between liquid yield and flowing BHP, and the high price differential between oil and gas, drawing the well down maximally does not neccesarily yield the highest revenues.
A 6,000-cell 1D model was run for three different oil and GC fluid systems with varying degrees of undersaturation. For each fluid system, the model was run with a constant flowing BHP for 100 days. Revenues for the 100-day period were calculated on the basis of an oil price of USD 100/STB, and a gas price of USD 3/Mscf. As the degree of undersaturation decreases, the optimum shifts toward lower flowing BHPs. For the base-model oil cases, with an in-situ GOR of 4,000 scf/STB, the 100-day revenue levels off for BHPs that are less than the saturation pressure. When gas comes out of solution in the reservoir, gas mobility quickly increases, and the liquid yield drops. The increase in gas production caused by higher drawdown offsets the reduction in liquid yield, and revenues remain close to constant. For the 1,500‑scf/STB oil system, less gas comes out of solution in the reservoir, and the gas/oil-mobility ratio is not affected as severely. Revenues monotonically increase as the flowing BHP decreases.
The highly undersaturated cases have a jagged shape when the flowing BHP is less than the saturation pressure. This is caused by banks of mobile oil developing in the reservoir and entering the wellbore at different times for different flowing BHPs.
Results for the GC reservoir with an initial pressure of 9,000 psia were verified with a highly refined 2D model (2,000×120 cells). The 2D model gives somewhat higher revenues than does the 1D model. The difference increases with decreasing flowing BHP. This difference is caused by the extra drainage area beyond the fracture tips in the 2D model. As the drawdown increases, more flow contribution from this area is seen. The 2D model shows the same optimum flowing BHP as the 1D model.
It is evident that, at least for an initial period, maximizing the drawdown in wells producing from undersaturated GC reservoirs does not yield maximum revenue. On the other hand, producing with flowing BHP equal to saturation pressure is not likely to be optimal in the long term. A suite of cases was run for the GC base model with an initial reservoir pressure of 7,000 psia. The models were run for 200 days, split into two periods. In each period, the well was produced with a constant flowing BHP. The duration of the first period and the BHP for the second period were varied. It was observed that first producing the well with pwf=4,250 psia anywhere between 100 and 170 days, then reducing pwf to the minimum possible value, maximizes revenue. Producing the well on flowing BHP equal to saturation pressure for either a shorter or a longer period will reduce the revenue. We also ran cases with a suboptimal BHP of 2,000 psia for the first period. We found that producing the well with a too-high drawdown for an extended period of time will result in permanently lost revenue. It is possible to get the well back to optimal production if the high-drawdown period is short enough.
In Fig. 4, the revenue profiles vs. time are shown for four of the cases. Revenue is lowest for the case with flowing BHP=500 psia for the first 100 days and flowing BHP=4,250 psia for the last 100 days. In this case, the well is shut in the entire last period. It takes a long time to make up for a period of suboptimal BHPs. The case giving the highest revenue is where flowing BHP=4,250 psia the first 100 days and flowing BHP=500 psia the last 100 days. A clear increase in revenues is seen when the BHP is lowered after 100 days. Note that when the well is produced with a constant flowing BHP of 500 psia, revenues are consistently lower.
The optimal production strategy for wells producing from highly undersaturated GC reservoirs likely features an initial period where flowing BHP is equal to saturation pressure, followed by a gradual increase in drawdown toward the minimum operationally possible BHP.
Optimizing Well Design
Well-design optimization can be performed on an existing, history-matched well to evaluate current completion strategies or to improve the design of new wells in the proximity of history-matched wells. The reservoir description is assumed to be known, and controllable well-design parameters are varied. To optimize the well design in terms of NPV, a cost model is required. The cost model must capture how the cost of the well changes with respect to all design parameters that are varied.
This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 166380, “Optimized Well Modeling of Liquids-Rich Shale Reservoirs,” by Aleksander O. Juell, SPE, and Curtis H. Whitson, SPE, NTNU/Petroleum Engineering Reservoir Analysts, prepared for the 2013 SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–2 October. The paper has not been peer reviewed.