A stochastic approach to forecast production from unconventional multi-fractured wells

Rate Transient Analysis (RTA) modeling has proven to be a powerful tool for studying the effective relationships between the reservoir petrophysical description, the evolution of completion design, and the performance history given by measured rates and flowing pressures for unconventional horizontal multi-fractured wells. Once a judicious RTA model match is achieved, it can be used to generate a variety of forecasts based on changing operating conditions. When compared to traditional Arp's hyperbolic rate projections which can easily generate recoverable reserves forecasts that far exceed the realistic original volume in-place, RTA is one of the few analysis tools that can ensure that reservoir parameter inputs are exposed for scrutiny and all physical principles are honored. This ensures that rate and reserve projections will always honor an appropriately history matched model. However, not all models are appropriately matched. The key problem areas the practitioner sometimes forgets are:

1. A properly placed first linear flow diagnostic line uniquely resolves the slope of the line which is related to the grouped term but it cannot uniquely determine the variables within the group.
2. The deviation of the data from the initial linear transient flow line (end of first linear flow) is diagnosed as the start of boundary dominated flow. In unconventional reservoirs, we are most often still in transient flow transitioning to another linear flow. This could lead to estimates of Stimulated Reservoir Volume (SRV) that are not representative.
3. The initial model match should always be minimized to use the minimum contacted volume.

Consequently, even a history matched model used to forecast reserves recovery will often contain a high degree of uncertainty. To mitigate the non-uniqueness issue, we need to incorporate probability modeling wherein input data are entered based on probability distribution ranges rather than best-estimate deterministic values. In this article, a stochastic approach to model matching is presented. This approach utilizes RTA models in combination with probabilistic sampling techniques to generate historical matches that conform to a pre-defined error tolerance. Models that achieve the acceptance tolerance within the historical production period are then set to forecast production subject to user-set constraints such as duration, an assumed flowing bottom-hole pressure profile, maximum rate limitations and minimum economic flowrate.

In unconventional multi-fractured horizontal wells (MFHW), the number of parameters that contain uncertainty is higher relative to conventional wells. This is mainly due to the fact that MFHWs exhibit a long transient flow period which makes it difficult to estimate reservoir size because boundaries are not reached yet. The long transient flow also makes it difficult to estimate permeability because linear flow analysis results in a product parameter of permeability (enhanced region permeability) and fracture half length. Furthermore, in MFHW, there is more than one permeability--enhanced region permeability and formation (or matrix) permeability. This adds an extra level of uncertainty because those two permeability values are not normally known. There are other parameters in MFHW that may, also, contain uncertainty such as initial reservoir pressure (P_i), fracture half-length (x_f), number of fractures (n_f), and fracture conductivity (F_CD).

The presence of uncertainty in modeling parameters and the stochastic nature of those parameters encourage the use of Monte Carlos Simulation, which provides for this uncertainty through random sampling of parameters that cannot be assigned a discrete value. To review how the Monte Carlo Simulation works, let us consider the simple equation below for estimation of original oil in place (OOIP) which is calculated as the product of the prospect area (A), average net hydrocarbon thickness (h), the average porosity (φ), and the oil saturation:

Figure 1: Distributions for Inputs of OOIP

Using the deterministic approach, OOIP can be estimated by simply multiplying the "best estimate" for each parameter involved in the algebraic equation. The deterministic approach assumes that the most likely value of every input is encountered simultaneously, which is generally unrealistic. The Monte Carlo Simulation approach, on the other hand, can make use of independent probability distribution to arrive at an overall probability distribution, as shown in Figure 1 for OOIP.

A Monte Carlo Simulation method begins with a model. Typically, an analytical model is utilized because of its quick run time. In IHS Harmony, the Probabilistic Module attaches the Monte Carlo Simulation to the analytical models, which provides a tool for a stochastic approach to forecast production performance. The below steps discuss the procedure to use IHS Harmony to obtain a range of forecast with different levels of confidence.

The first step in this stochastic approach is to identify the parameters that contain uncertainty. It is important to keep in mind that uncertainty is unique for each case and, thus, each case should be given enough consideration to determine what parameters contain uncertainty.

The second step is to assign proper ranges and distributions to those parameters. The below figures show the possible distributions that parameters can exhibit. Determining the proper distribution requires knowledge about the parameter. Typically, analog data serve as a guide towards determining the range and distribution. For example, having 100 wells drilled with logs can provide a sense for the proper range and distribution of reservoir thickness (h). Also, the number of effective fractures range is usually known from the knowledge of completion design. The maximum value for the effective number of fractures cannot exceed the total number of clusters. Usually, experience is the best guide towards setting the proper ranges and distributions.

Figure 2: Different types of distributions

Once distributions are set-up around parameters that contain uncertainty, a number of outputs can be constrained to those that fall within a defined error range. Certain parameters are set to automatic parameter estimate (APE) and those parameters are used to ensure the historical data are honored. APE parameters are used in regression analysis to obtain the best history match of the data. It is also worth pointing out that dependencies between parameters can also be specified in IHS Harmony. For example, if we know, from external knowledge, that the porosity and permeability in the reservoir are proportional, a correlation coefficient can be specified to represent this relationship.

At this point, forecasts are ready to be generated. Harmony will sample values for the parameters with distribution and will input those into the analytical model. Regression parameters are adjusted to obtain a history match and, then, a forecast is created. The process is repeated for a specified number of runs and forecasts that vary too much from the base model will be discarded (based on tolerance range that the user specifies). Once all runs are completed, the product will be a range of forecasts (based on accepted runs) that represent different confidence levels shown as P10 (optimistic case), P50, and P90 (conservative case).

An example of the output from IHS Harmony is shown below:

Figure 3: Example of outputs from Probablisitc Module in IHS Harmony

Ahmed Bajaber, Senior Analyst/Researcher, IHS Engineering

This article was published by S&P Global Commodity Insights and not by S&P Global Ratings, which is a separately managed division of S&P Global.